This is to certify that the
dissertation entitled
The Solubility of Xenon in Simple Organic
Solvents and in Aqueous Amino Acid Solutions
presented by

Jeffrey Frank Himm

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Physics

 

 

Mpikggggfl

Gerald L. Pollack

Date September 3, 1986

 

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

 

 

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THE SOLUBILITY OF XENON IN
SIMPLE ORGANIC SOLVENTS AND IN
AQUEOUS AMINO ACID SOLUTIONS

BY

Jeffrey Frank Himm

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics and Astronomy

1986

c?

(“a

C‘.\.

V97.

ABSTRACT

THE SOLUBILITY OF XENON IN
SIMPLE ORGANIC SOLVENTS AND IN
AQUEOUS AMINO ACID SOLUTIONS

BY

Jeffrey Frank Himm

We have measured the Ostwald solubility (L) of 133Xe in a variety
of liquids, including normal alkanes, normal alkanols, and aqueous
solutions of amino acids, NaCl, and sucrose. For the alkanes and
alkanols, measurements were made in the temperature range from 10-50 °C.
Values of L were found to decrease with increasing temperature, and also
with increasing chain length, for both series of solvents. Thermodynamic
properties of solution (enthalpy and entropy of solution) are calculated
using both mole fraction and number density scales. Results are
interpreted using Uhlig's model of the solvation process. Measurements
of L in aqueous amino acid solutions were made at 25°C. Concentrations
of amino acids in solution varied from near saturation for each of the
amino acids studied to pure water. In all solutions, except those with
NaCl, L decreases linearly with increasing solution molarity. Hydration
numbers (H), the mean number of water molecules associated with each

solute molecule, were determined for each amino acid, for NaCl, and for

sucrose. Values of H obtained ranged from near zero (arginine,

H-O.2:tO.5) to about 16 (NaCl, H=16.2510.3).

to my dad

ii

ACKNOWLEDGMENTS

First and foremost, I would like to thank Professor Gerald L.
Pollack, tuna generously provided guidance, encouragement, support, and
friendship to make this possible.

I would like to thank all of my friends, both in the department
and outside of it, whom i have come to know and love over the years.

I would like to thank Richard Kennan for his assistance in the
preparation of this thesis, and Dan Edmunds for all of his help with
troublesome equipment.

I would like to thank the Naval Medical Research‘and Development
Command (Contract numbers N0001u-80-C-0617 and N0001h-83—K—07N3) and the
ExxOn Corporation for their financial support.

And finally, I want to thank my family, especially Mom and Dad,

for their love and support.

111

TABLE OF CONTENTS

LIST OF TABLES.... ........... . ..... ..... ..... .. ........... ..........V

LIST OF FIGURES... ........ 0.00.0.0.0...00......OOOOOOOOOOOOOOOOOOOVii

INTRODUCTION.OOOOOOOOOOOOOOOOOOIOO0.0.0.0.0.0000...00.0.0000000001

2. THEORYOOOOOOOOOOOOOOOOOOOOOO0.00000000000000000000000.00.00.000005

2 1 IDEAL SOLUTION...........................................6
2 2 RAOULT'S LAW.............................................9
2.3 HENRY'S LAW.............................................11
2.” HARD SPHERES........I...................................13
2 5
26

KIRKWOOD'BUFF THEORY....................................18
APPLICATIONS TO EXPERIMENTS.............................23
2.6.1 ASSUMPTIONS......................................23
2.6.2 THERMODYNAMICS OF SOLUTION.......................2N
2.7 MULTICOMPONENT SYSTEMS......... ...... . ....... ...........27

3. EXPERIMENTAL.OOIOOOOOOOOOOOOOOO0.0.00.0.0...0.0.000000000000000033

SOLUTION COMPONENTS.....................................33
APPARATUS...............................................35
TEMPERATURE CONTROL.....................................37
SHIELDING...............................................37
ELECTRONICS.............................................38
VOLUME DETERMINATION....................................31
SOLVENT PREPARATION.....................................U3
LOADING THE APPARATUS...................................43
SOLUBILITY EQUATION.....................................u5

o
omqmszN".

wwwwwwwww
O

1‘. RESULTS AND CONCLUSIONSOOOOOOOOOO0.00...OOOOOOOOOOOOOOOOOOOOOOO.50

.1 ALKANES O O O I O I O I O O O O O C O O O O O O O I I ........ O O O ...... O O O O O O O I O 50
O 2 ALKANOLS O O O O O O O O O O O O O O O O C O O O O O O O O O ...... O O O ......... O O C . 77
3 AQUEOUS AMINO ACID SOLUTIONS...... ...... ...............107

«Elf-'4:

5. LIST OF REFERENCESOOOO..00...OOOOOOOOOCOOOOOOOOOOOOO0.0.0.0....135

iv

LIST OF TABLES

TABLE 1. Solubility data for experiments with 133Xe in the

normal alkanes. The first row gives the Ostwald solubility

measured for each alkane, and the second row is 10 x , where

x is the mole fraction solubility of Xe in the normgl alkanes

a3 1 atm partial pressure of Xe....................................51

TABLE 2. Chemical potentials in the mole fraction scale, Ana,
and in the number density scale, Au°p. The first row is Aug
and the second row is Augp. Units age cal/mol......................62

TABLE 3. Entropy and enthalpy of solution in both the mole
frap§§on scale and in the number density scale for solutions

or xe in the normal alkaneSOOOOOC0.00......0.0.0.00000000000000070
TABLE A. Comparison of experimental binding energies, Eexp’
of Xe in the normal alkanes with binding energies estim ted

from the heats of vaporization of the solute and solvent, ESSt.....76
TABLE3§. Ostwald solubility L and mole fraction solubility x2

for Xe in the normal alkanols. The Eirst row for each
alkanol is L, and the second row is 10 x2..........................78

TABLE 6.Chemical potentials in the mole fraction scale, Aug,
and in the number density scale, Au The first row is Au

09
and the second row is Augp. Units age cal/mol.............?........87

TABLE 7. Entropy and enthalpy of solution in both the mole

frac§§on scale and in the number density scale for solutions

of Xe in the normal alkanols. (Table 2 of reference 69).........95
TABLE 8. Comparison of experimental binding energies, Eexp’
of Xe in the normal alkanols with binding energies estiBategst
from the heats of vaporization of the solute and solvent, ED ....100
TABLE 9. Comparison of calculated and experimental thermodynamics

Of SOlUtionOOOOOOOOOOOOOOOOOOO0.0.0.0000...OOIOOOOOOOOOOOC0.00.00.102

TABLE 10. Comparison of calculated and experimental values for

the enthalpy and entropy of solution for mixtures of Xe in

some of the alkanes and alkanols. Values were calculated using
Pierotti's model, and the Lennard-Jones parameters of Wilhelm

and Battino.......................................................105

TABLE 11. List of solubilities measured for Xe in aqueous
solutions of the amino acids, sucrose, and NaCl. Also included
are the solution molarities (M): the solution pH, the volume

fraction water, and the hydration number calculated for each
experimentOOOOOOOOOOOOOOOOOOOOOOO0.0000000000.0.0.000...0.000.000.0108

TABLE 12. Hydration numbers of the amino acids....................115

vi

LIST OF FIGURES

Figure 1. Solubility measurement apparatus.........................36
Figure 2. Schematic diagram of the electronics.....................39
Figure 3. Schematic diagram of the degassing system................uu
Figure A. Schematic diagram of the gas handling system.............fl6

Figure 5. Normalized counting rate vs. time for a typical
experiment(Figure 2 of reference 67). The letter A indicates

the time the valve was opened, and the letter B indicates

the time a run might end, about 8 hours after equilibrium

has been reached...................................................u9

Figure 6. L vs. T for the normal alkanes. The numbers next to
the symbols are the number of C atoms in the alkane molecule.......53

Figure 7. x vs. T for the normal alkanes. The numbers next to
the symbols are the number of C atoms in the alkane molecule.......55

Figure 8. L vs. n for the n-alkanes at 5 temperatures..............57

Figure 9. x vs. n for the n-alkanes at 5 temperatures.............58

2

Figure 10. L vs. n for the n-alkanes; +, 20°C, our data;
A, 25°C, MakranczyE}.floooooooooooooo00000000000000.0000000000000060

Figure 11. x vs. n for the n-alkanes; +, 20°C, our data;
A, 2.500,Makganczye_t21.0.0000....0.00......OOOOOOIOOOOOOOOOO0.00.61

Figure 12. Au° vs. T for the n-alkanes. The numbers next to the
symbols are tge number of C atoms in the alkane molecule...........6h

Figure 13. Au°p vs. T for the nealkanes. The numbers next to the
symbols are tge number of C atoms in the alkane molecule...........66

Figure 1“. Au; vs. n for the n-alkanes at'S temperatures...........68

up
2

Figure 16. Entropy of solution for Xe in the n-alkanes.............71

Figure 15. Au vs. n for the n-alkanes at 5 temperatures..... ..... 69

Figure 17. Enthalpy of solution for Xe in the n-alkanes............72

Figure 18. Binding energy, surface energy, and enthalpy of
solution for the n-alkanes. (Figure 5 of reference 68).............75

vii

Figure 19. L vs. T for the normal alkanols. The numbers next to
the symbols are the number of C atoms in the alkanol molecule......80

Figure 20. x vs. T for the normal alkanols. The numbers next to
the symbols gre the number of C atoms in the alkanol molecule......82

Figure 21. L vs. n for the n—alkanols at 5 temperatures............8u

Figure 22. x vs. n for the n-alkanols at 5 temperatures...........85

2

Figure 23. Au° vs. T for the n-alkanols. The numbers next to
the symbols age the number of C atoms in the alkanol molecule......89

Figure 2A. Au°p vs. T for the n-alkanols. The numbers next to
the symbols age the number of C atoms in the alkanol molecule......91

Figure 25. Aug vs. n for the n-alkanols at 5 temperatures..........93
Figure 26. Augp vs. n for the n-alkanols at 5 temperatures.........9u
Figure 27. EntrOpy of solution for Xe in the n-alkanols............96
Figure 28. Enthalpy of solution for Xe in the n-alkanols...........97

Figure 29. Binding energy, surface energy, and enthalpy of
solution for the nralkanols. (Figure u of reference 69)............99

Figure 30. L vs. M for Xe in aqueous amino acid solutions.........118

Figure 31. L vs. v w for Xe in aqueous amino acid solutions.......122

t
Figure 32. L/L0 vs. Vt" - HM/55.3u6 for amino acid solutions......126
Figure 33. E vs. molecular weight. ............. ...................129

Figure 3uofiv30 SOIUtion pH......O....00.0.0.0...0.0.0.0000000000131

viii

INTRODUCTION

The fundamental goal of studies on the solubility of gases in
liquids is to understand solution processes from molecular first
principles. Given the physical properties of a solvent 1 and a solute 2,
we would like to predict the thermodynamics of salvation of 2 in 1.
Although this goal is not presently attainable, we have taken a step
towards understanding solubility by studying some simple gas/liquid
systems.

We have measured the Ostwald solubility, L, of 133Xe in a variety
of liquid solvents. Ostwald solubility is the equilibrium ratio of the

volume concentration of solute gas in the solvent to the concentration

8
2

molecules per unit volume) of solute 2 in the liquid and gas phases,

in the gas phase. If 92, p are the number densities (i_e_ the number of

respectively, then

R/pg. (1)

L" D2 2

Xenon was chosen as the solute gas because of its simplicity,
because of its importance in the biological and environmental sciences,
and because, as will be explained below, it is easy to work with. As an
inert gas, Xe interacts weakly with other molecules (short-range,

induced-dipole interactions). Due to these weak interactions, the inert

gases form prototypical solids and liquids, and have been the subject of

many studies."2 3

The general properties of these gases are well known.
133Xe is an inexpensive and easy to detect radioactive isotOpe of Xe.
This isotope is of environmental interest since it is a byproduct of

133x6’ as

nuclear power reactors. along with Kr, another radioactive

inert gas, were the major radioactive contaminants released to the
environment during the accident at Three Mile Island.”

At a partial pressure of 0.8 atmosphere (atm), Xe is an
inhalational anesthetic. The mechanism of anesthesia seems to be the
same for all anesthetic agents.5 Although there are indications that the
site of anesthetic activity is in the cell membrane, the exact mechanism
is not yet known.

Cell membranes are, simply put, lipid bilayers in which proteins
are imbedded. The building blocks of the bilayer are phospholipid
molecules. These molecules contain a polar head group bonded to 2
nonpolar hydrocarbon chains. They are thus amphipathic; polar (or
hydrophilic) at one end and nonpolar (or hydrophobic) at the other.
Since the cellular environment is aqueous and highly polar, it is
thought that hydrOphobic effects may be important in the formation and
stability of cell membranes.6’7

The two hydrophobic tails of the lipid molecule are straight
chain hydrocarbons, 16-18 carbons long. Thus, the environment inside a
cell membrane is similar to that in one of the normal alkanes, i.e. both
are nonpolar. This is one of the motivations for using the normal
alkanes as solvent.

The normal alkanes are a homologous series of straight chain,

saturated hydrocarbons. They are nonpolar, implying that interactions

with a nonpolar solute will be of the induced-d1pole/induced-dipole
type. Physical prOperties of the normal alkanes are well known and can
be found in the literature.8 Density as a function of chain length is
nearly constant, about 0.7 g/cm’, so that the number of carbon atoms, or
CH2 groups, per unit volume is nearly constant at about 3 x 1022/cm3.
Thus, a Xe atom in liquid n-dodecane will be surrounded by much the same
microscopic environment as one in liquid n-tridecane. The difference is

in the number of methyl (CH ) and methylene (CH2) groups with which it

3
interacts and in the geometry of these groups.

A second homologous series of solvents studied are the normal
alkanols. They differ from the alkanes in the replacement of a hydrogen
on a terminal carbon by a hydroxyl (OH) group. Adding the polar hydroxyl
group makes the longer chain alkanol molecules amphipathic. It also
changes the solvent environment radically. Intermolecular interactions
are stronger due to the non-zero dipole moment and due to hydrogen
bonding. These stronger interactions show up in increased surface
tensions, and in higher melting and boiling points for these liquids.9

We also measured the solubility of Xe in aqueous solutions of
amino acids, sodium chloride, and sucrose. In these solvents, we
consider complex, three-component systems. Water, in itself, is a highly
polar solvent. In addition, amino acids in solution (as the name amino
acid implies) become ionized, and have both positively and negatively
charged groups. Also, the amino acid side chain can be nonpolar, polar,
or charged. By comparing values of L for Xe in amino acid solutions with
that for Xe in pure water, we obtain information on both amino

acid/water interactions and on Xe/ amino acid interactions. The former

can be important in studying protein formation and conformation, while

the latter may aid in understanding Xe/protein interactions. Both types

of interaction may be important in studies of anesthetic activity.

THEORY

There are several important relationships that we will need later
and which we will now derive. In section 1, we introduce the concept of
the ideal solution. All of the gas/liquid systems we studied involved
dilute solutions of Xe in the solvent. These systems are known as dilute
ideal solutions; i.e. solutions in which the free energy of the solute
in solution is the same as that for an ideal solution.

In section 2, we derive Raoult's Law, a key prOperty of ideal
solutions. We also discuss why Raoult's Law is not applicable to our
systems.

Henry's Law, which is a generalization of Raoult's Law, is
introduced in section 3. We also derive here the relationships between
the three quantities KH, x2, and L, which are the Henry's Law constant,
mole fraction solubility, and Ostwald solubility, respectively.

Section 11 is a discussion of hard-sphere models of solubility.
Our results on the solubility of Xe in the alkanes and alkanols will be
compared with the predictions of some of these models.

Kirkwood-Buff theory is the topic of section 5. It may be
possible to use this theory to predict deviations from Henry's Law at
high pressures.

Section 6 brings together the relationships we will need to

analyse our results. Section 7 discusses multicomponent systems, and

introduces the concept of hydration numbers. We also derive the
equations we will use in our discussion of the Xe/amino acid/water

systems.

2.1 IDEAL SOLUTION

 

An important starting point in the study of solubility is the
concept of the ideal solution. Ideal solution theory provides a
framework with which real systems may be compared. As in the case of a
perfect gas, it is the deviations from ideality that yield information
on interactions.

A < ‘73)
moles of A, and

Consider two liquids, A and B, at a temperature T. Let V

be the molar volume of A (B). If we form a mixture of n

A

nB moles of B, then A and B form an ideal solution if‘o:
(AHm)T’P a 0 , (2)
(AVm)T’P - o = v - ”AVA - nBvB . (3)

H is the enthalpy, and V is the volume. The subscript m stands for
mixing. The first condition, that no heat is evolved or absorbed,
indicates that A molecules interact with B molecules as if they were A
molecules, and vice versa. The second condition, that no volume changes
occur, is necessary to eliminate changes in entropy from that source,

since

BS 3?

Pressure does change with temperature if the volume is held fixed. To
prevent changes in entrOpy on mixing, we must assume that the volume

does not change, so that

as

A3 ‘ (BVJT

AV = O .

The following conditions on the energy of mixing, (mm, and the

free energy of mixing, AGm,can also be derived.

(AUm)T,P a 0 a (AHm)T,P - P(Avm)T,P (5)
and
(AGm)T’P a -T(ASm)T,P . (6)
Note that
(AV)-(-a-AG) -o (7)
m 3? m T,n -
and
AG
2 3 m
(AHm) = ‘T [fi-(TJLD n = 0 . (8)

We can see that equation (8) is valid by performing the differentiation,
(3“)

5T . If we write

and using the relation S a -
P,n

11A) + ”BUB - 11g) (9)

we see (assuming that equations (7) and (8) hold for each component)

i :- A,B (10)

'The pi and u; are the chemical potentials of component i in the mixture
and in the standard state, respectively. The chemical potential is the
free energy per molecule, and the standard state is the pure liquid.

Equations (10) have as solution

111 = 112+ RTln(Xi) , (11)
so that

(ASm)T P a -n Rln(xA) - n

, A BRln(xB) , (12)

where we have xA and xB for the mole fractions, respectively, of A and

B.

 

 

= 1 - x . (13)

2.2 RAOULT'S LAN

 

Raoult's Law, which we will derive from the assumption of
solution ideality, is a simple relation between the mole fraction
solubility and the vapor pressure of a solution component.
Unfortunately, as we will see below, it is only valid in a few special
cases for real systems.

If the vapor phases of A and B are ideal, we have (in the gas

mixture)
1' j (l/ ) 11
u u 4’ mm P. I:o (1 )

I»
where Pi is the partial pressure of i, 111 is the chemical potential of

pure 1 in the vapor phase at unit pressure Po.
At equilibrium, the chemical potential of‘ i in the gas is equal
to that of i in the liquid. Then,

*
u; + RTln(xi) = “i + RTln(P /P,] . (15)

i

For pure 1, xi - 1 , P . P° the vapor pressure of pure 1, so that

i i ’

N
u; - u, + RTln[P;/P,) . (16)

Then

RTln(x1) - RTln(Pi/P°) - RTln[P;/P,J . (17)

10

01“

P1 - xiP; . (18)

Equation (18), which says that the partial pressure of component i in

the vapor phase is equal to the mole fraction of component i in the

liquid solution times the vapor pressure of pure liquid 1, is known as
Raoult's law.

There are a few real systems which behave ideally. Most are

isotopic mixtures, such as a mixture of 160 and 180 11

2 2’
optical isomers.12 It is not surprising that these systems should be

or mixtures of

ideal. However, there are other systems, such as the benzene/toluene
system at about 90° C, which behave ideally and are not in these two

13

classes. Other possible ideal systems are mixtures of. the rare gases.
There are only two rare gas systems, argon/krypton and krypton/xenon,
which can be studied over the entire range of composition. Davies_e_t
a_l_.1u investigated solutions of argon and krypton at the triple point
temperature of Kr (T - 115.77° K). They found deviations of 041% from
Raoult's law, and volume changes of less than 1.5% from the ideal over

the full range of composition. Calado and Staveley1S

found, in a study
of Kr/Xe systems, deviations of up to 12% (xKr . 0.3), and changes in
volume of about 1.5%. Thus, even when interactions are weak and short

range, deviations from Raoult's law are observed.

11
2;} HENRY'S LAW
If the temperature is above the critical temperature of one of

the components, a more general form of Raoult's law, known as Henry's

law, applies. Henry's law states:

P = K x. , (19)

i.e., the partial pressure of component i is proportional to its mole
fraction in the solution. However, the constant of proportionality, KH’
called Henry's constant, is not the vapor pressure of pure 1 as it is in

Raoult's law. When expressed in the more general form

f a K x (20)

where f is the fugacity of 1,7 Henry's law is valid for some gases up

i
to very high pressures, to 600 atm for N2 and CH” gases in liquid
solvents of H 0 and of aqueous sodium chloride.16

2

Henry's coefficient, K is simply related to the Ostwald

H9
solubility coefficient L. The mole fraction solubility of 2 in 1 is

) (21)

x = n /(n1 + n

2 2 2

where n1 is the number of moles of i in solution. For dilute solutions

(x2<< 1) we can write

12

 

2 1
R -
x2. 3“ =[——T—_—+1]‘ (22>
LPZV1 + 1 LPZV1
RT

where n2 - LPZVI/RT is the number of moles of 2 in volume V1, P2 is the

partial pressure of 2, and n1 - 1 is the number of moles of 1 in molar

volume V1. Solving equation (22) for P2 we see

 

x
RT 2
LV 2
1
For x2 << 1 ,
P2 = (RT/LV1)x2 (2n)

Comparison of equations (19) and (2H) gives
1% = RT/LV1 . (25)

Deviations from Henry's law can be related to solvent-solvent, solute-

solvent, and solute-solute interactions using the Kirkwood-Buff theory

17

of solutions. Kirkwood-Buff theory is discussed below.

13

2.11 HARD SPHERES

 

Besides the thermodynamic approach to solvation processes offered
by ideal solution theory, there is also an approach to solubility from
molecular theory. There are two models of liquids which have had some
success in predicting the physical properties of liquids and the
thermodynamics of liquid mixtures. Both models involve hard Sphere

molecules, i.e. molecules with intermolecular potentials of the form

(26)

where a is the radius of the molecule. The equation of state for a hard
sphere liquid is the same for both models, even though they involve
different assumptions and methods of derivation.

The first model is due to Percus and Yevick,18-22 who developed a
collective coordinate description of a system of hard spheres. Percus
and Yevick assumed that the pair distribution function was known, and
derived from it an integral equation for the system. (The pair

distribution function, (r), is the probability that there is aJ

2”

molecule a distance r from an 1 molecule.) Thiele23 and Wertheim

solved this integral equation, obtaining the equation of state of a hard

sphere liquid. Lebowi tzzs

later derived the equation of state for a
Percus-Yevick mixture of hard spheres.

The other model, deve10ped by Reiss, Frisch, Helfand, and
Lebowitz,2°'28 is known as scaled particle theory (SPT). In SPT, the
pair distribution function for a system of hard spheres is constructed,

and from it the equation of state is derived. This equation of state is:

1H

2
_P_.1+v+v
ka (27)

(1 - y)3

 

:3p/6 and p is the number density of the hard spheres. As

where y = na
noted above, this is the same as the equation of state derived from the

Percus-Yevick model.

29 3O

Uhlig and Eley proposed the following model of the solution
process. First, a cavity is created in the solvent which is large enough
to hold a solute molecule. Next, the solute particle is introduced into
the cavity and allowed to interact with the solvent. The reversible work
to create the cavity of radius r is given by
W(r) . Anr3P/3 + Anr20(1 - Egg) + Ko (28)

where a is the surface tension of the liquid, a is the solvent diameter,
1Q) is a constant which is small compared to the other terms, and 6 is a
factor which takes into account the non-zero curvature of the cavity
surface. The first term is the work done to create the cavity against
pressure P, while the second is a surface energy term.

31

Reiss approximates W(r) for r > a/2, using scaled particle

theory, by the polynomial

W(r) - k0 + K1r + K2r2+ K3r3 . r > a/2 (29)

For r S a/2, the exact expression for W(r) for a hard sphere fluid is

W(r) . -kT[ln(1-unr3p/3)] . r S a/2 (30)

15

2
If we require continuity of W, 3% , and-a—g at r - a/2 (so that the
Sr
function is at least smooth, if not well behaved, at r - a/2) then we
22-2u

get the following expressions for the K's

7:
I

 

2
kT[-ln(1-y) + g( 13y ) ] - nPa3/6

 

 

x - (AT-)1 6!, + 18( 11', 121+ «Pa?

(31)

. k: 12y y 2 _
K (2)[1_y +18( 1_y ) ] ZNPa

 

 

x

N
J:
a
"U
\
W
o

By comparing equations (28) and (29) we see that the surface tension can

be expressed as:

 

 

o a kT/(Nna2)[ 13; + 18( yy )2] - 33 . (32)

Comparisons of calculated surface tensions with experimental values

yield good results (correct order of magnitude) when applied to simple

27 32

liquids, and very good results (i 10%) when applied to fused salts.

Pierotti33 derived an expression for the Henry's law constant of

a gas in a liquid. He found

* 6
1n( ) - -5 33(5—) + -3 + ln(51) (33)
KH ' kT kT °

1

16

The factor c* is an interaction energy which is a function of the
polarizabilities and susceptibilities of solvent and solute. The first
term is thus related to the free energy of interaction of the solute
with the solvent. In the second term, the numerator Cc - W(r12), where

W(r) is given by equation (29) with the K's as in equations (31), and

+

the mean separation is r12 - (r1

diameters are r1 and r2 respectively. V1 is the molar volume of the

1!
solvent. The quantity 5 can be estimated from the equation

r2)/2. The solvent and solute

6* - (npch/o?2)[a1a2/((u1/x1) + (dz/x2))] . (3“)

Here the a are the polarizability and susceptibility, respectively,

1’ xi

of component i, m is the mass of the solute 2, and a as given

12" r'12

at
above. Using reasonable values for r and r2, and calculating c from

1
equation (311), Pierotti predicted the solubilities, heats of solution,
and partial molar volumes of gases in several liquids. The agreement
with experiment is good (110% in anH, 120% in 17b, and correct order of
magnitude in the enthalpy of solution).33

It is also possible to express 5* in terms of Lennard-Jones

parameters. In this form we have3u

* 3
ELJ - (2/3)1rpe12012 , (35)
where c - (e e )1/2 a - (o + o )/2 and c o are the Lennard-
12 1 2 ’ 12 1 2 ’ i' 1

Jones energy and distance parameters for component i.

17

* ,
Wilhelm and Battino35 have used ELJ and equation (33) to estimate

6 and a for several gases and solvents. We will use their Lennard-

i 1
Jones parameters to predict the thermodynamics of solution for Xe in

some of the alkanes and alkanols.

Yosim and Owens36

calculated heats of vaporization and fusion for
the inert gases, and the heats of vaporization for a number of diatomic
and polyatomic gases from the hard sphere equation of state. Agreement
with experiment was very good (:51) for most of the monatomic and
diatomic molecules, and was good (:10 to 20%) for the larger, polyatomic

molecules. Yosim37

calculated heat capacities at the boiling point for
these gases. Calculated heat capacities were within 10% of experimental
values for the symmetrical gases, and within 301 for the asymmetrical

37

ones. Yosim also predicted the compressibilities of Ar, H N 0

2’ 2’ 2’

and C6H6. Agreement with experiment was good (20%).

Why should experimental results compare so favorably with such a
simple model? Intermolecular potentials are essentially hard sphere,
repulsive, cores with a short range attractive component. Looked at in
this way, the attractive component serves primarily to determine the
density of the fluid. The density, p, appears explicitly on the left
side of equation (27), and implicitly on the right side in the parameter
y - npa3/6. So the model does take the attractive component into
account, at least in an averaged sense.

Longuet-Higgins and Widom38

proposed that a hard sphere liquid be
put in a uniform attractive potential, in order to make the attractive
component more explicit. Snider and Herrington39 used this idea in the

equation of state

.3. - 5.2
pm. - x(y) (RT) (36)

18

where x(y) is the right hand side1of equation (27), and A is an
1additional parameter. When generalized to binary mixtures, agreement of
calculated values of AHE(excess enthalpy of mixing), ASE(excess entropy'
of mixing), and AVE(excess volume of mixing) with experimental values

was found to be generally good (:30 to “0%) for 10 equimolar mixtures.39

2.5 KIRKHOOD-BUFF THEORY

 

In studies of solvation processes, and of solute and solvent
interactions, we gain information by varying temperature, pressure, and
composition of our systems. Temperature variations, as we will see
below, yield thermodynamic quantities, such as the chemical potential,
enthalpy, and entropy. Variations in pressure and composition, when
analysed according to the theory of Kirkwood and Buff, tell us about
other properties of the solution.

Kirkwood and Buff“0 developed a general statistical mechanical
theory of solutions. Using integrals of the radial distribution
functions of the different molecular pairs, they derived expressions not
only for the partial molar volumes (Vi) and the isothermal
compressibility (KT), but also for the osmotic pressure and the
derivatives of the chemical potentials (p13). Their equations are
applicable to multicomponent systems. For a two component system, it can

be shown that17:

19

KT - C/an (37)
V1 - [1 + p2(G22 — G12)J/n (38)
62 - [1 + p1(G11 — G12)]/n (39)
uij- gig; . uii = r 5% (no)

where
n ' D1 + D2 + p1°2<G11 I G22 "2°12)

. .. 2
c 1 + p1G G (G G 012).

11 + °2 22 + °1°2 11 22

GH = {7313(r) — 1)Anr2dr

Bui

11 -(—) 0'
ij BNJ T’P’NJ

In these equations, p1 is the number density of i, (r) is the 1,3

pair distribution function, and N is the number of molecules of type,j

J
in volume V. The prime (') in the expression for "ij indicates that all
N1 (except for i - J) are held constant.

For a dilute solution of B in A, we find

n - p1 , C - 1 + p1011 . (N1)

20

Equations (37)-(39) then become

KT = (1 + 91GHJ/kTp1 (“2)
v1 - 1/p1 (H3)
112 = [1 + p,(G,, - 0,2)1/91 (1111)

Note that both the isothermal compressibility and the molar volume of

the solvent reduce to their values for the pure solvent, as expected. It

can also be shown that“1

 

 

3(;3§)T . 1/x2 + 1 +p‘(261§ - f‘; - €23; ) (us)
x2 '°1 °1x2 11 22 12
and
(332) = 1 + 01(011 - G12) . 7 (us)
3? D1 + °2 + p1°2(G11 I G22 ' 2612) 2

We use the conventional symbol 8 = 1/kT in equation (H5). Equatitnl (H6)

is also an expression for V which is the partial molar volume of B.

2’

Note that the second osmotic virial coefficient, E3 is related

2!
to the solute-solute radial distribution function by the equation

a 2
32 = -(1/2)fo(g22(r) - 1)Anr dr = -(1/2)022 . (A7)

21

(The osmotic pressure, 1, is the difference in pressure across a rigid,
semi-permiable membrane which separates two containers of liquid, one of
which contains pure solvent A, and the second of which contains a
solution of B in A. For ideal solutions, there is an ideal equation of
state that is identical to the ideal gas equation of state; i.e., W =
nRT . B2 is the first term in the virial expansion of this equation.)

Our experiments will involve only dilute solutions. In the case

of dilute solutions, equation (M5) becomes:

Due

B(§§;)T,P,p1 ' 1/X2+ 01(261 ‘ G - G ) (“8)

2 11 22

Combining equations (u2)-(uu),(u7), and (M8) yields

311
2 - -
B(§;;)T,P,p1 a 1/x2+ p1(282 + V1 2V2 + kTKT) . (“9)

Now we can write the chemical potential of B in A by integrating

equations (H6) and (A9).
2 - _ o
u2(T,P,x2) - kT1n(x2) + C(T) + V2(P P )

kT - '
+«5-(282 + V1 2V2 + kaT)x2 . (50)

1

Equation (50) is correct to first order in (P-P°) and xb, where P° is
the unit of pressure (P°- 1 atm), and the superscript 9. indicates the
liquid phase. The term C(T) is a constant of integration which is a

function of temperature. The chemical potential of B in the gas phase is

22

f2(T,P)
(T,P) = u§(T) + len(——Fg———) (51)

where f2(T,P) is the fugacity cf B.10 At equilibrium, the chemical

potentials in the gas and liquid phases are equal. Combining equations

(50) and (51) by equating u: - pg gives:

f (T.P) -
len(-%-$-5—-) " 'U§(T) + C(T) ‘1' V2(P‘P°)
2
RT ' ‘
+ 5—(232 + V1 V2 +kTKT)X2 . (52)

1

Equation (52) reduces at low pressure, and consequently small x2, to:
P _ o _' o
len(§—§V) u2(T) + C(T) v2? len(KH) . (53)

2

In equation (53). KH is the Henry's law constant for B in A. (Hxnbining

equations (52) and (53) we obtain

f2(T’P) 1 _
ln‘——;;FV—) - ln(KH) + E? v2?
+ (1/V1)(ZB2 + V1 - 2V2 + kaT)x2 . (5H)
f (T,P) 1 _
By plotting 1n sz -'kT V2? as a function of x2, we can

determine the Henry's law constant, K from the intercept,anuithe

H!

second osmotic virial coefficient, B from the slope. Watanabe and

2’

23
Anderson”2 have noted an empirical relation betweenB2 andlqr They
prOpose that

B . a ln(KH) + a (55)

2 1 2

where a1 and 32 are constants. If equation (55) is valid, it should be

possible to predict deviations from Henry's law using equation (5”).

2.6 APPLICATION TO EXPERIMENTS

2.6.1 ASSUMPTIONS

 

we make several assumptions about the experiment in order to
perform a thermodynamic analysis of the data. First, we assume that the
gas phase is ideal, so that equation (1H) for the chemical potential as

a function of pressure is valid. This should be a good assumption, since

the equation of state of Xe at 25°C, derived by Michels_et_gl.,u3
predicts a deviation of less than 1% from ideality at 1 atm pressure.
We also assume that the Xe forms a dilute ideal solution17 in all

solvents used. For dilute ideal solutions, the chemical potential can be

written

“2 - u; + RTln(x2) (56)

211

where u; is a constant. The quantity pg is often interpreted as being

the chemical potential of a solute B in pure B, but with molecular
interactions as if the solute B molecules were surrounded by solvent A
molecules. Equation (55) should be valid, since at 1 atm pressure of Xe,

x2 is of the order of 0.01.

A third assumption we make is that the Ostwald solubility, L, is
constant over the range of pressure from 0 to 1 atm. Considering

equations (22)-(25), this assumption introduces an error of order x2,

assuming that Henry's law holds (KH - constant). The gas phase in most

133

of our experiments consisted of a dilute mixture of Xe in air, due to

the high cost of nonradioactive Xe gas. However, some experiments were

133

performed with mixtures of Xe in nonradioactive Xe. The value of L

obtained for the system (133Xe in Xe, H20) differs from that for (133Xe
in air, H20) by about 1/2 %, which is well within experimental error
(1%). This agreement, however, may be due to the low solubility of Xe in
H20 (L . 0.106 at 25°C). The corresponding mole fraction is about

x2 a 0.001, and changes in L would not be seen using our technique.

2.6.2 THERMODYNAMICS 0F SOLUTION

At equilibrium, the chemical potential of the solute in the gas
phase is equal to its chemical potential in the liquid. Equating

1 equations (1A) and (56) gives

4*
+ RTln(P (57)

“2 /Po) - pg + RTln x

2 2 °

At a partial pressure of 1 atm, P = P,, so that

2

25
*
Aug - u2 - u; - -RT1n(x2) . (58)

The entropy of solution is given by

BApg
A32 = -(_fi— P,n . (59)
Using Au; a AH2 - TA82 and equation (59).
Au°
2 3 2
AH2 — T [5T(_T—)]P n . (60)

If a plot of Auz as a function of temperature is linear, then the slope

is -ASZ, and the intercept is AH This is really an assumption that the

2.
2 and A82 are much slower than linear in T.

advocate the use of a different formula from

temperature dependences of AH
Ben-Naimlgt‘al.uu’u5
equation (58) for the chemical potential of solution. Their equation is
derived using statistical mechanical principles. It is based on a number

density scale. Our equation (58) is based on a mole fraction scale. Ben-

Naim's formula for the chemical potential is
Aug” - -RTln(L) (61)

where L is the Ostwald solubility. Equations (59) and (60) also hold for
09
Au2 .

Unfortunately, as will be seen below, the interpretation of the

data depends on which expression is used to determine the chemical

potentials, and.the conclusions drawn are inconsistent with each other.

There is no general agreement at present as to which of the two models

26

is preferable, and so our results will be discussed here in terms of
both equation (58) and equation (61).

The goal of these experiments is to be able to predict the
solubility of a gas in a liquid from the molecular preperties of the gas
and liquid. This is equivalent to predicting the entropy and enthalpy of

solution. Although we cannot yet predict the entropy of solution, we can

estimate the enthalpy of solution using the model of Uhlig29 and Eley.30
We can write
AH2 - EC - Eb (62)

where ED is the binding energy of solute to solvent, and Ec is the

amount of work done to create the cavity. The enthalpy is the heat

absorbed by a system at a constant pressure. E may be estimated as the

b

geometric mean of the heats of vaporization of solute and solvent. An

expression for the cavity energy is31

2 . 3
Ec Mnr2Y1NA + uanPNA/3 (63)

where r is the solute radius, Y is the solvent surface tension, P is

2

the pressure, and N

1

A is Avogadro's number. The first term is the surface

energy of the cavity, and the second is the work necessary to create a

spherical volume of radius r at pressure P. At pressures of the order

2

of 1 atm, the volume term is negligible compared to the surface term.

Thus at low pressures we can estimate the enthalpy

2
AH2 - Nnr2Y1NA Eb . (6")

27

2.7 MULTICOMPONENT SYSTEMS

The solubility of a gas in a liquid is even more difficult to
understand when the liquid solvent itself is made up of two or more
components. Interactions between the solvent components may produce a
liquid environment which is very different from the environment in
either pure solvent. This thesis reports our experiments on aqueous
solutions of amino acids, sucrose, and sodium chloride.

Donkersloot“6 studied the binary systems water/methanol,
water/butanol, and cyclohexane/Z,3-dimethylbutane using Kirkwood-Buff

l17

theory. In addition, Patil applied Kirkwood—Buff theory to the system

water/butanol. They found that the G1 (Kirkwood-Buff integrals) were

.1
strongly dependent on concentration, which indicates that interactions
between components are also concentration dependent. Kojima, Kato, and
Nomuran8 were able to approximate the results of Donkersloot for the
cyclohexane/Z,3-dimethylbutane system by assuming a Lennard-Jones type
interaction between components. Their method, however, failed for other
mixtures.

Since interactions in binary systems are so complex, changes
brought about by the introduction of a third component are not easy to
predict. The third component may be selectively solvated, leading to

salting-in and salting out effects,“9

or it may be "inert" with respect
to one of the components. For example, in a mixture of water and
marbles, we would expect the solubility of any solute to be prOportional
to the volume fraction of water. An early investigator of salting-out

50,51

effects was Van Slyke. Van Slyke deve10ped a method of measuring

gas solubility which depends on these effects. After saturating a

28

solvent with the solute gas, "salts" are added to a sample to force the
disolved gas out of solution. In this way, the volume of gas disolved in
a known volume of solution can be determined.

Surprisingly, Yeh and Petersonsz’53 found good agreement between
measured solubilities for Kr and Xe in blood, protein solutions, and
tissue homogenates, and solubilities predicted from known solubilities
in each of the components. For the system Kr/blood, Yeh and Peterson
obtained a value for the Ostwald solubility of Lexp - 0.0A55 i o.oouu at

37°C. They predicted a value of L - 0.0A33 by considering blood as a

pred
four-component mixture of water, hemoglobin, albumin, and lipid. They
also obtained very good agreement (11%) for the solubility of Kr in
rabbit muscle homogenate. Agreement between experiment and prediction
for Xe in blood and rabbit muscle homogenate was not as good (i 10% and
i 5% respectively).

Gas solubility in biological materials is very difficult to

determine. Weathersby and Homer,5u

in a review of the literature, found
a wide disparity in published data for gas solubilities in biological
fluids and tissues. This is probably due to the complexity of these
many-component systems, where a small change in composition can have a
large effect on gas solubility.

One of the earliest investigators of the salting out effect was

Setschenow.55

He derived an empirical relation between the solubility of
a gas in an aqueous salt solution and the concentration of the salt in

solution. This relation is known as the Setschenow equation:

log10 g9- - ksc (65)

29

where S is the solubility of a gas in a salt solution of concentration

0, So is the gas solubility in pure water, and k is a constant known as

S
the Setschenow coefficient. If kS > 0, the gas solubility is less in the
salt solution than in water, and salting out occurs. If kS < 0, the gas

solubility is greater, and salting in occurs.

56 57

Shoor and Gubbins and Masterton and Lee derived expressions
for the Setschenow coefficient from scaled particle theory. Agreement
with experimental values of the Setschenow coefficient was good for a

variety of gases (He,Ne,Ar,Kr,H 0 N CHA’CZHU’C2H6'SF6) in several

2’ 2' 2’
different salt solutions (NaCl, LiCl, KCl, KI). Masterton58 also used
scaled particle theory to predict Setschenow coefficients of 5 gases

(He, Ne, Ar, 0 N2) in seawater. The average difference between

2’
observed and calculated values of kS was of the order of 5% at 25°C.
Considering the large number of components in seawater, this is very
good agreement.

Euc ken and Hertzberg.59

studied the salting out of gases in
aqueous salt solutions. From their data, Eucken and Hertzberg were able
to calculate hydration numbers for each salt in solution. The hydration
number of a salt is the number of water molecules associated with each
anion-cation pair in aqueous solution. They made several assumptions
about the solutions in order to calculate the hydration numbers.

The first assumption is that water in an aqueous solution exists
in one of two states, either "bound" or "free". Bound water is
associated with the salt, and is unavailable to dissolve the solute gas.

The rest of the water is free. The solubility of the gas in free water

is the same as in pure water.

30

Eucken and Hertzberg also assume that the molar volume of both
free and bound water is equal to that of pure water. This model is based
on the excluded volume concept. The decrease in gas solubility occurs
because of a decrease in the volume of water available, and the gas is
excluded from the volume occupied by the salt ions and their hydration
shells.

Under these assumptions, one can derive the following expression

for the hydration number, H, of a salt:

L
H - (MHZO/M)(vtw - E6) (66)

Here, MH 0 is the number of moles of water per liter at temperature T, M
2

is the molarity of the salt solution, vtw is the volume fraction of

total water for the solution, L is the Ostwald solubility of the gas in

the solution at temperature T, and L is the Ostwald solubility of the

0

gas in pure water at temperature T.
We can invert equation (66) and write the solubility in terms of
the hydration number H.

H
(Msalt + MHZO

°salt °H20

 

L - L 1 - M )] (67)

0[

where M1 and p1 are the molecular weight (g/mol) and density (g/l) of i,

and M is the molarity. The fraction of the volume which is water, either

free water or hydration water, has been written as

31

M
v -1-Mi§lE. (68)

t" psalt

leing equations (65) and (67). we can relate the Setschenow coefficient

to the hydration number by:

M HM
kSM - -log10[1 - M[ salt + ——§19)] (69)
°salt °H,o

 

M HM
For dilute solutions, i.e., those for which M(__s_a_l_t +-——H-39) (< 1, we

salt °H,o
can expand the argument of the logarithm to obtain

 

 

M HM
kéM . ( salt + H30)M (70)
psalt °H,0
from which
M HM
k' . ( salt + H30) (71)

psalt szo

where ké =- 2.303kS . Since ké is of the order of 0.33 l/mol for NaCl
solutions, we would not expect equation (70) to be valid for our

systems. The Taylor series expansion of ln(1-x) is:

ln(1-x) - x + x2/2 + x3/3 + ..., (72)

so the fraction error made in neglecting second and higher order terms
is of the order of x/2. Since our solution molarities are of the order

of 0.5, and ké is of the order of 0.33, we make a 10% error hi

32

neglecting the higher order terms in equation (70). We will therefore

use equation (66) to interpret our results.

EXPERIMENTAL

3r.1 SOLUTION COMPONENTS

 

133Xe in trace

The solute gas in our experimental system is
amounts. The partial [pressure of 133Xe is typically about 1
picoatmosphere (patm) usually mixed with air at 1 atm total pressure.
Control experiments were also done in which 133Xe was mixed with
naturally occuring, nonradioactive Xe gas at a total pressure of 1 atm.
A variety of liquid solvents were used. These included several normal
alkanes and alkanols, as well as aqueous solutions of amino acids, NaCl,

133

and sucrose. For the experiments in which the-gas phase was Xe plus

nonradioactive Xe, the solvents were degassed before the run, and then

133

saturated with nonradioactive Xe. For experiments in which Xe was
mixed with air, the solvents were not degassed. In those cases, the
solvents were probably saturated with air which dissolved during
production and storage of the solvent. However, this had no measurable
effect on our values of solubility.

Xenon is one of the noble gases. Its atomic radius is 2.23 A,1
and it is therefore the largest and most polarizable atom of the 5
common inert gases (He, Ne, Ar, Kr, Xe). (A sixth noble gas, radon, has
only radioactive isotopes, no stable ones. The longest lived isotope of
radon is 222Rn, which has a half-life of 3.8 days.60 It is a product of

alpha decay of radium.) The particular isotope of Xe used in our

33

3”

experiments, 133Xe, is unstable and decays with a half-life of 5.2145

days.61 It decays by beta emission to an excited state of 133Cs. This

nuclear excited state decays60 with a half-life 6.3 x 10.9 sec by
eunitting an 81 keV gamma ray. We used the emitted radioactive intensity
of these gamma rays as a measure of 133Xe concentration.

Xenon-133 was purchased (Medi-Physics, Plainfield, New Jersey) in

20 milliCurie (mCi) aliquots. Typical amounts of 133

Xe used during a run
are of the order of 100 pCi. High purity, nonradioactive Xe is
commercially available (Matheson, New Jersey, 99.9+%).

The normal alkanes (Humphrey Chemical Co., New Haven,
Connecticutt) are simple, nonpolar organic molecules. They are
"straight" chains of carbon atoms saturated with hydrogen.62 Since they
are nonpolar, interactions between alkane molecules, or between an
alkane molecule and any other nonpolar molecule, are short range,
induced dipole to induced dipole interactions. The carbon to carbon bond
length is about 1.5 11,62 so a Xe atom interacts directly with only a
portion of a long alkane molecule.

'The normal alkanols (Aldrich Chemical 00., Milwaukee, Wisconsin)
differ from the n-alkanes in the addition of a hydroxyl group (Chi) to a
terminal carbon.62 Although bond lengths are not affected, the molecule
is polar. Thus we would expect stronger interactions between Xe and
alkanol molecules than between Xe and alkane molecules.

For the experiments involving amino acids (Aldrich), solutions of
amino acid in distilled water were made at 25.0 °C. We measured the pH
of the amino acid solutions, but made no attempt to control the pH, i.e.

no buffers were used since these would inevitably add yet another

component to the solutions.

35

Physical properties (density, surface tension, etc.) for the

8.9.63

alkanes and alkanols were taken from the literature, as were the

molecular weights of amino acids, and the solubilities of amino acids in

water.6u

3 . 2 APPARATUS

 

A diagram of the apparatus is shown in Figure 1. The apparatus
can be disassembled at the threaded Joint for cleaning and loading. Two
valves, along with several machined brass pieces are soldered together
to form the upper portion of. the apparatus, i.e., above the threaded
Joint. The bottom portion is a Pyrex container whose mouth is Joined as
shown to a glass-to-metal seal. A brass nut is soldered to this seal.
The nut and large ball valve form the threaded Joint, which is sealed
by wrapping with Teflon tape before assembly.

During a run a glass encased magnetic stirring bar runs inside
the bottom vessel, which contains the solvent. Commercial stir bars are
coated with Teflon. It was necessary to remove this coating since xenon
concentrates in it, apparently because xenon is highly soluble in
Teflon. We encase the stir bar in glass so the bare stir bar will not
corrode in the experimental solvent, which is acidic in some cases.
Teflon is used in two other places; in the threaded Joint as tape, as
noted above, and in the solid packing material in the ball valve. We
iglore any contribution of these seals to the measured solubility. In
both cases, the surface area of Teflon exposed to Xe is small. This, in

light of the very slow diffusion rate of gases in solids

Detector

L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pb Shield“).
\. _ luelte Window
mu. w'v. —_#
. . ~ . Bel Volvo
/ ‘ '\' .
H
Pb Shield“). "read“ Joint -
q t
\. 1 ' 'Vhb
Gloss to Metal Seal ‘ Brass Nut
(
V
Vee = th-vhb we”

Figure 1. Solubility measurement apparatus.

 

 

 

r

Stir Bar

37

9 cmz/sec), leads to a negligible contribution. Also, we have

(D - 10'
never seen any evidence of a Xe sink, which would have shown up in

either leak tests or dilution runs.

3;}TEMPERATURE CONTROL

 

Temperature was controlled to 10.1°C (Lauda/Brinkmann K-2/RD
circulator) both during a run, and in making up experimental solutions.
The bath fluid was an approximately 11:1 mixture of water:ethylene
glycol. The ethylene glycol decreases the problem of freeze-up of the

float in the circulator.

3 . 11 SHIELDING

 

We used Pb shielding of thickness 5 1 cm to reduce background

radiation and to prevent emissions due to 133Xe decays outside of volume

V“) from reaching the detector. One cm of Pb attenuates 81 keV gamma

rays by a factor of 106.6:5 Shielding effectiveness was checked by

putting ”’Xe in V with the apparatus and shielding in place. In

rest

these cases, we did not observe anything above the background rate.

38

3 .5 ELECTRONICS

 

A diagram of the electronics is shown in Figure 2. Gamma rays of
energy 81 keV are detected with an NaI(Tl) scintillation detector
(Harshaw, type 7SF8). A high voltage power supply (Power Designs, Inc.
model 15700 supplies 1100 volts for the photomultiplier via the pre-amp
(Ortec model 276). Detector output passes through an amplifier (Ortec
model 1185), then through a single channel analyser (SCA, Ortec model
1406A). The window on the SCA is set to exclude energies below about 10
keV and above about 90 keV. The window was set by feeding signals of
known amplitude into the amplifier, and observing the output on a
multichannel analyser. The resulting output was then compared to a 133Xe
spectrum. Two timers (Ortec model 719) are externally supplied a 0.1 sec
timing pulse by a minicomputer (Micro DevelOpment T001 1000).

The computer is programmed to take data and print out the
results. It counts the number of decays in A00 sec, makes suitable
corrections to the total, then prints out the result. It then waits an
additional 200 sec before counting again. Each hour the average of the
previous six values is printed out.

Two corrections are made to the data. Due to the nature of the
electronics, a pulse into the detector is not counted at the computer if
it too closely follows an earlier pulse. This "dead time" can be
measured by putting signals of a known frequency into the electronics,
and observing the output. In this way, we determined the dead time for

our system to be about 1 ~ 3.33 x 10"6 sec.

39

HIGH VOLTAGE
POHER SUPPLY

 

GIGNGL

 

TRIGGER
COMMEBTIONG

 

 

 

 

 

 

Figure 2. Schematic diagram of the electronics.

MO

Radioactive decay is a random process, and consequently,tflm
probability of k events, given a mean of u events, is given by the

Poisson distribution66:

k
P(k) - —‘-‘-—

. (73)
kieu

P(k) is the probability of k events per unit time, give a mean of u
events per unit time. If we let T, the dead time, be our unit of time,
and u be the mean number of events per time T, then the probability that

a single signal occurs within time 1 of an earlier signal is given by

9(1) . ° . ne'“ . (7n)
1!eu

 

The mean number of signals per unit time 1 is p, and is typically of the

order of 2 x 10-3, so we may use the approximation:

P(1) ~ u(1 -‘u) ~ u . (75)

The actual counting rate, Nact' can therefore be approximated by

Nact a Nobs(1 + u) ’ (76)

where Ni, is the observed counting rate. We have programmed the

be
computer to make this correction to the data.
The second correction which must be made to the data is to remove

excess counts due to natural background radiation. We measure background

”1

radiation several times over periods of several hours with the apparatus
and shielding in place, but without any 133Xe in the apparatus.
Background is subtracted after the dead-time correction has been made.
Typical backgrounds for a run are about 1100 counts in NOD sec. Counting
rates due to 133Xe vary from about 250,000 counts/1100 sec at the start

of a run, to about 50,000 counts/H00 sec at the end of a run.

3.6 VOLUME DETERMINATION

 

Volumes are indicated in Figure 1. There are seven volumes which

Vm
8

and Vee’ are the same for every run. The remaining two, V

must be determined for each run. Five of them, , V V V

hb’

are

rest’ sb’
(2) and V
(1)

determined at the beginning of each run. The gas volume V8

2!
is the

volume above the ball valve which initially contains all of the 133Xe.

(2)

The gas volume V8 is the remaining gas volume. The volume of the

liquid solvent is V The volume of the glass encased stirring bar is

£0
vsb and vhb is that of the small hole in the ball of the valve. The

volume below the ball valve is designated by vee’ and vrest is the total
(1)

volume excluding volume Vg .

To determine vee (ee stands for everything else), we weigh the
apparatus before and after filling Vee with water at a known
temperature. We make a buoyancy correction for the weight of air

displaced by the water. If mo is the observed mass, then the true or

bs

actual mass, m is:

act ’

”2
P
m air,T]

p
H20,T

/[1 ' e (77)

act ' mobs

where p1 T is the density of i at temperature T. Vee is then

to
v ”—53“— . (78)

9° pH20,T

Vhb (hole in ball) was calculated from measurements made on a
disassembled ball valve. For V ,
rest
vrest ' vee + vhb ' (79)

The volume of the glass-encased stirring bar, V8b , was determined by
measuring the water displaced when the stirring bar was immersed in a

known volume of water in a graduated cylinder.

(1)

We determined the initial gas volume V8 , by using a dilution

(1)

 

measurement. Xenon-133, initially confined to volume Vg at a
concentration of C1 , is allowed to expand throughout the volume V21) +
Vrest . If the final concentration, corrected for decay of 133Xe is Cf ,
we define the ratio a to be:
Cf vé1)
a . _ ' (17" g (80)
1 vg + vrest

from which

v“) - —-9‘—- v . (81)

g 1 - a rest

‘13

3.7 SOLVENT PREPARATION

 

Alkanes (99% pure) and alkanols (purities: methanol,99.9%;
propanol and butanol, 99+%; pentanol, octanol, decanol, and undecanol,
99%; hexanol, heptanol, and dodecanol, 98%; nonanol and tetradecanol,
97%; 200 proof ethanol) were used as purchased. Amino acid solutions

were prepared in 250.0 1 0.1 cm3

volumetric flasks in the following way.
To a predetermined mass of amino acid, we added distilled water to fill
the flask to within 1 cm3 of the 250.0 cm3 mark. For experiments
involving Xe atmospheres, the water was first degassed by boiling under
vacuum (Figure 3), then was saturated with Xe under a Xe pressure of 1
atm. The amino acid and water were also mixed under a Xe atmosphere.
After temperature equilibration at 25.0°C, enough water was added to
bring the total solution volume to 250.0 cm3. The outside of the flask
was‘ carefully dried, then the flask and solution were weighed, with the
usual buoyancy correction being made for the weight of displaced air or
IXe. Solution density was calculated, along with the volume fractions of

both water and amino acid. A small sample, about 5 cm3

, of the solution
is used to determine the pH (Brinkmann pH meter with combination

electrode).

3.8 LOADING THE APPARATUS

 

(1)

With the ball valve closed, air is evacuated from volume Vg

through the Hoke valve. A trace amount of 133

into V(1)
8

Xe is allowed to expand

, and then air or Xe is let in to bring the pressure to 1 atm.

NM

 

to Vacuum Pump

 

 

 

 

 

 

 

 

 

 

 

Figure 3. Schematic diagram of the degassing system.

”5

(1)

When using nonradioactive Xe, V8 was loaded using the gas handling

system shown in Figure A. The Hoke valve is then closed.

Approximately 220 cm3

of solvent is poured into the glass portion
of the apparatus, and is weighed. The gas handling system of Figure 14
was also used to load the solvent under a Xe atmosphere. The buoyancy

corrected weight divided by the solvent density yields the volume of the
(2)

liquid solvent, V2. The secondary gas volume, V8 , is:
(2) _ _
V8 - vrest V8b V1 . (82)

After putting in the stirring bar, the apparatus is assembled. Six to
seven turns of Teflon tape are used to seal the threaded Joint. Scratch
marks on the ball valve and on the brass nut ensure that it is assembled

reproducibly.

3.9 SOLUBILITY EQUATION

 

Solubility is calculated using conservation of 133Xe. Initially,
(1)

133Xe is confined to volume Vg

at a concentration of C1 .When

equilibrium has been reached, the 133Xe is distributed throughout
(1) (2)

volumes V ,
8 8

amount of 133Xe in the solvent is Cvai’

solubility of 133Xe in the solvent, and C
(1)
8

and V as well as throughout the solvent. The total

where L is the Ostwald

f is the equilibrium

concentration of 133Xe in volume V .Then

146

3

13
To Vacwm PUMP 3.“ Valve Pot Loading Xe

1'

...... r—1

Gauge

 

 

Solvent
Beauvoir

Nonraoioeotlve No my

 

 

 

Promo Fitting
Comeote to
upper Portion ot Apparatus

 

' 0 Valve

 

 

Lower Portion of WING

Figure A. Schematic diagram of the gas handling system.

"7

C V(1) . C eAAt(V(1) + V22)

1 g f 8 + Lvll . (83)

133

where )1 is the decay constant for Xe ( A - 0.9177 x 10-” min-1), and

At is the time elapsed between measurement of C and C . The term em“;

1 f
133Xe atoms. We can also see that LV

is a correction for the decay of A

is the "effective gas volume" of the liquid solvent.

Rearrangement of equation (81) gives

 

(1) (1) (2)
c v v + v
L = file Mt—é— - 3 v 3 . (811)
r 9. 9.

Equation (8A) is valid for measurements at a single temperature.
Experiments involving the alkanes and alkanols were done at a variety of

temperatures. The temperature dependent form of equation (8A) is:

 

Ci -AAtv(1) v(1) + V(2)
L(T) = -C—-e -%—a(i~) - 3 V 3 3(1) + 1 - R(T) (85)
f 9. 2.

where R(T) - p(T)/p(T2) is the ratio of the solvent density at

temperature T to the solvent density at temperature T the loading

2"

temperature. For the alkanes and alkanols, T was usually taken to be

9.

20.0°C, except for those which were solid (heptadecane, octadecane,

nonadecane, and eicosane) at that temperature. In these cases, T was

2
taken to be either 30°C or 110°C, depending on the melting point of the
alkane.

During a run, C1 is measured hourly for six to eight hours. Each
value is corrected for decay, and the mean value is calculated. After

the gas is uniformly distributed in Vé”, as determined from the

N8

observed decay rate, the main valve is opened and the stirrer is
Started. We calculate the Ostwald solubility, L, each hour. WhenI.
reaches a constant value, equilibrium has been reached. Time to
equilibrium is typically 12 hours. We wait an additional 8 to 12 hours
to be sure of equilibrium (see Figure 5. Figure 5 appears as Figure 2 in
reference 67). The equilibrium values of L are averaged to determine the
Ostwald solubility. For amino acid experiments, a second pH sample is

taken at the end of the run.

A9

 

 

  

50" r I I I I I I I I I I
—-40 u: I r l I 1 l I l I I-
{.2 A.
c°° . -1
:1 , -
>30 . -
b 0
E " . '
'2: .

1% - ._

7. °. . I

6 . ° .—

.s ..

4 ..

lmXele"At larb

 

Time [hours]

Figure 5. Normalized counting rate vs. time for a typical
experiment(Figure 2 of reference 67). The letter A indicates
the time the valve was opened, and the letter B indicates
the time a run might end, about 8 hours after equilibrium
has been reached.

RESULTS AND CONCLUSIONS

The results for Xe solubility in the normal alkanes and normal

68,69

alkanols have been previously published. In addition, some of the

results on the solubility of Xe in aqueous amino acid solutions have

also recently appeared.70

 

ii . 1 ALKANES

We measured the Ostwald solubility, L, of 133Xe in normal alkanes
at five temperatures in the range from 10°C to 50°C.68 Values of L, and
the mole fraction solubility, x2, are listed in Table 1. Mole fraction
solubilities were calculated using equation (21). Figures 6 and 7 are

plots of L versus Temperature (T) and x versus T, respectively, for the

2
normal alkanes. Figures 8 and 9 show L versus n, the number of carbon

atoms, and x versus n, respectively, at five different temperatures.

2
The Ostwald solubility decreases with both increasing T and increasing
n, while the mole fraction solubility decreases with T, and increases
with n. Thus, even though the number of Xe atoms per unit volume
decreases with increasing n, the number of Xe atoms per alkane molecule

increases with n. The decrease of Xe solubility with increasing

temperature is typical of gas/liquid systems.

50

51

TABLE 1. Solubility data for experiments with 133Xe in the normal alkanes.
The first row gives the Ostwald solubility measured for each alkane, and

2, where x2

the normal alkanes at 1 atm partial pressure of Xe.

the second row is 102x is the mole fraction solubility of Xe in

 

 

Temperature 10°C 20°C 30°C “0°C 50°C
Number of
carbons in
n-alkanes
5 L 6.u1:o.12 5.A8:0.11
x 3.03 2.56
6 5.91:0.03 5.07:0.10 u.55:o.o3
3.18 2.68 2.36
7 5.u110.03 u.67i0.07 u.1310.07 3.7510.07 3.37:0.0
3.26 2.77 2.u1 2.15 1.90
8 n.9910.03 h.36i0.05 3.9010.02 3.A7i0.05 3.3110.06
3.3” 2.86 2.51 2.20 1.95
9 A.70:0.02 n.1uio.o3 3.70:0.03 3.32:0.0M 2.99:0.03
3.95 2.99 2.62 2.30 2.0“
10 u.u2 3.9210.03 3.52:0.0A 3.1h 2.8V
3.59 3.08 2.71 2.38 2.11
11 n.1810.ou 3.7210.03 3.35:0.ou 3.00 2.71
3.62 3.16 2.79 2.A5 2.18
12 9.03 3.5910.02 3.22:0.01 2.9010.01 2.6a
3.76 3.28 2.88 2.55 2.28
13 3.88:0.0 3.uuto.o1 3.0910.02 2.80 2.53
3.87 3.37 2.96 2.63 2.3a
1h 3.76:0.01 3.3510.02 3.02:0.01 2.72 2.N9
u.oo 3.fl9 3.08 2.73 2.uu

 

52

TABLE 1 (cont'd.).

 

 

Temperature 10°C 20°C 30°C N0°C 50°C
Number of
carbons in
n-alkane
15 L 3.2“:0.02 2.9210.01 2.69 2.91
x2 3.59 3.17 2.81 2.51
16 3.19:0.01 2.85:0.03 2.5710.0 2.35:0.0
3.67 3.26 2.89 2.59
17 2.7610.03 2.51i0.01 2.30
3.3” 2.98 2.68
18 2.7110.01 2.u7i0.01 2.2510.01
3.A5 3.08 2.76
19 2.9210.01 2.21:0.01
3.17 2.8”
20 2.3610.0 2.17:0.0
. 3.29 2.92

 

4.5

Ostwald Solubility

‘0”

4.25

4.00

3.75

2.75

Ostwald Solubility'

+ I I I I
+ 5 ..
A .A a
El 7
m '1’ o e "
V 9
o A -
‘V
El A d
o
‘7 El _‘
0
gr C!
o -
v 0
v —
l L, l l ' L
to so so 40 so eo '
Temperature (°C)
, .l. I r I I
-+ :o -
A A :4
B D :2 q
o 4' <> :3
V A V 14 .7
C3 +_ _
o
9' AA
1
a +
8 A _
m +
3' a ‘
1) .—
1 l l l l
:0 so so 40 so so
Temperature (°Cl
Figure 6. L vs. T for the normal alkanes. The numbers next to the

53

 

 

 

 

 

 

 

 

symbols are the number of C atoms in the alkane molecule.

Ostwald Solubility

511

 

 

 

 

r l I l I
4- 15
D 17
A to :e
3.00 - ‘7 19 ,_
4.
Al
2.75 - E; ‘-
4.
2 50 £5
. 1-
% + 1
- g _
2.00 l l l l l
0 10 20 30 40 50 60
Temperature (°C)
Figure 6. (cont'd.).

55

 

 

 

 

 

 

 

 

3'50 v I I I I
6 + 5
A
3 U 7
+ . O G
0
1:
2.73 G _
.3 P A v
4.1
8 2.50 r- + o _
t a v
2.25 - -
3 B
o
1: 24m+- g -
‘.75 L l l l I
0 :0 ~20 so 40 so 30
Temperature (°C)
4°25 I I T r F
4.00 — v + to ..
o 0 A 11
o 3.75 - El El :2 -
('1
A 0 13
x sAm- + v ‘V “ -
c: o
D 3.25 h- E T
°'" A
m s. 8
L A
ll. 2.75 " + V ""
m 8
H 2.50 - v -
g t
2.25 F- a d
2.00 l l l E f
0 io 20 so 40 50 so

Temperature (°C)

Figure 7. x vs. T for the normal alkanes. The numbers next to the
symbols are {he number of C atoms in the alkane molecule.

Mole Fraction x 100

3.75 I

56

 

 

 

 

A r I I
+
3.50 '- o «-
[3
3.25 '- A o —I
-P ‘7
<>
3.00 " a d
+ 15 A '
£5 16 .p ‘7
2J3I' c] 17 To -
0 1! B
V 19 A
2.50 "' + d
2.25 I 1 1 1 ' I
0 10 -20 30 40 50

Figure 7. (cont'd.).

Temperature (°C)

57

 

8'5 4: I I I I I I I I I I

 

 

 

I47 I I I I
°°° "' + + 10°C ‘
>, _ A 20°.c .
o
r-o 5.0 _ A 4- ° ‘°.,° -
44 4- ‘7 50 C
a 4 5 - 3 A "
3 ° A + ._
0 E] A A +
:3 3.0 VI <9 ‘9 c]
‘7 <9 - C] c]
'5 25 v v V 3 ° ° 0 a
. "' v 0 o '1
2.0 "- ‘
1.5 I L I, I, l I ,L, I I I L, I I I, I J
4 5 B 7 a 9 10 11 12 13 14 15 1B 17 1a 19 20 21

Number of Carbons.

Figure 8. L vs. n for the n-alkanes at S temperatures.

58

 

Mole Fraction x 100

 

 

 

1-5 I I I I I I T I I I I I I I II
4.0- + -
+ +
+ AA
+ A A a
+ E! o
+ A El
3.0-+ AA an 0 v-
0
A alt! .0 v
‘ BB 00. V + 10°C
0° 7V A 20°;
0 777 u 30%:
2.0- v7 o 40°04
V 50°C
1.5 I LII I LglJl I III II
455789101112131415161718192021

Number of Carbons

Figure 9. x2 vs. n for the n-alkanes at 5 temperatures.

59

71

Makranczy _e_t_ ii. measured the Ostwald solubility of Xe in the

normal alkanes n'pentane through n-hexadecane. Their data are plotted,
along with our data for 20°C, in Figure 10. The mole fraction
solubilities are shown in Figure 11. It is interesting to note the

differing behavior of x as a function of n. The data of Makranczy_e_t

2

El- show a decrease in the mole fraction solubility with n.

72

Clever gt a_1_. measured the solubility of He, Ne, Ar, and Kr in

the normal alkanes n-hexane through n-decane, n-dodecane, and
n-tetradecane at several different temperatures. Their data show a

decrease in x2 with with increasing n for He and Ne, but Ar shows an

initial decrease in x2, followed by an increase for the longer chains.

The mole fraction solubility of Kr in the n-alkanes increases with

increasing n. This would lead you to believe that the mole fraction
solubility of Xe in the normal alkanes should increase with increasing
n.

In table 2 are values for Aug. calculated using equation (58),

09
2!

function of temperature, and as a function of n, are shown in Figures

and Au calculated using equation (61). The chemical potentials as a
12, 13, 111, and 15. A least squares fit of the A112 versus T data for
both Au; and Augp, yields straight lines (r 2 0.999) for each of the
alkanes. It is from the slope and intercept of these straight lines that
we obtain the entrepies and enthalpies of solution.

The entrOpy of solution, obtained via equation (59), is the
negative of the slope of the best fitting line, and the enthalpy is the

intercept on the ordinate axis. Values of the entropy and enthalpy are

listed in Table 3, and are plotted versus n in Figures 16 and 17.

60

 

 

 

 

I I I I I I I I I
+ This Work

5'5 " + A Mokronczy 0t. 01. ‘
>
:I': 5 o '- t q
H
or! 5 4-
n 4 — -
3 A -+
H

+
C3 .. .-
(D 4.0 A +
.9

E 3.5 - A + + -
ID 4' 4.
35 so A "'
m ' A .
C) At

2.5 P- 45 .4

A
20 I 4 I I I I I I I I 9 H,
4 5 6 7 8 9 10 11 12 13 14 15 1B 1

Number of Carbons

Figure 10. L vs. n for the n-alkanes; +, 20°C, our data;

A, 25°C, Makranczy 33 El‘

Mole Fraction x 100

61

 

4'00 T I I I I I I I I I I I
+ This work
3'75 - A Nakranczy at. 21. + A
+
3.50 — + q
4.
335r- + -
.p
+
3.00 +- + -I
+
2J5- A -t _
i! £8
24m _ +' 9* A ,3 A, A A
2.25 - .1
2.00 I I I L I I I I I I L I

 

 

 

4567891011121314151817
Number of Carbons

Figure 11. x vs. n for the n-alkanes; +, 20°C, our data;
A, 25°C, Makganczy _e_§ _a_1_.

62

TABLE 2. Chemical potentials in the mole fraction scale, Ap°, and in the
number density scale, Au°p. The first row is An; and the segond row is
Augp. Units are cal/mol.

 

 

Temperature 10°C 20°C 30°C 90°C 50°C
Number of
carbons in
n-alkanes
5 Au; - 1967:8.9 213618.?
Aug” - -10u5:8.u -991:8.7
6 1991 2109 225719.0 '
“999 “995 “91319.0
7 1926 2089 2296 2390:9.3 2596t9.6
“950 “898 “859 -82219.3 “78019.6
8 1913 2071 2218 2376 2529
“909 “858 “820 “779' “769
9 1899 2095 2195 ' 2397 2998
“871 “828 “788 “797 “703
10 1879 2027 2173 2327 2977
“836 “796 “758 “712 “670
11 1867 2012 2157 2307 2958
“805 “765 “728 “689 -690
12 1897 1991 2136 2283 2929
' -73u ~7uu -709 -662 -623
13 1830 1976 2120 2269 2911
“763 “720 “679 “691 “596
19 1811 1955 2096 2291 2383

“795 “709 “666 “623 “586

 

63

TABLE 2 (cont'd).

 

 

Temperature 10°C 20°C 30°C 90°C 50°C
Number of
carbons in
n-alkane
15 Au; .p 1939 2080 2223 2366
Aug - “685 “695 “609 “565
16 1926 2062 2209 2395
-667 “631 “587 “599
17 2098 2186 2325
“612 “573 “535
18 2027 2166 2306
“601 “563 “521
19 2199 2286
“550 “509
20 I 2139 2270
“539 -998

 

69

 

 

 

 

 

       

259° I I I I I
2500 I- “F 5 “
.A 0 .
A 2400 P a 13 "
H
O 0 17
E3 2300 r- .—
"\ 9
F.
g 2500 r- -
o m 2100 - " “
3.
q 2000 - ,1 “
1900 *- .—
I‘ I I L I
.00
1 0 1° 20' 30 4° 50 50
Temperature (°C)
2000 I I I I
4.
2500 '- A
D
.. 2400 - o
H
C:
E§"2300 “-
‘\.
'3 2a”
3 b
ON 2100 1-
3.
‘<3 2000 "
1'00 "
1500 ‘ l J

 

 

 

0 10 20 so 40 50 50
Temperature (°C)

Figure 12. 00° vs. T for the n-alkanes. The numbers next to the
symbols are tie number of C atoms in the alkane molecule

65

 

 

 

 

2800 I I I I I
amor- -+ 0 '
A 12 -,
2400 - D ‘° . '4
:3 0 20 r
2 a... '
\ o
'3
£3 zm0- ‘ ‘
o
o 01 2100 r- '
é a
2000 r- '
1000 - n '
1000 ~ ‘ l l L J
0 10 20 30 40 so 00

Temperature (°C)

 

I I I

An: (cal/mol)

 

 

l
0 10 20‘30 ‘0 5° 3°

Temperature (°C)

 

 

Figure 12. (cont'd.).

66

 

 

 

 

 

In" I I I I I
Z:
O
E
\
H
I!
3
8a
3.
d
-1000 - +
+ -
l l l, l I
- o .

Temperature (°C)

 

A1129 ° (cal/mol)

 

 

l l l 1, l

 

 

'1100

0 10 20 :0 40 50
Temperature (°C)

Figure 13. Au°p vs. T for the n-alkanes. The numbers next to the
symbols are t a number of C atoms in the alkane molecule

67

 

A1129 (cal/Illa 1)

 

-1100

Apt?” “(cal/mull

-1000

'1100

Figure 13.

I

 

 

_l l l ' l

 

20' 30 40 so 00

Temperature (°C),

 

 

I I I I

 

I J I I

 

 

10

(cont'd.).

20 30 40' so
Temperature (°C)

68

 

2400

2100

Aug (cal/mall

1900

 

lllJJll
4 5 B 7 B 9101112131415181‘718192021

 

 

1800

 

Number of Carbons

Figure 1”. Au; vs. n for the n-alkanes at 5 temperatures

69

 

 

 

 

"00 I I‘ I I I I I I l' I I I* I I I I
-500 '- V v V d
V 0
f... -800 "' v V 0 a a -
‘5. V 0 ° D B A A
H -700 r- V 0 a a A A .1
u 3 A +
v V D A +
'300 F- + -I
‘0» C1 45 -F
<> 40°C
' -1000 - A + V mac 4
4.
_1‘00 I .L I II I II Iiil I I I I I L I I
4 5 B 7 B 9 10 11 12 13 14 15 1B 17 1B 19 20 21

Number of Carbons

09

Figure 15. A02

vs. n for the n-alkanes at S temperatures

70

TABLE 3. Entropy and enthalpy o{3§olution in both the mole fraction scale and in the number
density scale for solutions or Xe in the normal alkanes.

 

Hole Fraction Scale Number Density Scale
Enthalpy of Entropy of Enthalpy or Entropy of Temperature
Number or Solution Solution Solution Solution Range of

Carbons AH; (cal/mol) ASS (cal/moi K) Aflgp (cal/mol) As;-p (cal/moi K) Experiments

 

5 “2818 t 200 “16.90 t 0.69 “257“ t 200 “5.90 t 0.69 10 “ 20°C
6 “2691 t 132 “16.37 t 0.U5 “2230 t 132 “H.35 t 0.US 10 “ 30°C
7 “2H15 t 61 “15.36 t 0.20 “2120 t 61 ~u.1u t 0.20 10 “ 50°C
8 “2929 t 77 “15.3“ t 0.26 “2120 t 77 “4.29 t 0.26 10 “ 50°C
9 “2378 t “5 “15.09 t 0.15 “2050 t “5 “H.16 t 0.15 10 “ 50°C
10 “2351 t 51 “13.93 t 0.17 “2010 t 51 -u.16 t 0.17 10 “ 50°C
11 “2308 t 55 -1u.7u t 0.18 “1970 t 55 “H.11 1 0.18 10 “ 50°C
12 “2278 t 2H “1u.56 t 0.08 “1930 t 2H “H.0“ t 0.08 10 “ 50°C
13 “2278 t 32 “1H.51 t 0.11 “1930 t 32 “9.13 t 0.11 10 “ 50°C
1" “2239 t 23 “1“.30 t 0.08 “1860 t 23 “3.93 t 0.08 10 “ 50°C
15 “2233 t 30 “19.23 t 0.10 “1860 t 30 —u.01 t 0.10 20 “ 50°C
16 “2180 2 b0 “19.00 t 0.13 “1830 1 “0 “3.97 t 0.13 20 “ 50°C
17 “215“ 1 102 “13.68 t 0.33 “1770 t 102 “3.8“ t 0.33 30 “ 50°C
18 “2191 t 38 “13.91 t 0.12 “1810 t 38 “3.99 t 0.12 30 “ 50°C
19 “2152 t 97 “13.73 t 0.31 “1820 t 97 “0.07 t 0.31 N0 “ 50°C
20 “2117 3 23 “13.58 t 0.08 “1690 t 2“ “3.68 t 0.08 “0 “ 50°C

 

71

 

 

 

 

0 I I I I I T I I I I I I I I I I

-2 — -
.. -« - A A A A AAA A A A A A A A A A.-
X

-5 .. £5 .—
H o
\
'3 -10 - A A529 --4
u
v -12 ’- .1
> '1‘ "' + + + + +
a- + + + '1' '1' '1
° + + + +
t; +
m '16 _ —d

-20 L I I 14 I I I I I L J I I L I

4 5 B 7 B 9 10 11 12 13 14 15 18 17 1B 19 20 21

Number of Carbons

Figure 16. Entropy of solution for Xe in the n-alkanes

Enthalpy (cal/moi)

“1500
“1700
“1800
“1900
“2000
“2100
“2200
“2300
“2400
-2500
“2300
“2700
-2800
“2900
-3000

72

 

 

.+ AH?

A AH"?D

+

I l l l. L IA 1. l I II L

 

 

*—
4

l l l l
5 B 7 B 910111213141515171819

Number of Carbons

Figure 17. Enthalpy of solution for Xe in the n-alkanes

73

From Figure 16, we see that both As; and 1339 are negative, and
increase slowly with n for n S 8. We can interpret this in several
different ways. One explanation is that the Xe has more freedom of
movement, or is less constrained in solution, for larger n. A second
interpretation is that the Xe has a greater disordering effect on the
liquid molecules for large n. The actual situation is probably a
combination of these two.

Clever73 has calculated the entropy of solution of Xe in
n-hexane, n-dodecane, and isooctane. He obtained values of “15.92,
-15.511, and -15.51 cal/(mol K), respectively. The agreement with our

results is good. Clever gt 11,72

calculated the entropy of solution for
He, Ne, Ar, and Kr in the normal alkanes n-hexane through n-decane,
n-dodecane, and n-tetradecane. All exhibit nearly constant As; (He,
“10.“ 1 0.7; Ne, “10.8 1 0.“; Ar, “13.0 i 0.0; and Kr, -13.7 i 0.2
all in dimensions of cal/mol K). For Xe in the same seven solvents, we
determined ASE - “15.13 :I: 0.25 cal/mol K. This is about the value we
would expect if we view the inert gases as a homologous series.

g and AHEp, are negative

and generally increase with increasing n. This is the proper qualitative

Like the entropies, the enthalpies, AH

effect we would expect according to the cavity formation model of

29 30

[Htlig and Eleyu Assuming the Xe/alkane interaction is nearly

constant as a function of n, we would expect this increase in AH, since
the surface tension of the alkanes increases with chain lenght, and it
is more difficult to create a cavity in a liquid of higher surface
tension.

73

calculated AHg for Xe in n-hexane, n-dodecane, and

isooctane. His values are -2582, “2273, and ~2089 cal/moi, respectively.

Clever

711

Our values for these same quantities are -2691 :1: 132 for n-hexane and
“2278 :1: 211 for n-dodecane, taken from Table 3. Our value for n-octane,
“21129 :I: 77, also compares favorably with his value for isooctane. The
agreement with our data is good.

Figure 18 is a plot of the three quantities in equation (6H) for
the alkanes n-pentane through n-hexadecane. The binding energy shown has
been calculated from the enthalpy, AHE,

uwrgY1NA. As expected, the binding energies are nearly constant, varying

by a few percent from the mean of ”500 cal/mol. The gradual increase in

and the surface energy,

Eb with n is consistent with the stronger interactions between Xe and

alkane at large n.

A plot similar to Figure 18 can also be made for A1151). However,

the difference in enthalpies, AH°p - AH° is nearly constant, about 350

2 2'

cal/mol, and the behavior of E will be much the same.

b
Table u lists values of E calculated from equation (6“), and the

b
binding energy estimated as the geometric mean of the heats of
vaporization of Xe and the alkanes at their normal boiling points.
Agreement is good, within 20%, for all of the alkanes shown. The
estimated binding energy also shows an increase with increasing n, much

as the values obtained from experiment. However, the estimated values

increase at a greater rate.

75

 

5°°°IIIII

 

 

 

I I I I I I I
El E1
4500 +— 0 E, :1 13 El '3 a q
E! D [g

:2 4000 - ' + - Enth5lpy -1
g A Surf5c5 En5rpy
\ 3500 .. D Binding En5rgy _
H
(D
3 3000 - -
> + +

2500 - A q
co 4- + A
‘- + + A 4* 4‘ 7 +
00 A A +
C 2000 - A -4
LIJ A

£5
1500 - A _
1000 I I I I I I I I I I I I
4 5 6 7 B 9 10 11 12 13 14 15 18 17

Number of Carbons

Figure 18. Binding energy, surface energy, and enthalpy of
solution for the n-alkanes. (Figure 5 of reference 68).

76

TABLE u. Comparison of experimental binding energies, Eexp, of Xe in

the normal alkanes with binding energies gggimated from the heats of
vaporization of the solute and solvent, Eb .

 

 

Number of EexP Best
b b

Carbons per

n-alkane (cal/moi) (cal/moi)
5 u261 1071
6 0306 H307
7 0226 M510
8 0373 A701
9 MN33 R860
10 uu9u 5026
11 u526 5167
12 “558 5299
13 “615 5u1u
1A 0628 5539
15 M668 5636

16 N651 1 5751

 

77

”.2 ALKANOLS

 

We also measured the Ostwald solubility of 133Xe in the normal
alkanols at five temperatures in the range from 10°C to 50°C. The values

we obtained for L and x are listed in Table 5.

2
Figures 19 and 20 are plots of L versus T and x2 versus T. As
with the alkanes, both L and x2 decrease with increasing temperature.
7H

Komarenko and Manzhelii measured the solubility of Xe in
n“propanol in the temperature range from “80°C to -30°C. They found that
the mole fraction solubility decreased with increasing temperature, not
only for Xe in n-prOpanol, but also for a variety of gas/alcohol

systems. Solute gases were spherically symmetric (Ar, Kr, Xe, CH , and

u
CF”) and solvents included methanol, ethanol, n-prOpanol, and n-butanol.

The behavior of L and x2 as a function of. n is more complicated
for the alkanols than for the alkanes. Figure 21 shows L versus n at
five different temperatures. The sharp initial increase, followed by the
slow decrease, is probably due to the change from the highly polar
environment of methanol to one which is becoming more alkane-like for
large n.

Figure 22 shows x versus n at five temperatures for Xe
solubility in the normal alkanols. As with the alkanes, the number of
dissolved Xe atoms per alkanol molecule increases with increasing n. The

mole fraction solubility also has its greatest rate of change at small

n, when the liquid environment is presumably changing most rapidly.

78

TABLE 5. Ostwald solubility L and mole fraction solubility x2 for ‘3’Xe
in the normal alkanols. The first row for each alkanol is L, and the
second row is 102x2.

 

 

Temperature 10°C 20°C 30°C “0°C 50°C
Number of
carbons in
n-alkanol
1 L 2.“6 2.20:0.01 1.98:0.02 1.79
x 0.“23 0.370 0.325 0.288
2 2.79:0.00 2.“?20.02 2.22:0.00 2.02:0.02 1.8510.01
3 3.0210.01 2.6510.05 2.38:0.06 2.16 1.9810.01
“ 3.0“ 2.6810.01 2.“0 2.17 1.98
1.17 1.01 0.88“ 0.782 0.699
5 2.97 2.6210.00 2.36 2.1310.00 1.95
1.35 1.17 1.02 0.903 0.809
6 2.97 2.61:0.02 2.3“ .12 1.92
1.55 1.33 1.17 1.0“ 0.920
7 2.91 2.5710.01 2.31 .09 1.91
1.73 1.“9 1.31 1 16 1.03
8 2.86 2.52:0.03 2.2510.02 2.05 1.88
1.89 1.62 1.“2 1.26 1.13
9 2.79 2.“9t0.00 2.2“
2.0“ 1.77 1.55

 

TABLE 5 (cont'd.).

79

 

 

Temperature 10°C 20°C 30°C “0°C 50°C
Number of
carbons in
n-alkanol
10 L 2.7“ 2.“3¢0.02 2.20 2.00 1.83
x2 2.19 1.89 1.67 1.“9 1.33
11 2.3“10.01 2.1110.01 1.92 1.76
1.98 1.7“ 1.55 1.39
12 2.12:0.02 1.9“:0.01 1.78
1.89 1.68 1.51
1“ 1.91:0.01 1.76:0.01

1.91

1.72

 

80

 

 

 

 

 

 

 

 

- A + 1
> 5.00 a A s
4-1 U 7
:2 edsh- ° <0 5
"1 A V 11
g B
'3 2.50 - + o
(D V 3
73°. 2 00 v a '
o P A
1.: "' v a
C1 +
1.75 r- 17
1.50 l l J l I
0 1o .20 so 40 . s0
Temperature 1°01
3°25 r I I f - I
+ 2
, 2.00 p 3 A 4
. j: I: 5
«u 4- <> 12
,., 2.7s -
dd 45
a £3
£3 2.50 " 4.
8 8
2.25 '- 4.
u
w. o 8
‘3' 2 00 r- '1'
1; ' ° 9
o 1.7s - °
.so ' ' . 1 ‘ '
1 0 10 20 so 40 so

Temperature (°C)

Figure 19. L vs. T for the normal alkanols. The numbers next to
the symbols are the number of C atoms in the alkanol molecule.

81

 

 

 

 

+ 5
3.00 r- T
,. + 1A 5
t: A D 10
..., 2.7s - 13 ° ‘1 ‘
4-0
a X
H 2.so - a “
O +
a)
u 2.2s 1- e '1
.3 +-
3 2.00 L 6 "‘
+a - o +
m o
o
1.7s - ° "
1.1s0 L ' L ' L
0 10 20 so 40 so 00

Temperature (°C)

Figure 19. (cont'd.).

82

 

 

 

 

 

 

 

 

+ 1
V .A 2
a 1.28 - . D 5 ‘
g V o 4
V 3
x 14m - ° 7 “
a.
C: 49 17
.3 can a o» v
‘6 ' A '3 °
0! ‘ ‘5 E)
L A '3
u. 0.50 - A . 7
CI 4- 4. A“
r4 4L .*
g 0.. - -
0.00 I I. I l I
0 1o 20 so 40 so 50
Temperature (°C1
. + 5
CI 0
"' '3 o 5
S + a o
4-0
. (J
m E!
I. + A
“- 1.8 - El ..
+ A
.2 + 9
E 1.00 - A “
4.
‘,:73 l l I I ' I
0 1o 20 so 40 so 50

Temperature (°C)

Figure 20. x vs. T for the normal alkanols. The numbers next to
the symbols gre the number of C atoms in the alkanol molecule.

-M01e Fraction x 100

1.75

1.50

1.25

1.00

83

 

 

 

 

Temperature (°C)

Figure 20. (cont'd.).

l T I F I
+ T
A d
+ 3 °
A -I
+ B o
-+ 10
A to 2 t:
c. .. . W
0 14 +
I I I I l
10 20 30 40 so so

8h

 

 

 

3°50 I I I I I I I I I I I I I I
+ 10°C
3.2: h- A 20°C -+
5. + D 30°C
. 3.00 - + o 40°C _
.3 + + + V so°c
..., +
.g 2.75 - + A 4' + ..
3 2.30 - + A a _ A A A ..
'0 ° ° 0 o m
3 o o o <-> B
CD 4> ‘V’ ‘7
1.75 - V V v ..
1.50 I, I _I I I I I I .I j, I I

 

I I
o 123400700104112431415
Number of Carbons

Figure 21. L vs. n for the n-alkanols at 5 temperatures.

Mole Fraction x 100

85

 

 

 

 

235 I I I I I I r I I I U l I
a00+~ +' A -
+ .A c1 0
1.75 - A ..
+ A E! B 0 7
14m - ‘* A ‘3 o G’Iv .
. -P A; [3* , ‘7 V?
ijflr- '3 o -
+ A El 9 V
1.00 r + A I3 ‘9 V +' 10°C A
A B e V A 20:0
__ <9 ‘7 E] 30 C
°°75 4. El v o 40°C V
A $ v 50%
04m- 8 _
0.25 J I I I I‘ I L I I L I L L I
0 I 2 a 4 a a 7 a 9 i0 11 12131415

Figure 22. x

2

Number of Carbons

vs. n for the n-alkanols at 5 temperatures.

86

7h

Komarenko and Manzhelii observed similar behavior for solutions

of Kr in methanol, ethanol, n-propanol, and n-butanol at a variety of
temperatures.

Table 6 also contains Aug and A1459 for the Xe/alkanol systems.

°p respectively, as a function of T.

2 9

Figures 25 and 26 show the same chemical potentials as a function of n.

Figures 23 and 2” show Au; and Au

As with the alkanes, least squares fits to the Au versus T data
yield straight lines with slope -AS and intercept AH. Entrepies and
enthalpies of solution are listed in Table 7 (Table 2 of reference 69),
and are plotted versus n in Figures 27 and 28.

We see the same type of transitional behavior in the Au versus n
graphs as we saw in the solubility versus n graphs (Figures 21 and 22).
It would be interesting to extend these measurements to higher
temperatures and larger n to see if the Xe/alkanol systems become more
like the Xe/alkane systems.

133

Entropy of solution for Xe in the alkanols is very close to

that of Xe in the alkanes. The behavior of both As; and ASE,p as

functions of n are the same as for the alkanes, and are about 10% larger
in magnitude. We conclude that the Xe is either more constrained, or has
less of a solvent disordering effect (or more of a solvent ordering
effect), in the alkanols than in the alkanes.

7” a value of

75

We obtain from the data of Komarenko and Manzhelii,

AS° - 49.114 cal/mol K for Xe in n-propanol at -55°C. Abraham lists

2
the entropy of solution for Ar, Kr, and Rn in methanol (-16.0, -17.lI,
and -22.14 cal/mol K) and Ar and Rn in ethanol (-15.1 and -18.1
cal/mol K) at 25°C. These compare favorably with our values for Xe in

methanol and ethanol (-18.82 and -17.87 cal/mol K, respectively).

87

TABLE 6. Chemical potentials in the mole fraction scale, Au°, and in the

number density scale, Au°p. The first row is Au° and the se and row is
09 2 2

Au2 . Units are cal/mol.

 

Temperature 10°C 20°C 30°C 10°C 50°C

 

Number of
carbons in
n-alkanol

1 3076 1 8 3263 i 9 3152 1 9 3610 t 9

Au -
50;" - '507.1¢8.1 -160.138.7 -111.5:9.o -362.319.3

2 2800 2983 3163 3311 3515110
~577.9 -527.9 -181.5 ~136.0 -395.1:9.6
3 2619 2800 2975 3116 3316
-621.3 ~567.7 -521.3 -178.9 ~137.1
1 2501 2677 2819 3019 3187
-625.8 -571.7 ‘ -527.1 -182.16 -139.0
5 2121 2591 2760 2929 3093
-613.3 -561.3 -516.5 -169.7 -127.2
6 2313 2515 2680 2811 3011
-611.9 -559.1 -512.7 -167.0 -119.6
7 2281 2152 2611 2776 2936
-601.6 -591.1 ~503.3 -157.5 -113.5
8 2231 2101 2563 2721 2877
-590.7 -537.3 -189.6 -115.8 -1o1.1
9 2191 2351 2509

-577.5 “530.5 -181.5

 

TABLE 6 (cont'd.).

88

 

 

Temperature 10°C 20°C 30°C 10°C 50°C
Number of
carbons in
n-alkanol
10 Au° p - 2151 2311 2161 2618 2773
in; - -567.8 -518.1 -175.5 -132.0 -388.1
11 2286 2111 2593 2716
-196.2 -119.8 -106.3 ’363.8
12 2392 2512 2691
-153.5 -110.8 -369.6
11 2165 2609
-101.0 -361.8

 

89

 

Aug (cal/mol)

 

 

 

 

2200 I I I 3L1 I
0 10 20 30 40 50

Temperature (°C)

 

320° I I I I I

3000 -

2000 -
l

2400 -

Aug '(caI/mol)

 

 

 

 

200° 3 I J L I I
0 10 20 30 40 50

Temperature (°C)

Figure 23. Au° vs. T for the n-alkanols. The numbers next to

the symbols age the number of C atoms in the alkanol molecule.

2400

Aug (cal/mol)

Figure 23.

 

 

 

r I I I I
+ 10
p A 11
1:1 :2
o u /,,
///////i I I I I
10 20 30 40 50
Temperature (°C)
(cont'd.).

 

A029 (cal/moi)

Apgp .(callmolI

Figure 21. Au
the symbols a

é

ééééé

2 6

’2

2

I

91

 

 

 

I I I I,
10 20 30 40 50 00

Temperature (98)

 

 

I I I I

 

I I I I I
to 20 so 40 so 00

Temperature (°C)

‘9 vs. T for the n-alkanols. The numbers next to
go the number of C atoms in the alkanol molecule.

 

 

92

 

 

 

 

‘350 I F I I
..400 .-
:3
3 «so P
"\
I".
8 -um b
8‘.»
:1, -550 -
<
4mo-
450 J I I I
0 10 20 30 40

Figure 21. (cont'd.).

Temperature (°C)

 

93

 

3700

 

 

5 I I I I I 1 1 l I I l l l
3500 - D V 'I' 10°C -1
A 20°.c
.. ° 7 [:1 30°C q
:3 3300 A o 40%
O E] 0 V V 50°C
H A B 0 V
d! 2900 L. <> ‘7 ‘7 ‘_
3 + A 13 o
m 0 v v
i + A .B a 0 e V
G 2500 h- + A 13 ° ..
2300 r- + + A A A ..
+ «1-
2100 I I I I I I I ‘I' I I I I

 

ll
0123453709101112131415
Number of Carbons

Figure 25. Au; vs. n for the n-alkanols at 5 temperatures.

91

 

 

 

’3“ I I I I r I I I l fi I I I I
-sso - -
<> ‘7 my ‘7
'000 '- v v -1
::: C1 ‘7 ‘7 " <> 4) <>
0 <-> v v V 0
E5 1-450 '- <> C] E] -1
\ A o o e
E!
'3 soo 1:1 0 o ' E' A
u - - + 13 E] q
A. A E] 13 B A A A
-550 - A -
:L + 4. +. + 10%
_,_ + + , a.
+ Cl 30 c
'550 '- 0 40°C .—
‘7 50°C
_700 L 4 L L L I L I I L I L

 

I L
0123456789101112131415
Number of Carbons

°p vs. n for the n-alkanols at 5 temperatures.

Figure 26. A02

95

TABLE 7. Entropy and enthalpy 0(33olution in both the mole fraction scale and in the number
Xe in the normal alkanols. (Table 2 of reference 69)

density scale for solutions of

 

Mole Fraction Scale

Number Density Scale

 

Enthalpy of Entropy of Enthalpy or Entropy of Temperature

Number of Solution Solution Solution Solution Range of

Carbons Aflg (cal/mol) As; (cal/mol K) AHEp (cal/mol) ASEp (cal/mol K) Experiments
1 -2250 1 120 -18.82 1 o.uo -1880 1 120 -u.8u 1 0.h0 10 “0°C
2 -2257 1 88 -17.87 1 0.29 -1869 1 88 -u.57 1 0.29 10 50°C
3 ~2300 1 88 -17.39 1 0.29 -1910 1 88 ~u.57 1 0.29 10 50°C
3 -23u5 1 88 -17.13 1 0.29 -19u3 1 88 -u.66 1 0.29 10 50°C
5 -2331 1 88 -16.79 1 0.29 ~192u 1 88 -u.6u 1 0.29 10 50°C
6 -236H 1 88 -16.6u 1 0.29 ~19S9 1 88 -u.77 1 0.29 10 50°C
7 -2317 1 88 -16.26 1 0.29 -1922 1 88 -u.67 1 0.29 10 50°C
8 ~23ou 1 88 -16.05 1 0.29 -1900 1 88 -u.6u 1 0.29 10 50°C
9 -2310 1 180 -15.90 1 0.62 -1890 1 180 ~M.65 1 0.62 10 30°C
10 -223u 1 88 ~15.50 1 0.29 -1826 1 88 -u.u5 1 0.29 10 50°C
11 -2210 1 130 -1S.3S 1 0.u1 -1790 1 130 -u.u1 1 o.u1 20 50°C
12 -21h0 1 210 -1u.96 1 0.66 ~1720 1 210 -u.2o 1 0.66 30 SO’C
In -2ouo 1 “30 -1u.uo 1 1.30 ~1630 1 R30 -3.90 1 1.30 no 50°C

 

96

 

 

 

 

° IIIIIIIIIIIIII
—2I— u-I
A - _ - Ad
3“ AAAAAAAAAAAA
9..
c, .3 .. .—
5 .4
H "P + AS?
3-“... -
v A AsgP
>-sa- -
'3
c: -18 P- 4. '+- 'F 4- ‘-
UJ .5 4' 4'
4.
-1e- 4- -
+ .
_20 I Ll LI L I Ll LL!

l l
0123455739101112131415
Number of Carbons

Figure 27. Entropy of solution for Xe in the n-alkanols.

97

 

 

 

 

"500 I I I I r I I I I I I I I A
o
A o
E
‘\. AL Al £5
r4 -1900 r- 45 AL -4
(D A A A
3 A
-2000 - _
3., -F
2' -ano - -
IO '4-
I:
té-amop- 4. ~
In '* + +
'-amo + + -
T" + + + +-
4400 L L L I L T I I L L I I I I
O 1 2 3 4 ‘5 B 7 B 9 10 11 .12 13 14 15

Number of Carbons

Figure 28. Enthalpy of solution for Xe in the n-alkanols.

98

The transitional behavior of the chemical potential as a function
of n is thus due to the enthalpic contribution of the solvation process.
This contribution is shown in figure 28. The initial decrease, followed
by the increase, of enthalpy versus n contrasts with the Xe/alkane
systems, where AH is an increasing function of n.

Our value of AH; - ~2250 cal/mol for Xe in methanol is

75

intermediate in value to the data listed by Abraham of -1170 and -3820

cal/mol for Kr and Rn in methanol, respectively. The data of Komarenko

and Manzhelii7u

yield AH; - ~2758 cal/mol for the system Xe/n-propanol
at -55°C. Our value is -2300 cal/mol for the same system at 25°C.

The chemical potential in the mole fraction scale is dominated by
the entropic contribution for the alkanols, Just as for the alkanes.
Here, TASE is about twice AHé. The number density scale yields the
opposite conclusion, namely that the solution process is enthalpically
dominated.

Figure 29 is a plot of the three quantities in equation (6“) for
the alkanols methanol through n-dodecanol. The binding energy Eb was

calculated from AHS and unrgY1NA through rearrangement of equation (6“).

The average binding energy of the Xe/alkanol systems is about 31 higher
than that of the Xe/alkane systems, and is due to the greater surface

energy contribution. Table 8 lists both our experimental E and Eb

b’
estimated from heat of vaporization data, for the normal alkanols. As
with the alkanes, estimated values agree to within 201(fi’the
experimental values. Here, too, the estimated values increase with n at
a greater rate than the experimental values.

75

Abraham has compiled values of the standard free energy,

enthalpy, and entropy of solution for many gaseous nonpolar

99

 

 

 

 

550° I I I I I I I I I I I l
5000 i- B E '4
E3
.. a £3 E] B
F1 4500 *- C] .a
g '3' '3 + em 1
‘ . DY
E 4000 P A Surface Energy
‘0 El Binding Energy
13 mmo- 1
>
E, 3000 '- -‘
a) ‘5’ £5 ‘5
lu + .1 4- t :1 " 4- +
A '+ +
2000 - A A ..
1500 L I I I I I I I I I I L
0 1 2 3 4 5 5 7 8 9 10 11 12 13

Number of Carbons

Figure 29. Binding energy, surface energy, and enthalpy of
solution for the n-alkanols. (Figure A of reference 69).

100

TABLE 8. Comparison of experimental binding energies, Eexp’ of Xe in
the normal alkanols with binding energieseggtimated from the heats of
vaporization of the solute and solvent, E

 

 

b .
exp est
Number Eb Eb
of
Carbons (cal/mol) (cal/mol)
1 AZ?” ”708
2 “271 “990
3 nu32 5182
h R628 5266
5 R650 5358
6 ”721 5579
7 5562
8 "777 5H89
9 14853 5911!
10. “831 5658

 

101

nonelectrolytes in a variety of nonaqueous solvents and in water. He

found that the data could be correlated using an equation of the form:

AP; . £8 + d (86)

where P stands for the free energy G, enthalpy H, or entropy S. R is a
parameter, close to the solute's radius in A, characteristic of the
solute gas, and i and d characterize the solvent.

Table 9 lists the values of AGE, Aha, and A83 at 25°C, calculated
from Abraham's parameters for the solvents shown, using a value of 2.16
for R for Xe. The agreement with our experimental values is good.
Calculated free energies of solution are about 10% too high for all
solvents. The calculated enthalpies of solution are all within 101 of
experiment, except for 1-decanol, which is 180% too small in magnitude.
The agreement between calculated and experimental entropies is
excellent, within 5% for both the alkanes and alkanols.

We can calculate the thermodynamics of solution from Pierotti's

33

model. From equation (33) above:

Gc Gi RT
ln(KH) - ET + ifi" + ln(Vf) , (87)

where

102

TABLE 9. Comparison of calculated and experimental thermodynamics of

 

 

 

 

solution.
calculated Experimental

0 0 0 O 0 0

A02 AH2 A82 AG AH2 A82

cal cal cal cal cal cal
SW9“ (EST) (5:31") (mmol x) (as: (as: (“—1.01 x)
hexadecane 2200 -2210 -1fl.7 199“ -2180 -1H.00
decane 2210 -21uo ~1H.5 2100 -2351 -1h.93
hexane 2230 -2330 “13.7 2183 -2691 -16.37
1-decanol 2710 -1580 -15.5 2398 -223fl -15.50
1-octanol 2720 ~2090 -16.8 2M82 -230M -16.05
1-butanol 2930 '2590 '17.9 2763 -2395 '17.13
1-propanol 3070 -2170 -17.7 2883 -2300 -17.39
ethanol 3220 ‘2180 “18.1 3073 '2257 -17.87
methanol 3500 '2120 ‘18.8 3358 '2250 '18.82

 

c 12 2 _ 12
‘fif ' 6(1_y)[2(;:‘) (FT-)]
2 1‘122 r'12 1
+ 1817¥§) [(FT—J ‘ (r1 ) + 3] ‘ ln(1-y) (88)
and
0 e
i _ 12 3

fi- 3.5551Ip(--—kT )r12 . (89)

If we compare equations (25) and (87), we see that

-1nL-—‘=‘+—. (90)

We have for the free energy of solution in the mole fraction scale

RT '
2 - -RTln[(E-v-5-§— *1)1] . (91)

Au; - -RT1nx
1 2

The entropy of solution is given by equation (59).

o.j_ 0
AS 8T(A"2) . (59)

2 P,n

r and e are independent of

It is easy to show, assuming that r 12, 12

1!

temperature, that

1ou

G

- 1 - - l._$
As; - Rlnx2 + RT(x2 1)1T up (up + TJRT

“P Go
' T=§Lfif + ln(1-y) ' Y
i" l"
.1. 2 .13 2 - .12 1
+181,.,) [(,1 ) (,1 1+ ,1) . <92)

where up is the thermal expansivity of the solvent, and

Aug . -RT1nx2 + TAS§ . (93)

35 and

Using the Lennard-Jones parameters of Wilhelm and Battino,
equations (92) and (93) , we can calculate the entropy and enthalpy of
solution for some of the alkanes and alkanols. These calculated values
are listed in Table 10, along with our experimental values for the same
solvents. The agreement with experimental values is very good (1101),
except for AH; for tetradecane (1251). Agreement is not as good for the
two alkanols. Calculated entropies and enthalpies differ from
experimental results by 20% and 50%, respectively.

The deviation of the theoretical values from the experimental
results occur in the regions we might expect. For the alkanes, the
largest deviations occur for the longer molecules. The free energy of
cavity formation, 0c, is calculated assuming the solvent molecules are
hard spheres. Since the normal alkanes are decidedly non-spherical, such
deviations are to be expected.

Methanol and ethanol also show large differences between

calculated and experimental values. We believe the source of these

105

TABLE 10. Comparison of calculated and experimental values for the enthalpy and
entropy of solution for mixtures of Xe in some of the alkanes and alkanols. Values
were calculated using Pierotti's model, and the Lennard-Jones parameters of Wilhelm
and Battino.

 

Calculated Values _ Experimental [glues
Enthalpy of Entropy of Enthalpy of Entropy of
Solvent Solution Solution Solution Solution
AH; (cal/mol) ASE (cal/mol K) AH; (cal/mol) A85 (cal/mol K)

 

 

Hexane -2517 -16.57 -2691 “16.37
Heptane —2u95 -16.38 -2A15 -15.36
Octane -2932 “16.22 ~2fl29 “15.3“
Nonane -2337 -15.97 -2378 -15.09
Decane -196u -15.60 -2351 -1u.93
Dodecane -2056 -15.61 ~2278 -1u.56
Tetradecane -1738 ~1H.90 -2239 ~1h.30
Methanol -3195 -22.76 -2250 -18.82
Ethanol -3158 -21.60 -2257 ~17.87

 

106

differences is also the free energy of cavity formation term. The
difficulty in this instance, however, is probably the strong
dipole/dipole interactions of the alkanols. Because of these
interactions, they are not "hard" spheres.

There are several possible directions in which this work might be
extended. First, further studies should be done on Xe solubility in the
normal alkanes and alkanols at higher temperatures, and with longer
molecules. The goal here would be to see if the thermodynamics of the
Xe/alkanol systems becomes more alkane-like for large n. It might also
be interesting to study the solubility of Xe in solvents consisting of a
normal alkane "doped" with one of the alkanols.

A second course of research would be to extend these studies to
the solubility of Xe in other homologous series of nonpolar solvents,
specifically the halogenated normal alkanes such as the perfluoroalkanes
and.perchloroalkanes. These liquids have stronger intermolecular
interactions than the alkanes, as evidenced by increased melting and
boiling points. However, these higher boiling points would permit
solubility measurements to be made with the shorter, more spherical
molecules.

A third direction for further research is to modify the hard
sphere theory. Modifications would include the addition of an attractive
potential to the hard sphere equation of state, similar to thatcn’

Longuet-Higgins and Widom.38

This would take account of strong
interactions between solvent molecules. A second possible modification
of the theory might take into account the non-spherical shape of a

solvent molecule.

107

L3 AQUEOUS AMINO ACID SOLUTIONS

‘We measured the Ostwald solubility of 133Xe in aqueous solutions
of NaCl, sucrose, and 20 amino acids at 25°C. Some of these results have

70 Values of L obtained are listed in Table 11.

recently been published.
Also included in this table are the solution molarity (M), the solution
pH, the total volume fraction of the solution that is water (vtw)’ and
the hydration number H as calculated from equation (66). Our values for
the mean hydration number for each amino acid are listed in the column
at the left of Table 12.

Our method for calculating v w has been described in section 1.7

1:

above. The values of Vt" can also be calculated from the solution
molarity M, and the partial molar volume vpm of the amino acids, via the

equation:

vtw - 1 - Mvpm/1000 . (87)

Using equation (87), and partial molar volumes of the amino acids at

25°C given by Lilley,76

we can calculate the volume fraction water.
Agreement with values obtained using our method is good.

For several of the amino acids, we were not able to obtain good
values for the hydration numbers. These include isoleucine, leucine,
phenylalanine, tyrosine, and tryptophan. The ILE data seem to fall into
two different groups, with mean values of 13.3 and 5.8. We were unable

to obtain a consistent value for this amino acid, since its solubility

in water is too low.

108

TABLE 11. List of solubilities measured for Xe in aqueous solutions of the amino
acids, sucrose, and NaCl. Also included are the solution molarities (M), the
solution pH, the volume fraction water, and the hydration number calculated for
each experiment.

 

 

Volume
Ostwald Solution Solution Fraction Hydration
Amino Solubility Molarity pH Water Number
Acid L M v H
tw
Alanine 0.09h 0.N50 6.2 0.973 10.60
(Ala) 0.090 0.661 6.55 0.973 9.21
0.088 0.873 6.35 0.9fl6 7.3“
m.w. 89.09 0.088 0.900 6.1 0.9“” 7.00
0.076 1.350 6.27 0.917 8.20
0.079 1.500 6.00 0.908 6.00
0.070 1.800 7.03 0.889 7.03
Arginine 0.100 0.N38 10.6 0.9u5 0.20
(Arg) 0.100 o.u39 11.3 0.995 0.20
0.093 0.919 10.8 0.88“ 0.fl0
m.w. 17N.20 0.09“ 0.920 11.h 0.88“ -0.17
0.103 0.300 10.6 0.963 -1.60
0.095 0.600 11.1 0.925 2.65
0.098 0.760 11.0 0.905 -1.u2
o.o9u 0.760 11.0 0.905 1.33
Glycine 0.082 1.0u3 6.35 0.953 9.52
(Gly) 0.092 0.500 6.50 0.978 12.18
0.085 1.066 6.0 0.953 7.85
m.w. 75.07 0.089 1.071 6.96 0.952 8.2“
0.075 1.500 6.2 0.93“ 8.36
0.065 2.130 6.96 0.903 7.53
0.068 2.131 5.8 0.9ou 6.82
0.06u 2.132 6.uu 0.903 7.77

 

109

TABLE 11 (cont'd.).

 

 

Volume
Ostwald Solution Solution Fraction Hydration
Amino Solubility Molarity pH Water Number
Acid L M v H
tw
Hydroxyproline 0.09“ 0.5u8 6.0 0.953 6.69
(Hyp) 0.097 0.5u9 5.9 0.953 3.82
0.083 1.156 5.96 0.901 5.65
m.w. 131.13 0.086 1.160 5.8 0.901 n.28
0.078 1.589 5.9 0.86M h.u6
0.070 2.173 5.7 0.813 3.89
0.069 2.3 5.6 0.790 3.35
0.068 2.399 6.0 0.797 3.66
Lysine 0.09“ 0.510 9.9 0.9”5 6.32
(Lys) 0.088 0.511 9.5 0.9“6 12.5h
0.079 1.07 9.7 0.885 7.23
m.w. 1H6.19 0.082 1.09A 10.0 0.880 5.38
0.053 2.19 9.9 0.763 6.65
0.06u 2.19 10.3 0.756 3.8V
0.056 2.775 10.5 0.687 3.17
0.05h 2.800 10.3 0.687 3.51
Sucrose 0.097 0.250 0.9h8 7.28
0.090 0.M98 0.893 n.88
m.w. 3h2.3 0.085 0.750 0.8“1 2.89
0.075 0.998 0.788 u.u6
0.062 1.500 0.679 3.97
0.052 2.000 0.570 2.20
0.0u6 2.250 0.516 2.02

 

110

TABLE 11 (cont'd.).

 

 

Volume
Ostwald Solution Solution Fraction Hydration
Amino Solubility Molarity pH Hater Number
Acid L M vW H
Proline 0.101 0.300 6.25 0.976 ”.27
(Pro) 0.100 0.600 6.29 0.950 0.61
0.098 0.600 6.26 0.950 2.35
m.w. 115.13 0.092 0.779 6.50 0.935 n.77
0.096 0.900 6.19 0.925 1.19
0.093 0.900 6.12 0.926 2.99
0.091 1.199 6.18 0.901 1.96
0.090 1.200 6.23 0.900 1.76
0.086 1.600 6.2“ 0.867 1.93
0.088 1.600 6.18 0.867 1.27
0.078 2.098 6.25 0.825 2.35
0.082 2.098 6.11 0.825 1.36
0.073 2.88fl 6.26 0.758 1.33
0.071 2.88“ 6.08 0.758 1.69
0.069 3.151 6.15 0.737 1.51
0.065 3.u22 6.88 0.711 1.58
0.063 3.518 -- 0.703 1.71
0.065 3.518 6.2” 0.705 1.uu
Serine 0.09“ 0.383 5.9 0.977 13.0u
(Ser) 0.101 0.171 6.0 0.990 12.03
0.099 0.277 6.13 0.983 9.80
m.w. 105.09 0.095 0.383 6.1 0.977 11.67
0.101 0.171 6.3 0.990 12.03
o.1ou 0.085 6.1 0.995 9.03

 

111

TABLE 11 (cont'd.).

 

 

Volume
Ostwald Solution Solution Fraction Hydration
Amino Solubility Molarity pa Hater Number
Acid L M Vt H
w
Threonine 0.070 1.uuu 6.0 0.887 8 69
(Thr) 0.090 0.680 6.1 0.9u7 7 97
0.090 0.680 6.1 o.9u7 7.97
m.w. 119.12 0.101 0.300 --- 0.977 u.u6
0.08u 1.060 5.9 0.918 6.56
0.095 o.u9o 5.9 0.962 7.u3
0.081 1.250 6.15 0.903 6.15
0.083 0.870 5.2 0.933 9.5a
0.098 0.300 5.6 0.977 9.68
0.072 1.uuu 5.3 0.887 7.96
0.105 0.150 6.5 0.988 ----
Cysteine 0.097 0.509 5.75 0.962 5.10
(Cys) 0.080 1.158 n.93 0.913 7.57
0.097 0.509 6.0 0.963 5.21
m.w. 121.16 0.081 1.158 5.8 0.91u ' 7.16
0.091 0.680 5.2 0.9“9 7.37
0.098 0.350 u.8 0.97“ 7.82
0.086 1.000 5.5 0.925 6.29
0.088 0.8u0 5.7 0.938 7.10
0.102 0.180 5.2 0.9870 7.61

 

TABLE 11 (cont'd.).

112

 

 

Volume
Ostwald Solution Fraction Hydration
Amino Solubility Molarity Water Number
Acid L M v H
tw
Valine 0.098 0.3h3 0.968 7.01
(Val) 0.097 0.3uu 0.969 8.67
0.103 0.153 0.986 5.17
m.w. 117.15 0.102 0.158 0.985 7.96
0.099 0.3uu 0.969 5.6V
0.102 0.155 0.986 8.h8
0.100 0.250 0.978 7.66
0.1036 0.080 0.9931 10.9
0.1036 0.080 0.9932 10.93
Histidine 0.100 0.259 7.91 0.97“ 6.5a
(His) 0.103 0.126 7.80 0.987 6.72
0.100 0.259 7.25 0.97” 6.5u
m.w. 155.16 0.102 0.126 7.25 0.988 11.30
0.101 0.192 7.32 0.981 8.12
0.1025 0.126 7.88 0.9878 9.1a
0.103 0.060 7.15 0.99” 20.57
0.1031 0.0601 7.75 0.99u7 17.68
Isoleucine 0.100 0.192 6.h1 0.979 10.26
(Ile) 0.102 0.09u3 6.78 0.990 16.28
0.099 0.192 6.2 0.980 13.27
m.w. 131.18 0.105 0.0h70 6.3 0.995” 5.69
o.1ou 0.0939 6.2 0.9905 5.5
0.1027 0.1u3o 6.6 0.98u6 6.09
0.101u 0.1921 6.73 0.9802 6.80
0.1031 0.1u3o 6.69 0.9853 n.92

 

113

TABLE 11 (cont'd.).

 

 

Volume
Ostwald Solution Solution Fraction Hydration
Amino Solubility Molarity Water Number
Acid L M vt H
w
Glutamine 0.098 0.219 5.0 0.979 13.77
(Gln) 0.102 0.100 5.30 0.990 16.35
0.100 0.160 “.8 0.985 1“.39
m.w. 1“6.15 0.0989 0.219 5.0 0.9801 11.90
0.10“1 0.0501 6.68 0.9960 15.36
0.1033 0.0999 5.7 0.9910 9.1“
0.095 0.219 “.6 0.980 21.17
0.100 0.100 “.7 0.991 26.35
0.102 0.050 5.“ 0.996 31.12
Methionine 0.101 0.215 5.8 0.977 6.22
(Met) 0.103 0.103 5.9 0.989 9.30
0.101 0.160 5.6 0.98“ 10.78
m.w. 1“9.21 0.1000 0.215 6.17 0.9772 8.70
0.1038 0.1029 6.35 0.9895 5.5“
0.100 0.103 5.7 0.989 2“.50
0.103 0.050 5.9 0.995 25.79
0.098 0.215 5.7 0.977 13.51
0.1036 0.0501 6.78 0.9955 20.00
Asparagine 0.098 0.186 5.5 0.983 17.“0
(Asn) 0.103 0.0758 5 6 0.993“ 15.85
0.103 0.0759 5.5 0.9931 15.61
m.w. 150.1“ 0.101 0.131 6 1 0.988 1“.86
0.100 0.186 7.0 0.983 11.78
0.10“ 0.0381 7.1 0.9970 23.05

 

11“

TABLE 11 (cont'd.).

 

 

Volume
Ostwald Solution Solution Fraction Hydration
Amino Solubility Molarity pH Hater Number
Acid L M v H
tw
Leucine 0.103 0.15“ 6.“0 0.983 “.06
(Leu) 0.1009 0.15“0 6.9 0.98“3 11.65
0.10“0 0.1150 6.7 0.9881 3.35
m.w. 131.18 0.1057 0.0369 6.95 0.9965 -1.00
0.102“ 0.0750 6.8 0.9922 19.3
0.107 0.0751 6.67 0.992 -12.85
0.0989 0.0750 6.7 0.9920 “3.5
Phenylalanine 0.101 0.1“5 5.90 0.982 11.13
(Phe) 0.103 0.0686 6.51 0.991 15.57
0.1029 0.1“50 6.“ 0.9818 “.22
m.w. 165.19 0.1051 0.0351 6.85 0.9963 7.55
0.1052 0.0690 6.“ 0.9913 -0.92
0.1031 0.1070 6.“ 0.9870 7.“3
Sodium Chloride 0.088 0.500 0.991 17.80
(NaCl) 0.082 0.750 . 0.987 15.75
0.075 1.000 0.981 15.13
m.w. 58.““ 0.055 2.001 0.961 12.23
0.039 3.001 0.9“0 10.55
0.023 “.000 0.917 9.69
0.018 5.251 0.888 7.57
0.098 0.250 0.996 15.72
0.063 1.500 0.972 13.93

0.090 0.500 0.991 15.71

 

115

TABLE 12. Hydration numbers of the amino acids.

 

 

Amino Acid This Work Reference Reference Reference
(77) (78) (79)
ALA 7.9 1 0.6 3.3 1 0.3 3.5 1 0.2 3.35
ARG 0.2 1 0.5 ------- “.1 1 0.5 ----
ASN 15.1 1 0.9 6.1 1 0.3 """" ""
CYS 6.8 1 0.3 ------- “.3 1 0 2 ----
GLN 13.3 1 1.0 13.3 1 0.“ ------- ----
GLY 8.5 1 0.6 8.2 1 0.3 3.“ 1 0.3 3.“0
HIS 7.“ 1 0.5 35.6 1 2.8 “.6 1 0.8 “.62
HYP “.5 1 0.“ 16.2 1 0.8 ------- ----
ILE ------- 2“.0 1 0.“ ------- ----
LEU ------- 8.3 1 0.“ “.3 1 0.2 “.53
LYS 6.1 1.1 20.1 1 0.5 ------- ----
MET 8.1 1.0 21.1 1 0.8 “.5 1 0.5 “.53
PHE -------------- “.6 1 0.2 “.“8
PRO 2.0 1 0.2 29.9 1 1.6 3.3 1 0.3 3.26
SER 11.3 1 0.6 “.2 1 0.3 ------- “.0“
THR 7.6 1 0.5 -------------- “.06
VAL 8.0 1 0.7 “.9 1 0.“ 3.8 1 0 2 “.22
SUCROSE 3.9 1 o 7 25.8a ------- 3.u2
NaCl 16.2 1 0.5 ------- 20.2b ----

 

a Reference (81);b

Reference (59)

116

The difficulty with calculating a hydration number for these five
amino acids stems from their low solubility in water. Consider equation
(66):

H

55.3“60 _ L(M)
I T[Vt ] o (66)

w 0.1060

Since the experiments with LEU, PHE, TRP, and TYR all involved dilute
solutions, with M S 0.15“, and the coefficient which multiplies the
square bracket is large. For M << 1, both terms in the square brackets
in equation (66) are within a few percent of unity. Thus, a 11 change in
either v or L(M) results in a large change in H. The uncertainty in

tw

our values of L(M) are of the order of 1%. This uncertainty is probably
the source of the large variation in calculated H values for these five
amino acids.

He must also mention a possible problem with the H values
calculated for cysteine. In each of the runs, we observed a white
precipitate forming during the course of the experiment. The precipitate
is probably cystine, which forms from aqueous cysteine solutions in the

presence of air. We estimate the mass of the precipitate to be about

0.56 g, which is the amount of cysteine which can form in the presence
(1) v(2)
8 8

volume of V1 ~ 5 cm3). Cystine is very insoluble in water; a liter of

water will dissolve only 0.112 g of cystine at 25°C. Thus, nearly all

of 130 cm3 of air (V - 70 cm3, - 55 cm3, and the effective

the cystine formed precipitates out of solution. We did not correct the
measured solubilities for cysteine for changes in volume, molarity, or

in vtw’ which occurred as a result of this effect.

117

The solubility data can be presented in several ways. Figure 30
is a plot of L versus M. Figure 31 is a plot of L versus Vt". In both
graphs, the data for each amino acid can be approximated by a straight
line which passes through the point for pure water. The linear
dependence of L on both the solution molarity and the volume fraction of
water suggests that the hydration number for each amino acid is a
constant, i.e., each additional amino acid molecule decreases the volume
of water available to disolve Xe by a constant amount.

The assumption of constant H is borne out if we consider Figure

32, which is a graph of L/L, versus v w - HM/55.3“6 . The ordinate can

t
be recognized as the volume fraction of free water as measured by Xe
solubility. The abscissa is the volume fraction of free water in a

solution of molarity M and volume fraction of water v assuming a

tw’
constant mean hydration number H. The data, for the most part, closely

follow the line L/Lo - v w - fin/55.3116 . Deviations tend to be at high

t
solution molarity, where we might expect, as in NaCl solutions, a
deviation from a constant H.

What properties of amino acids determine the hydration number?
Figure 33 is a plot of the mean hydration number as a function of the
molecular weight of the amino acid, which is a rough measure of the size
of the amino acid molecule. From this plot, we can see that there is no
obvious correlation between H and the size of the molecule. The data are
also broken down according to the type of side chain, whether it is

7 When viewed in this way, some

nonpolar, polar, or positively charged.
observations do suggest themselves.
If we first consider the amino acids with nonpolar side groups,

we see that the majority have hydration numbers in the range from 7 to

118

 

 

 

 

 

0°“ I I I I I
4:. + ALA
0.10 r- A Ana
3 A D LYS
or! n ‘ -
H
. - +
I; 0 09 E]
3
0 A30
‘3 ommu- a +
4.
U
'3 omn -
3
C3 0.06 - LYS
E
0.05 I I L I I
mo me go L5 26 as
Solution Molarity
0°“ F I I I I r I
‘\\b 4- ax
>‘ 0.10 r- . A 99°
4.:
or. \o‘ x U HYP
i: MN 4
a + '3‘ x
3 ammu- ‘\‘~-
H
o n
U) - .
0 00 F- -*L Q
:3 ' u .A. Fan
In
3 mm
4.)
8 0.07 1- ELY ...,,“
. LA
0.“ L I I I I I I

 

 

 

(L0 as 14: L5 2m 21: 1L0 15
Solution Molarity

Figure 30. L vs. M for Xe in aqueous amino acid solutions.

119

 

0.11

 

 

 

 

 

>5
4‘ 0.10
«4
r4
«4
.D
a 000’
.1...
C3
00
13 0.00
r4
(0
I!
13
CD 0.07
0.05 I I I I I. I I
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.8
Solution Molarity
°-1°7 I I 1* I I I I
-F VAL
> 0.10 A HIS _,
4a ‘ E] GLN
I.
«4 _k.\
F4 .
«4 0.10 2 “\.. + '-
D 9\
:3 E] E] 4 '
r4
C3 .. - .—
0, 0.101
t! E] n -
p4 VIL
4; :1 H18’ 4-
U)
I, I I I EL1 I I I

 

 

 

055* ..
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

Solution Molarity

Figure 30. (cont'd.).

120

 

0. 107

 

 

 

 

 

 

 

 

 

r I I I I
>5 .—
4; 0.105 At
..4 a A
H
«4 + +
n A
0.10 + L -
3.
o \\
00 £1 MEJ’ A;
g 0.101- 4. M51» -. + + ..I
m A ILE ILE
ASN
In
0 0.09 A _.
El 4-
0.09 L I g I I
0.00 0.04 0.00 0.12 0.10 0.20 0.24
Solution Molarity
0409 I I I. I I I f
5, 0.10%- + -
4.3
4-0
H
«4 0.10
n
:J
H
o
(D 0.10
E
m 0.101
I!
4.!
In
D 0.0 + —I
0.0 I? L I L I I I I
0.00 0.02 0.04 0.00 0.00 0.09 0.12 0.14 0.1!

Solution Molarity

Figure 30. (cont'd.).

121

 

 

 

 

 

Solution Molarity

Figure 30. (cont'd.). ‘

° F

o —I
f; 0 mci "
«4 Sucrose
.4 o -
«4
3 o 4
H
a . -
‘D 0
.... T
In
5 ° '1
m J
0 ° +

o «-

° '.

Ostwald Solubility

Ostwald Solubility

Figure 31. L vs. v

122

 

 

 

 

 

 

 

 

 

 

Water

tw for Xe in aqueous amino acid solutions.

°4‘ I I I I I
00‘0 ~ -
A’ an
A A a
009 + -
us a
a
009 + _
+ 4- MJ
A. an
0.07 an :1 our -
a
0.0. I I . l I I
0.09 0.90 0.92 0.94 0.95 0.90 1.00
Volume Fraction Water ”
0.00 I I [H
0.10 e/4 ..
0
P
04%;
009 a -
° A
.0»: -
007 -
mm
mm
009 an -
0&5 1
00 07 0a 09 L0
Volume Fraction

123

 

0.11

0.10 '-

0.07

Ostwald Solubility

 

III

I“

3
06+
333

 

I L I I

b

 

0.90 0.92 0.04 0.00 0.00 1.00

Volume Fraction Water,

 

Ostwald Solubility
.°
3
1‘

 

 

L I I I

 

 

use 050 099 030 :00
Volume Fraction Water

Figure 31. (cont'd.).

12“

 

 

 

 

 

 

 

 

0.10 _I
>
«u A A El
’2 0.10 .2. :‘I A d
o!"
‘9 mm +
3 0.9011- A =- v -1
o
a) A 1:! + A +
E. 0.09 _ A ++ a
co + 0w
5", °-°‘7" am A m "
m ‘ ASN U ASN
O 0.095 + -

04m: ' l ' '

0.975 0.990 0.955 0.990 0.995 . 1.000
Volume Fraction Water
' +
.3-0Am5 +
0H
r4 AL ‘5
4-0
'3 0¢m4 + -
'3 A A
m +
t: 0.102 "
H + 1.50
g + A we
‘3 _
o 0.900
O I +
L I I
0'069900 0.995 0.990 0.995 1.000

Volume Fraction Water

Figure 31. (cont'd.).

Ostwald Solubility

0.11
0.10
0.00
0.00
0.07
0.06
0.06
0.04
0.03
0.02

0.01

125

 

9+

 

I

NaCl
Sucrose

J

I

 

4.

-F
I

 
 
 
 

 

 

0.5 0.6

0.7

0.0

0.9

Volume Fraction Water

Figure 31. (cont'd.).

126

 

LIMI/Io

 

 

 

 

o 5 I I I I
0.5 0.0 0.7 0.0 0.9 1.0

_ v,W - FIN/55 . 345
1.0 , ,

 

l 1 l I

LIMI/Lo

 

 

 

 

0.3 I I I I I I
0.3 00‘ 005 °C. 0.7 00' 0.9 ‘00

Figure 32. L/Lo vs. vtw - HM/55.3“6 for amino acid solutions.

127

 

 

 

 

 

 

 

 

 

 

o
..I
\
3
..I
' 0.5 0.5 0.7 0.5 0.9 1.
V'w " HM/55.346
1.00
0.90 -
o
..I
2 . 0.90 -
3:3
..I
0.94 —
0 92 I I I
' 0.92 0.94 . 0.95 0.99 1.00

Figure 32. (cont'd.).

128

 

L (M1 /L0

 

 

 

 

I I I I
0‘11.“ 0.90 0.99 0.94 0.95 0.95 1.00
v,W - FIN/55 . 345
1.00

 

L (M) /L°

 

Figure 32. (cont'd.).

 

 

I I I
0.94 0.95 0.95 1.00

Hydration Number

129

 

 

 

 

‘3 I I I I I I I I I
15 - A -
1‘ F'- I—
12 4
u C A _
10 "' ‘5
0 " ‘ ‘-

7 - +
A «—
B - 4- «4
5 __ + 1 charge _‘
A polar . A

g " 0 nonpolar '-
2 - 0 -(
1 - -
o .. 4-..

_1 L I I I I I I I I I

70 60 00 100 1 10 120 130 140 150 160 170 160

Figure 33.

Molecular Weight

H vs. molecular weight.

130

9. Glycine, which has a molecular weight of 75.07, has a hydrogen atom
as its side group, and although it is included in the polar group, it
might also be included in the nonpolar group. GLY has an H of 8.5, which
is in the proper range.

The amino acids with polar side groups tend to have higher H
values. The exceptions are THR, CYS, and HYP. Hydroxyproline will be
discussed below. Cysteine has the difficulty discussed above, namely a
large uncertainty in H due to the cystine precipitate. Threonine is the
third anomalous amino acid in this group. We would expect, based on the
similarity of structure of serine and threonine, that these two amino
acids would have nearly identical hydration numbers. The large
difference is puzzling.

The amino acids with positively charged side groups may have
slightly lower hydration numbers than the nonpolar group. It is
interesting to note that ABC and LYS display a large difference in H,
despite a strong similarity in structure. Arginine, with H - 0.2 1 0.5.
probably has some affinity for Xe.

Proline differs from other amino acids in that the nitrogen atom
in the amino acid head group is also bound to the side chain, forming a
ring structure. Since it is bound, the amino group is no longer ionized
in solution. The low hydration number for PRO, H - 2.0 1 0.2, could be
due to either a Xe affinity, or to the loss of the dipolar charge of the
amino acid head group. The slightly higher value of H - “.5 1 0.“ for
hydroxyproline, which is a proline molecule with an additional hydroxyl
(OH) group, could be due to the addition of the polar OH group.

Figure 3“ shows H versus pH, with the same breakdown according to

R group as in Figure 33. There is no obvious correlation between H and

131

 

 

 

 

‘5 I I I I I I I
16 - A d
14 b A + 1 charge "
13 " A polar -
C. .—
a) if .. A 0 nonpolar :
I:
C: 6 " Age’fib’ -F .—
O 7 r A .-
..u-g +
u 5 '- -
m — -
L 5 A
‘U 4 f- _
2 " 0 _
1 f- 4—1
0 I- + '-
_1 I I I I I I I
4 5 5 7 a 9 10 11 12

Solution pH

Figure 3“. H vs. solution pH.

132

pH, although there may be some decrease in H with increasing pH for

PH>7.

Eucken and Hertzberg59

have measured the solubility of the rare
gases in a variety of alkali/halide salt solutions. The calculated
hydration number of NaCl is H - 20.2, which agrees favorably with our
value of 16.2 1 0.5. Goto80 reports a hydration value ofli-:22 for
NaCl, calculated from effective volumes of electrolytes in aqueous
solution.

There are several other methods which may be used to calculate
hydration numbers. These methods include ultrasonic interferometry, near
infra-red spectrophotometry, and analysis of molal volume and adiabatic
compressibility data.

77

Hollenberg and Ifft used the spectrophotometry method to

measure hydration numbers of amino acids in solution. Hollenberg and
Hall also used this method to measure hydration numbers of sugars. Some
of their values are listed in Table 12. Also included in the table are

78

hydration numbers from the work of Millero et. a1. and of Goto and

79 The former analysed apparent molal volume and compressibility

Isemura.
data, and the latter used ultrasonic interferometry. Our values are
included for comparison.

The data of Hollenberg and Ifft are highly variable, even for
similar molecules. For example, LEU and ILE have hydration numbers of
8.3 1 0.“ and 2“.0 1 0.“, respectively. This, along with other

82

considerations, probably indicate that we should discard their

results.

133

What can we conclude about our hydration numbers? Why do our
values differ so markedly from those of Millero_e_t_a_l. and Goto and
Isemura? Our method of determining hydration numbers is quite different
from that of either of these groups. Our values of H are actuallyaa
measure of many different effects. We assume that the excluded volume
effect is the only process which causes a change in solubility. This is
certainly a naive model, since we are working with a three component
system, and interactions between the components are undoubtedly very
complex. At the least, there is probably a second contribution to the
hydration values from Xe/amino acid interactions, such as is hinted at
by the hydration number of arginine.

The difference between our values, and those of Millero e_t §_1_.
and Goto and Isemura, may be due to differences in the strength of the
water/amino acid "bond". If water were tightly bound only to the polar
head group of an amino acid, and not to the rest of the molecule, it is
possible that only this tightly bound water would affect such bulk
properties as the partial molal volume, adiabatic compressibility, and
sound velocity.

Although our model of amino acid hydration is not altogether well
defined, it does explain the linear dependence of L on solution
molarity. It also shows that there may be an attractive interaction
between Xe and arginine in aqueous solution.

There are several avenues of research to pursue here, also.
First, a buffer might be added to the amino acid solutions to control
the pH. This would be closer to physiological conditions in which the pH
of the cell is controlled. A disadvantage to this approach is the

addition of a fourth component to an already complex system.

13“

Second, experiments could be done with polyamino acids in aqueous
solutions. The advantage here is that the contribution to hydration from
the polarity of the amino acid head group is eliminated, since these
groups are bound to each other in the formation of the polypeptide
bonds. These experiments would be very expensive to undertake at the
present time, but as improvements are made in the production process,
the cost of polyamino acids should decrease.

Third, studies might be done on the solubility of Xe in solutions
«of the amino acids in the normal alkanes and alkanols, or in olive oil,
which is a biological, nonpolar solvent. The liquid environment in these

solvents is similar to that in the interior of a cell membrane.

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11.

12.

13.

1“.

15.

16.

135

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U S

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