THE KENETECS C? THE OXEDA‘FlCN-REDSCTION
REACTION BETWfiEN MANGANhYE AN!)
PERRU‘SHENA?E ANEGNS {N
AQUEOUS ALKAL!

The“: {:or {fine Degree of DE. D.
MECEEGAN STATE UNWERSETY

E. Victor Luoma
1966

 

”35’s 'J LIBRARY

This is to certify that the

thesis entitled
THE KINETICS OF THE OXIDATION-REDUCTION

REACTION BETWEEN MANGANATE AND
PERRUTHENATE ANIONS IN AQUEOUS ALKALI
presented by

E. Victor Luoma

has been accepted towards fulfillment
of the requirements for

Ph.D

. degree in Chemistry

I:

Major professor

Date May 20, 1966

 

0-169

‘ Michigan State
University

_A

—- ~— ——-— gnu—- —.—..~—.———.-M__ A

‘ c—......

1‘!

Hit r

I
l

' i'
s f- ’

‘u‘. L .

R'w

‘o‘; '.

ABSTRACT

THE KINETICS OF THE OXIDATION-REDUCTION REACTION
BETWEEN MANGANATE AND PERRUTHENATE ANIONS
IN AQUEOUS ALKALI
by B. Victor Luoma
The kinetics of the oxidation-reduction reaction between
manganate and perruthenate anions was studied at 20.0°C
in alkaline aqueous solution. The rate was determined
spectrophotometrically. The reaction is first order with
respect to each ion and has.a measurable equilibrium constant.

Rate constants ranged between 500-150011-1

sec.-1, depending
on experimental conditions. The rate is a function of the
cation present, and increases with an increase in the size
or concentration of the cation. The temperature dependence
of the reaction was studied and Ea = 7.65 kcal/mole, AS* =
—10.7 e.u., and AG: = 10.2 kcal/mole were obtained. The
equilibrium constant is 4.32 i 0.25 at 20.0°C. lThe tempera-
ture dependence of the equilibirum constant was determined
and 933 - 3.95 kcal/mole, égfl = -0.85 kcal/mole, and égfl =
-10.6 e.u. were calculated. The results of the rate study
are compared with the theory of R. A. Marcus.

A preliminary study of the electron exchange reaction
between ruthenate and perruthenate at 0°C in 0.10 §.sodium
hydroxide solution was made. The exchange was too fast to

. . -1 -1
measure and a minimum value of‘~10‘ M sec. for a second

order rate constant was estimated.

THE KINETICS OF THE OXIDATION-REDUCTION REACTION
BETWEEN MANGANATE AND PERRUTHENATE ANIONS
IN AQUEOUS ALKALI

BY

E: Victor Luoma

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1966

DEDICATION

This work is dedicated to my father, Ernie S.
Luoma, who taught me the value of diligence and

education.

ii

ACKNOWLEDGMENTS

The author gratefully acknowledges the suggestions and
encouragement of Professor Carl H. Brubaker, under Whose
guidance this research was conducted; the patience and
Spartan existence of Mrs. Joan M. Luoma, wife of the author;
the financial aid and education leave from The Dow Chemical
Company; and the many trips made to Midland by a number of

Professors.

iii

TABLE OF CONTENTS

Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . 1
II. HISTORICAL . . . . . . . . . . .A. . . . . . . 3
III. THEORETICAL . . . . . . . . . . . . . . . . . 5
A. The Rate Law . . . . . . . . . . . . . 5
B. Theoretical Prediction of the Rate
Constant . . . . . . . . . . . . . . 7

IV. EXPERIMENTAL . . . . . . . . . . . . . . . . . 13

A. Preparation of Reagents . . . . . . . 13
B. Analytical Methods . . . . . . . . . . 16
C. Procedure . . . . . . . . . . . . . . 19
D. Competing Reactions . . . . . . . . . 23
E. Errors . . . . . . . . . . . . . . . . 26
V. RESULTS . . . . . . . . . . . . . . . . . . . 29

A. Determination of the Kinetic Order . . 29
B. Dependence of the Rate on Cation . . . 31

C. Dependence of the Rate on Ionic
Strength 0 o o o o o o o o o o o o o 48

D. Dependence of the Equilibrium Constant
on Temperature . . . . . . . . . . . -49

E. Dependence of the Rate on Temperature. 49

VI. DISCUSSION . . . . . . . . . . . . . . . . . . 55

VII. LITERATURE CITED . . . . . . . . . . . . . . . 61
APPENDIX - THE ELECTRON EXCHANGE BETWEEN

PERRUTHENATE AND RUTHENATE IN
ALKALINE AQUEOUS SOLUTION' f ; . . 64

iv

TABLE

II.

III.

IV.

VI.

VII.

VIII.

IX.

XI.

XII.

XIII.

XIV.

XV.

XVI.

XVII.

XVIII.

XIX.

LIST OF TABLES

Molar absorptivities at 20.0°c . .

The equilibrium constant
various media . . . . .

The
The
The
The
The
The
The
The
The
The

The
at

The
at

The
at

The
at

The
at

The
at

The

The

rate in

rate in
rate in
rate in
rate in
rate in
rate in
rate in
rate in
rate in

rate in
20.0°c

rate in
20.0°c

rate in
20.0°c

rate in
20.0°c

rate in
20.0°c

rate in
20.0°c

rate in

rate in

0.189 LiOH

I:

0.379 LiOH

IS

0.946 LiOH

l3

0.101 NaOH

l3

0.202 NaOH

IS

0.299 NaOH

l3

0.405 NaOH

l3

0.608 NaOH

l3

0.697 NaOH

I:

at

at

at

at

at

at

at

at

at

at

1.01 M NaOH at

0.199 M NaOH +

0 . 199 M NaOH

0 . 199 M NaOH

0 . 199 M NaOH

0 .199 M NaOH

0 .199 91 NaOH

+

O

0.090 M KOH at

0.180 M KOH at

20.0°c

20.0°c
20.0°c
20.0°c
20.0°c
20.0°c
20.0°c
20.0°c
20.0°c
20.0°c
20.0°c

o.1oo:g

0.2oo'g

0.3oo‘g

0.200'5

0.600‘M

0.600‘M

20.0°c

20.0°c

NaNO3

NaClO4

PAGE

17

30
33
34
34
35
36
37
37
38
38
39

39

40

40

41

41

42
42

43

TABLE

XXII.

XXIII.

XXIV.

XXVI.

XXVII.

XXVIII.

XXIX.

The
The

The
at

The
at

The
at

The
at

LIST OF TABLES(Cont.)

rate in 0.360 M

rate in 0.720 M

rate in 0.199 M

20.0°c

rate in 0.199 M NaOH

20.0°c

rate in 0.199 M NaOH

20.0°c

rate in 0.199 M NaOH

20.0°c

Summary of

Dependence

Dependence
on temperature .

Dependence of the rate on temperature

the rate at 20.0°c

of the rate on ionic strength
in sodium hydroxide solutions at 20.0°c .

of the equilibrium constant

in 0.299 M NaOH .

KOH at

KOH at

NaOH +

vi

+

+

+ 0.100

20.0°c
20.0°c

9 :95 g 12192304

0.10 E. Rb2504

0.050

E.

E;

(252804

(252504

PAGE
44
44

45

45

46

46
47

48

50

52

FIGURE

1.

LIST OF FIGURES

Visible absorption spectrum of
2.39x104MMn02 in 1.0MNaOH . . ..

Rate curves for some typical data . . .

Temperature dependence of the equilibrium
constant in 0.299 M NaOH . . . . . . .

Temperature dependence of the rate constant
in 0.299 M NaOH . . . . . . . . . . . . .

vii

PAGE

20
32

51

53

I. INTRODUCTION

In recent years there has been much kinetic and
mechanistic work in the field of inorganic chemistry (1).
Although the bulk of this work has been in the area of
ligand substitution reactions, there has been considerable
work in the field of electron transfer reactions (2,3,4,5,6).
A few of the reactions studied have been of the type where
simple electron exchange is a possible mechanism, such as
the case of the manganate-permanganate electron transfer

reaction studied by Sheppard and Wahl (7).

 

2 _ * .—
> MTIO4 + MHO‘

Mn0;_ + MBOE- <____
Symons (33) has shown that there is no interpenetration of
the first coordination spheres and hence the reaction must
proceed gig an "outer-sphere" mechanism.

This investigation originally started as a study of the
electron transfer reaction between ruthenate and perruthenate,
which was chosen because its close resemblance to manganate-
permanganate might provide further data for elucidating the
mechanism of electron transfer reactions in complexes with
inert first coordination spheres. The reaction proved to be
too fast to measure and only a minimum value for the rate
constant was determined. The ruthenate—perruthenate work
is discussed in the Appendix.

It was decided to investigate the oxidation of manganate
by perruthenate, since such a study might give additional

1

2

kinetic information involving the species discussed above.

> Ruo42' + MnO4-

«—

 

Ru04- + Mn042-

In this system there was no need to use tracers since there
is a net chemical change. All four anions absorb strongly
in the visible region and spectrOphotometry could be used
to determine the initial concentrations of the reactants
and to follow the course of the reaction.

The reaction turned out to be an equilibrium process
in which Egg'was not very large (~4) and thus it was pos-
sible to determine the free energy, enthalpy, and entropy
of reaction in addition to the usual kinetic constants.
The study of the reaction was complicated by competing re-
actions which will be discussed later. The competing reac—
tions made the determination of the equilibrium constant for
the perruthenate-manganate reaction difficult and restricted
the kinetic study to alkaline media between 0.10 M and

1.0 M hydroxide.

II. HISTORICAL

Electron transfer kinetics has become an active area
of research since radioisotopes became readily available.

It has only been since about 1950 that sufficient experi-
mental work has been published to allow attempts at quanti-
tative explanations of the factors which govern the rates of
electron transfer. A number of systems have been studied
and the effects of acids, bases, anions, cations, heavy
water, alcohol, and other agents have been examined
(2,3,4,5). From these studies, it now appears that there
are three possible paths for effecting transfer of electrons
(6). In any given reaction one or more of these paths may
be operative.

In some systems it appears that bridged species are
formed in which the reactants are joined together in the
transition state by an ion or group. Another process in-
volves the actual transfer of an atom, radical, or molecule.
These two processes are referred to as "strong over-lap
mechanisms". In some cases it is possible to distinguish
between them but more frequently there is an ambiguity.

In either case, however, the strong over-lap mechanisms are
considered to involve the first coordination sphere of the
reactants directly.

In systems where the ligands are inert to substitution
a "weak over-lap mechanism" has been prOposed. The activated
complex is designated as an outer-sphere complex but its

3

4

structure is difficult to ascertain. In such a mechanism
the transfer of the electron is considered to be a quantum
mechanical, barrier penetration. Electron transfer in sys-
tems considered to be examples of the weak-overlap mechanism
is fast and only a few have been studied. The example of
prime interest in this study is manganate-permanganate in
which the rate of exchange was found to be on the order of

1000M-lsec-1

at 0°C and to have first-order dependence on
each reactant: a second-order reaction (7). The rate was
also found to depend on both the cation concentration and
nature.

There are several theoretical approaches to the weak-
overlap mechanism. The work of R. A. Marcus (12,13,14,15)
has achieved the widest acceptance and derives rate ex-
pressions with no adjustable parameters. The R. A. Marcus
model will be applied to this investigation in the follow-
ing section. Other theories include one by R. J? Marcus,
Zwolinski, and Eyring (11) in which an experimental system
is necessary for the calibration of parameters. Hush (8)
has derived an "adiabatic" theory which gives essentially
the same results as those of the R..A. Marcus model. The
approach by Laidler (9,10) in his "non-adiabatic" theory
is similar to that of Marcus,vaolinski, and Eyring. The
various theories have recently been reviewed by R. A. Marcus
(16) and there is a discussion of some of the recent work
applied to theory by Strehlow (17). In all of the theories
a knowledge of the transition state is required and is not

generally obtainable from rate studies alone.

III. THEORETICAL

A. The Rate Law

In simple systems determination of the rate law for a
chemical reaction generally involves mixing of the reactants
and following the concentrations versus time at constant
temperature. The data obtained are then fitted to various

rate expressions of the type:

dC
——A' = a 6 yes... [1]
dt k Cacscc

where M is the specific reaction rate constant: 51, Q, 1
are often integers; and CA"E§f Cco-oo are the concentrations

of the chemical species A, g, g.---- present in the reacting
system at time 5, various graphical and mathematical methods
are available for determining the values of g, g, 1 "--
which will give a constant value for §_(18).

If the system under study is more complex, i.e., has
opposing, concurrent, or consecutive reactions, then the
mathematics becomes such that general methods of solution
are impractical or impossible. ~In this case the data are
fitted to equations for the various possible rate laws to
determine which one is Obeyed. Additional information about
the reaction in question such as its stoidhiometry and the

concentrations at equilibrium.can help narrow the search for

the correct rate law.

6
In this investigation the reaction was determined to
have an observable equilibrium constant and the stoichio-

metric equation was found to be:
RO-+Mn02- —->R02-+Mn0—
u 4 4 < u 4 4 -

Data were successfully fitted to the rate law for second-
order, Opposing reaction. Such a rate law is developed by

Benson (19) for the general case represented by the

 

equation:
k1
A + B < > C + D .
k2
The rate law is:
[$3] = _k1[A][B] + k2[C] [D] [2]

or by letting A = A0 - x :

g%'= k1<A0 " x)(BO ' x) ‘ k2(Co + X)(Do + Xl-[3]

The solution has the form:

1n X + (B - 9.:{zl/2Y = tql/l'g + 9 [4]
(6 + q ’2)/27

1/2

 

where: 9 = B - qi]
B+q 2
q = kiiAo ‘ Bolz + kg(co " Dolz
+ 2k1k2[(Ao + BONGO“+ D0) + 2A0130 + ZCODO]
B = ’ (k1Ao + k1130 + k2C0 + kzDo)
‘7=k1+k2
t = time.

7
With a knowledge of the equilibrium constant, K, for the
reaction it is possible to factor out 5; from gf/a, Q”
and 1_so that there are no rate constants in the log term.

The equation then becomes:

x + (Beta —_Q1/3)/gamma = kthI/Z + 9 [5]

 

ln
1
x + (Beta + Q /;)/gamma
where:
1/2
e _ 1n Beta :jlg

 

Beta +IQI72

1 2
Q = (A0 ‘ Bolz + §2(Co + Co)2 + §T(Ao + 30)

(Co + Do) + ZAOBO + 2Cebu]

Beta = " [A0 + Bo + %(Co + 130)]

1
Gamma — 2(1 — K)

K = equilibrium constant.
A plot of the log term versus time for a given reaction
1 . .
gives a slope of kJQ /2 from which k1 is readily deter-

mined. Note that the term

1
(Beta + Q /2)/gamma
in the denominator of the log term is the equilibrium con-

centration of E:
B. Theoretical Prediction of the.Rate Constant

The equations derived from the model due to R. A.
Marcus will be used for comparison with the experimental

data of this investigation. Marcus' theory is applicable

8
to systems in which there is only small orbital overlap
between the reactants in the activated complex. Such is
considered to be the case when the first coordination sphere
of the reactants is non-labile and when the ions are only
weakly solvated. The first condition of non-lability is
probably met in the manganate-perruthenate system but there
is a question about hydroxide ion association which will
be discussed later.

The equations given below summarize the results of the
Marcus theory and are taken from Rasmussen and Brubaker (20).
A detailed development of the theory may be found in the.
original papers (12,13,14,15). The factor exp[-Kr] used
by Rasmussen and Brubaker to correct for ionic strength will
be used here, although Marcus has recently published the

ionic strength correction in a somewhat different form (13).

 

kr = z exp[-AGi/RT] [6]
AG: = :1:2 exp[—Kr] + mzh [7]
s
where:
kr = rate constant
Z = collision number in solution equals about 1011
T = absolute temperature (0K)
Ds = dielectric constant of the solvent
AG* = free energy of activation (Gibbs)
e1e2 = charges on the reactants
r = distance of closest approach of the reactants

K = "Debye-Huckel kappa" equal to (5.03 x 109>¢u7DST

where:

ionic strength

 

AGO + — * 1

[- - 27“" w] - 5 (ref. 15) [8]
1 1 _ l_ 1 _ 1__ 2

(2a1 + 282 r)(fi2' Ds).(Ae) [9]
KjK.P 2

z ——J———P (Aqg) [101

3 Kj + Kj

free energy of reaction

work of bringing together reactants and
separating products.

a1 + a2

refractive index of the solvent

amount of charge transferred as a result of the
reaction.

force constants of the jth vibrational coordin-
ate for a species as reactant and product
respectively.

change in the bond distance in the inner
coordination sphere of each reactant.

"lambda outer"; contribution to A of surround-
ings of activated complex.

"lambda inner"; contribution to A of changes in

the first coordination sphere.

To determine hi, the summation is over the 1' normal

modes of each reactant and over all bonds involved in a

10

particular mode. In a regular tetrahedron only one of the
j_norma1 coordinates involves significant deformation on
going from reactant to product (21). This corresponds most
closely to bond stretching. To estimate hi { the equi-
librium bond length change, {932, and the-fzrce constant of
the bond in each reactant and product must be determined.

The Mn-O distance in potassium permanganate has been
determined to be 1.598 (22). Sheppard and Wahl have esti-
mated the Mn-O distance in potassium manganate to be
1.60-1.612 (7). The value 1.6052 will be used here, giving

a Aq° - 0.0153 for the manganese contribution to ~hi .

Silverman and Levy (23) have determined the Ru-O distance
in potassium perruthenate to be 1.792., Using the relation-

ship given by Pauling (24):
2
- n-1
z = (.2.» [11]

 

where n!‘ 10 for ruthenium, a value of 1.8043 was calcu-
lated for the Ru-O distance in potassium ruthenate. For

the ruthenium contribution to A1 . Aq° = 0.0148.

The force constants are estimated using an empirical

rule of Badger (25):

1/
(C/K) 3 = re - dij [12]

where: C1/3 - an empirical constant equal to 0.500 for a
bond between first and third row atoms and

0.490 between first and fourth row atoms.

11

dij = an empirical constant equal to 1.06 for a
bond between first and third row atoms and
1.18 between first and fourth row atoms

re = equilibrium bond length in Angstroms

K = force constant of bond in megadynes per centi-
meter.
By use of the above rule, the force constants are:

7.97 x lo5 dynes/cm.

Mn(VI) - o

Mn(VII) - O 3 8.39 x 105 dynes/cm.

3% X I

Ru(VI) - O 4.85 x 105 dynes/cm.

5.19 x lo5 dynes/cm.

Ru(VII) - 0 K

Substituting into the equation for hi yields:

A.

l Ai(Mn) + Ai(Ru)

hi = 1.41 x 10-1‘ ergs. [13]

To calculate An» the value of one-half the Mn-Mn and Ru-Ru
distances in potassium manganate (22) and potassium per—

ruthenate (23) will be used for a1 and ‘31, respectively.

This makes '31 = 2.9552 and a2 = 2.8053. At 20°C,

DS = 80.4 and q = 1.33 for water. Substitution of these

values gives:

A0 2.22 x 10"12 ergs [14]

A 2.23 x 10.12 ergs. [15]

It is easily seen that "lambda inner" makes very little
contribution to the total, which is not surprising in view
of the very small changes in bond distances which accompany

the transfer of the electron.

12
To calculate E. from equation [8], AGO = -5-85 x 10"14
ergs/molecule determined from the equilibrium constant for
the reaction (see Results section of this thesis) is used.

-10 2
) e.s.u.

This makes m_= - 0.487. For elez (2)(4.8 x 10
is used. Substitution of the apprOpriate values into equa-

tion [7] gives:

AG:F = 8.21 kcal/mole [16]

kr = 7.8 x 104 grlsec‘l. [17]
This value for the rate constant is for reaction in a solu—
tion of ionic strength .E = 0.20 and for the reactants ap-
proaching as closely together as they might in a crystal.
If a water molecule intervenes between the two anions, the
value of £_ increases to about 10.18. Recalculating the
above values we find:

AG$

4.31 kcal mole [18]

1

k
r

6.2 x 107 Mflsec: [19]

These two values for kr will be compared to the experi-

mental value in the Discussion section of this thesis.

IV. EXPERIMENTAL

A. Preparation of Reagents

Reagent grade materials were used except for lithium
hydroxide from the Amend Drug and Chemical Company, cesium
iodide from the Fairmount Chemical Company, and rubidium
sulfate and ruthenium metal from K and K Laboratories,
Incorporated. Low carbonate (< 0.35%) sodium hydroxide
was used. The water used to prepare solutions was distilled
and then passed through a mixed-resin ion-exchange column
to give a metal ion content of less than one part per mil-
lion, determined by conductance. Contamination of the water
by organic matter from the resin was reduced by discarding
the first quantity of water passed through the resin.
Glassware was washed thoroughly with hot bleach ("Clorox"),
rinsed with distilled water, and air dried. V

Stock solutions of lithium, sodium, and potassium
hydroxides were prepared by diluting concentrated solu-
tions after decantation from residual solids. Hydroxide
concentrations were determined by titration to the acid
side of methyl orange to include alkali-metal carbonate
content, since it was anticipated that the reactions would
be dependent upon cation concentration. Stock solutions
of sodium phosphate, sodium sulfate, sodium perchlorate,
sodium nitrate, rubidium sulfate, and cesium sulfate were
prepared by weighing the reagent, after it had been dried,
and diluting to a known volume.

13

14

Cesium sulfate was prepared by adding dilute sulfuric
acid to cesium iodide and evaporating onéa hot plate until
sulfuric acid fumes appeared to remove the iodine which had
formed. The resulting mass was heated to ~600°C to remove
the excess sulfuric acid. More sulfuric acid was added
after the mass had cooled and it was heated again to'~1000°C.

A stock solution of Ru(III) was prepared by fusion of
ruthenium metal with potassium hydroxide and potassium
nitrate at 600°C (26). The fused mass was dissolved in
water and acidified with sulfuric acid. The solution was
evaporated to sulfuric acid fumes. During the evaporation
several portions of hydrochloric acid were added to destroy
excess nitrate. The resulting solution was diluted with
water and sulfuric acid to make a Ru(III) stock in 3:M
H2804. Perruthenate solutions were prepared by oxidizing
Ru(III) with sodium bismuthate in hot 3 M_HZSO4 (27). The
resulting ruthenium tetroxide was swept from the solution
with a stream of air and carried into a solution of hydrox-
ide of known concentration (~d M) where the ruthenium
tetroxide decomposed to give perruthenate. A measured
volume of this solution was then diluted to give the desired
alkalinity. The perruthenate concentration was controlled
approximately by the amount of Ru(III) stock added to the
still. Perruthenate solutions containing sodium perchlorate,
sodium sulfate, etc. in addition to hydroxide were pre-
pared by adding a measured volume )f the apprOpriate stock

solution before diluting the alkaline perruthenate to final

15
volume. Perruthenate solutions were stored in an ice bath.
Perruthenate solutions in high hydroxide concentrations
(> 0.6 M), had to be used the same day as prepared. For
lower concentrations of hydroxide, the solutions could be
stored for up to a week.

Three different procedures were used to prepare man—
ganate solutions. In the first manganese dioxide was fused
in sodium hydroxide and was subsequently diluted to give a
manganate stock in 3 M_OH-. In the second method potassium
permanganate was decomposed in > 3‘M OH- and diluted to the
required hydroxide concentration. Even though this second
method contaminated the sodium hydroxide solutions to the
extent of about 0.1% with potassium ion, the same rates
were obtained for these solutions as for those prepared by
the first method. Neither of these two methods is suitable
for the lithium hydroxide solutions, because lithium ion
accelerated the decomposition of manganate solutions. In
the third method of manganate preparation potassium per-
manganate was dissolved in hot, concentrated potassium
hydroxide. After it was cooled, the resulting potassium
manganate was filtered off, washed with cold 1 M potassium
hydroxide, and air dried. Manganate solutions were then
prepared by adding a few crystals of the potassium manganate
to water with the desired hydroxide and cation concentra—
tions. This last procedure was used for all experiments

with solutions containing lithium hydroxide and for about

16
half of those with sodium and potassium hydroxide. All man-
ganate solutions were stored in an ice bath and had to be
used within one day after preparation and usually were used

within about four hours.
B. Analytical Methods

Spectrophotometry was used to determine the initial
concentrations of reactants and to follow the course of the
reaction. Molar absorptivities, §_, reported in the litera-
ture for the four species, ruthenate, perruthenate, manganate,
and permanganate, are somewhat contradictory (27,28,29,30,
31,32,35,43,44). Therefore, absorptivities were determined
for each anion at several wavelengths.

Solutions of known ruthenate concentration were pre~
pared by oxidizing ruthenium metal to perruthenate with
hypochlorite in 1 M NaOH and then decomposing the per-
ruthenate to ruthenate in 5-8 M NaOH. The absorbancies at
385 and 465 mu were measured periodically during the con-
version until there was no further change, i.e., until the
ratio of EAG5/E385 had reached a maximum. The molar ab—
sorptivities at several wavelengths were then determined
by means of a Beckman, Model DU, spectrophotometer, and are
listed in Table I. The only maximum in the visible region
for ruthenate is at 465 mu. Ruthenate of known concentra-
tion was then oxidized to perruthenate with 0.05 M NaClO
in 1 M NaOH to determine the molar absorptivities for per-

ruthenate. The results are given in Table I and agree well

17

 

 

 

 

Table I. Molar absorptivities at 20°C.
cmvfivelengtzu €12qu ERuOi " EMnO; EMnOi '

26,000 385 2150 840 340 1200
24,110 414.7 1075 1075 40 1080
21,500 465 260 1740 395 760
21,150 472.8 250 1720 560 560
19,700 507 170 1120 1805 240
19,000 526 120 610 2395 420
16,500 608 70 30 200 1570

 

18

with those of Larsen and Ross (27). The ratio 5465/5385 was
found to be 0.121 for solutions of perruthenate prepared by
the above method. This same ratio was also found for fresh
samples of perruthenate prepared by the decomposition of
ruthenium tetroxide in alkali of 1‘M or lower. The ratio.
0.121, agrees with that reported by Nowagrocki and Tridot
(28). Visible Spectra given elsewhere (27,28,29,30) were
confirmed. Solutions of both ruthenate and perruthenate
were found to obey Beer's law, at all wavelengths, up to

the highest concentrations studied (5 x 10—4

M) . Dilution
of a solution containing perruthenate from one concentration
of alkali to another was found to cause a change in the rela-
tive proportion of perruthenate and ruthenate present and,
so, concentrations had to be determined after dilution.
Standard solutions of permanganate were prepared
by dissolving electrolytic manganese metal in dilute nitric
acid to give manganese(IIL and subsequent oxidation to per-
manganate with periodate (31). The molar absorptivities
at several wavelengths are given in Table I. Manganate
solutions were prepared by decomposing permanganate in
> 5 M_OH- and subsequently diluting the solutions to 1 M_OH—.
It was found that dilution had to be performed carefully to
prevent diSpr0portionation of the manganate. By use of ice
cold 0.1 M OH- as the diluent and by rapid stirring, the
disproportionation reaction was prevented. The concentra-

tions of manganese in these solutions were determined

spectrophotometrically after acidification of measured

19
volumes with phOSphoriC acid and periodate oxidation to
permanganate. The molar absorptivities for manganate are
given in Table I. Figure 1 shows the visible spectrum for
manganate. In addition to the maximum at 606 mu (§_- 1570),
there are two others in the visible region at 438 and 353 mu
with molar absorptivities of 1270 and 1610, respectively.
These values differ somewhat from those found (1260 and
1530) by Bennet and Holmes (32). The latter values could
be duplicated, if small amounts of permanganate were present
in the manganate solutions. Solutions of manganate and
permanganate were found to obey Beer's law at all wave-

4

lengths up to the highest concentrations studied (5 x 10- M).

All of the molar absorptivities were determined at 20°C.
C. Procedure

Samples of each reactant were warmed to 20°C and the
absorbancies were measured at 385 and 465 mu for the per-
ruthenate stock and at 507 and 608 mu for the manganate
stock to obtain the concentrations of perruthenate, ruthenate,
permanganate, and manganate ions. The absorbancy of the
perruthenate stock was also measured at 507 or 608 mu, de-
pending on which wavelength was to be used to measure the
kinetics. The absorbancies were measured in the reaction
cell with a Cary, Model 14, spectrOphotometer which was
also used to monitor the reaction.

The pyrex reaction cell was cylindrical and had a

capacity of 65 ml and a 10.2-cm light path. The opening of

20

 

 

 

 

DAL
o.
o
o
C
o
a
b
o
m
.n 0.2 r-
<
o. I!»
O C l l l 1 L l l
' 350 400 450 500 550 600 650

Wavelength (mp)

Figure 1. Visible absorptionagpectrum of
2.39 x 10 4 ll. mo in 1.0 E. NaOH.

 

21
the cell was approximately 2-cm in diameter and was formed
by a glass tube about 5-cm long to permit rapid filling of
the cell. A special cover with an opening was built for
the spectrophotometer cell-compartment which permitted the
cell to be filled while the cell and cover were in position.

For each rate determination, a measured volume of each
stock solution was pipetted into a separate electrolytic
beaker. The beakers were covered with watch glasses and
placed in a constant temperature bath. The bath temperature
was measured with a precision thermometer, which had been
compared with a calibrated Beckmann thermometer (cali-
brated against a platinum resistance thermometer). The bath
temperature was held to within i 0.01°C. Water from the
bath was circulated by a centrifugal pump through the water—
jacket of the spectrophotometer cell-compartment.

The reaction cell was washed with deionized water,
dried by suction, and placed in the thermostatted cell-
compartment. When the cell had come to bath temperature,
the two reactants were removed from the bath, mixed by
being poured back and forth from one beaker to the other,
and then were transferred quickly to the cell through the
Opening in the cover. The opening in the cover was then
closed and the instrument turned on to record the absorbancy
versus time at a fixed wavelength. The temperature of solu-
tions, after the reaction was complete, had not changed from

the bath temperature.

22

The extent of reaction was determined by use of the
molar absorptivities given in Table I. Because of the com-
peting reaction, the absorptivities of only a few solutions
could be measured, at more than one wavelength, after the
reaction was completed. This was done to determine the
validity of the use of net absorbancy change as a measure
of the reaction variable §_(equation [3], Section III-A).
The validity of that assumption was upheld when it could
be checked and the additional assumption was made that the
absorbancy change at a single wavelength could be used in
all experiments. A few reactions were run at 608 mu to
observe the disappearance of reactant. Duplicate reactions
were repeated at 507 mu to observe the appearance of product.
The same values for the rate constant were obtained at both
wavelengths. The bulk of the reactions were then carried
out at 507 mu, because the absorbancy change for a given
set of reactants is about 75% greater at 507 mu than 608 mu.
Since the quantity desired was the slope of the line obtained
from the function:

/
x + (Beta — Q1’2)/qamma

1 = kth1/2 + 9
x + (Beta + Q 2)/gamma

In

zero time was taken at the first absorbance reading of a
given eXperiment. The rate constants were determined by
a least—squares analysis of the data performed by a Control

Data-3600 computer.

23

D. Competing Reactions

 

In addition to the reaction
Ru04— + MO42— = Ru042- + Mn04- [20]

there are at least five competing reactions which take place
in alkaline solutions of manganate, permanganate, ruthenate,
and perruthenate.

The decomposition of perruthenate at 25°C has been

studied by Carrington and Symons (34). The reaction

 

4 Ruo4' + 4 OH‘ > 4 Ruo42‘ + 2 H20 + 02 [21]

was found to follow the rate law

§%-= k[Ruo4‘]2[0H‘]3 [22]
where: k = 7.1 x 10—2 Mf4sec71

except for the first 10-20% of the reaction where the rate
appears to be proportional to [RuO4-]3. A measurement of
the rate of reaction [21] at lower OH- concentrations

(0.02 - 1.0 M), made during this investigation, showed that
the rate constant was approximately the same as that given
above. At these lower OH— concentrations, however, the
ruthenate formed in the reaction [21] decomposes. The
ruthenate decomposition has been studied by Connick and
Hurley (29) in the region pH = 10 — 11, and is a disproporw

tionation reaction:

 

3Ruo42‘ + (2-X)H20 > 2Ru04— + Ru02°XHZO + 40H? [23]

<————

. . . . -1
The equilibrium constant was estimated to be about 10 0.

24

The net result of this reaction and reaction [21]--for loss

of ruthenate--can be represented as:
2Ru042_ + (2+x)H20 ———> 2Ruo,-xH,o + 30H" + 02 . [24]

In the present perruthenate decomposition studies the rate
of decomposition of ruthenate was found to be approximately
equal to that of the perruthenate in the range of 0.1-0.2 M
0H7. At lower alkalinity, ruthenate decomposition was
faster than that of perruthenate.

The manganate-permanganate system has been studied by
Jezowska-Trzebiatowska and Kalecinski (35,36,37). The de-
composition of permanganate (35) at 25°C in 0.88 M KOH

solution:
4Mn04- + 40H- -——> 4Mn042- + 2H,o + 02 [25]
obeys the rate law:

MnO '
g=k-——-——-[ ‘1

_ [261
dt [Mno42 ]

where: k = 2.5 x 10-7 M sec:1

The reaction is also first-order with respect to [OH-]. The
disprOportionation of manganate in 0.0676 M KOH at 30°C was

also studied by the above authors (36). The reaction
3Mn042- + 23,01———> 2MnO‘- + Mno, + 40H" [27]

obeys the rate law:

25
The reaction is believed to be proportional to [OH-1-2. The
result of reaction [25] followed by reaction [27] gives a

net decomposition of manganate represented by

 

3Mn022‘ + 2H20 > 2Mno2 + 4OH— + 02 . [29]

Reaction [25], the decomposition of permanganate, is inhibited
by telluric acid (39). In this investigation, it was found
that the decomposition of permanganate is accelerated by
ruthenate-perruthenate.

At low concentrations of hydroxide (< 0.2 M) the re-
action

Ru042‘ + 2Mn042_ + 21120 """> R1102 + 2.011104.- + 40H- [30]

was found, in this investigation, to become significant,
which is not surprising because the potential for the reac-
tion becomes positive at about 0.1 M_OH- (39).

Solutions containing ruthenate, perruthenate, manganate,
and permanganate decompose within a matter of hours to form
nearly colorless solutions which contain finely-divided
dark solids, assumed to be hydrated oxides of Ru(IV) and
Mn(IV). The rate of decomposition depends upon the cation
present, with solutions containing cesium ions decomposing
the most rapidly. The order of decomposition rates with
the various cations used in this study is

+2: +

+ + .+
Cs>Rb>K Na <Li

Lithium ion is anomalous. The anomaly may be explained by
the observations that manganate solutions decompose more

rapidly with lithium ion present than with the other four

26
cations and stable manganate solutions could not be pre—

pared in concentrated lithium hydroxide.

E. Errors

 

There are several sources of error in this investi-
gation. SpectrOphotometry is limited to a maximum accuracy
of about 1%, depending upon the magnitude of the absorbancy
reading, and introduces an error of about i 1% in the
initial concentrations of the reactants. The error is
magnified in determining the extent of reaction since the
extent was determined as a difference between two absorbancy
readings. For reactions in which the initial concentra-
tions of the two reactants are approximately equal, the
difference is nearly as large as the larger of the two
absorbancy readings and the error is therefore still about
i 1%. With an increase in the concentration of one re-
actant over the other the error in determining the extent
of reaction increases, because the difference in absorbancy
readings becomes small compared to the absorbancy readings
themselves.

The greatest source of errors in this investigation is
caused by the competing reactions discussed in Section IV—D.
At low alkalinity (0.2 Mgor less), ruthenate begins to
oxidize manganate to permanganate. Regardless of whether
one follows the loss of manganate at 608 mu or the formation
of ruthenate and permanganate at 507 mu, the net result of

the ruthenate-manganate reaction is an increase in the

27
apparent reaction rate for the perruthenate-manganate
system. The error caused by this competition is somewhat
greater for solutions in which manganate ion is higher in
concentration than ruthenate.

Although the decomposition Of permanganate is a com-
peting reaction in all of the rate studies, it does not
appear to become significant until the [OH—] reaches about
0.4 M, This decomposition regenerates manganate which
has been oxidized by perruthenate. In samples in which
the manganate concentration was higher than the per-
ruthenate, the decomposition reaction caused the Observed
rate constant to be low. Conversely, when the initial per-
ruthenate concentration was higher than that of manganate,
manganate regenerated by the permanganate decomposition was
reoxidized by perruthenate thus forming still more ruthenate
than indicated for the oxidation-reduction reaction under
study. Thus the Observed rate constant would be high. At
high [OH-], the error caused by the permanganate decomposi-
tion was i 10%. In spite Of the errors caused by the com-
peting reactions, rate constants determined in duplicate
experiments generally agreed to within 2%. The kinetic data
were taken during the first 80-85% Of each reaction to
minimize the complications caused by the competing reactions.

Because of the competing reactions, it was only pos—
sible to determine the equilibrium constant for the reaction
under investigation between 0.2-0.4 M_OH—. The error in

the equilibrium constant caused by spectrOphotometric error

28

is, at least, 4% when the initial reactant concentrations
are equal. When these concentrations differ, the error is
magnified. Fortunately, a 10% variation in the equilibrium
constant caused a change Of only 1% in the calculated rate
constants.

The temperature of the reaction was controlled to
: 0.01°C and the time was measured from the chart paper
which was driven by a synchronous electric motor. There—
fore, errors caused by time and temperature were considered

negligible.

V. RESULTS
A. Determination Of the Kinetic Order

The establishment of the rate dependence on the concen—
tration variables is essentially a fitting process as dis-
cussed in the Theoretical section Of this thesis. It became
evident in this investigation that the reaction was revers-
ible. Either the rate constant for the reverse reaction
or the equilibrium constant for the reaction had to be
established before the kinetic order could be determined.

In this system it was easier to determine the equilibrium
constant. Because of the competing reactions, it could be
determined only over the range of 0.2-0.4 M_OH_. The equi-
librium constants listed in Table II are for

[RuOZ'IIMno4'1

K = . [3].]
eq [RuO4-] [3411042-]

 

It was assumed that the activity coefficients would nearly
cancel and therefore Ke should be thermodynamically valid.
The value Of the potential, M3, for the reaction can be

calculated from the relationship:

0: 5T.
E nF an [32]

where: R = gas constant
T = absolute temperature
n = number of Faradays
F = Faraday

K = equilibrium constant.
29

30

Table II. The equilibrium constant at 20.0°c in various
aqueous media

 

 

Initial concentrations (M|x 105)

 

 

Medium RuO4- Mnoi’ Ruoi’ MnO4- Keq
0.405 M NaOH 3.09 4.30 0.12 0.00 4.37
0.405 g»; NaOH 4.12 3.23 0.16 0.00 4.19
0.405 M NaOH 4.12 3.23 0.16 0.00 4.21
0.405 M NaOH 3.09 4.30 0.12 0.00 4.03
$393093 $132230, 2.52 2.35 0.05 0.02 4.67
333%- $322504 2.52 2.35 0.05 0.02 4.49
0.360 g KOH 4.24 4.73 0.10 0.03 4.12
0.360 E KOH 4.45 4.41 0.10 0.02 4.31
0.360 g KOH 4.24 4.73 0.10 0.03 3.96
0.299 M NaOH 3.15 3.70 0.104 0.00 4.71
0.299 11 NaOH 3.93 2.46 0.130 0.00 4.16
0.299 11 NaOH 3.15 3.70 0.104 0.00 4.65

4.32:0.25

X‘
Standard deviation Of the mean.

31
The value §3_= 0.037 volts has been calculated using the
above relationship. By use of the value §£'= -0.558 volts
(43) for the half-cell:
Mno42' = Mno4' + e" [33]
the value §£_= -0.595 volts at 20°C has been determined

for the half cell:

RuO42- = Ru04- + e [34]
which is in good agreement with the value of §2_= -0.59
volts determined by Connick and Hurley (29).

With a value Of 4.32 i 0.25 for the equilibrium constant
at 20.0°c, it was then possible to test the data against
various rate laws. As was indicated in the Theoretical
section, the data fit the second-order rate law for revers-
ible reactions, first—order in each reactant:

x + (Beta — Q1/2)/gamma

1 = le/zt + 9 [5]
x + (Beta + Q 2)/gamma

ln

1 .
where Beta, gamma, Q /2, and 9 are functions of initial con—
centrations and are defined in section III-A. Figure 2

shows some typical rate data.
B. Dependence of the Rate on Nature of the Cation

As was anticipated from the study of manganate-per-
manganate electron exchange (7), the rate of reaction was
found to depend on both the concentration and nature of

cation present in the solution. The reaction was carried

out in the presence of each of the first five members of

 

l
x + (Beta - (35)/gamma
gamma

x + Beta-t-

In

32

 

 

 

 

I
'62 l l J ‘ l l l
o s to 24 32 40 49
Ti m e (seconds)
Figure 2. Rate curves for some typical data.

Curve I - 0.189 M LiOH Table III)

Curve II - 0.299 M NaOI-I Table VIII)

Curve III - 0.199 M NaOH + 0.100 M
Rbaso4 (Table XXIV).

 

 

33
the alkali series and the rate of
the size of the cation. The data
are given in Tables III-V, sodium

sium in Tables XIX-XXII, rubidium

and cesium in Tables XXV and XXVI.

reaction increased with
for the lithium cation

in Tables VI-XVIII, potas-
in Tables XXIII and XXIV,

The deviation in the

rate constants given in the last column of each of the

above tables is the percentage variation in the slope Of

the line (and hence in the rate constant) permitted by one

standard deviation of the individual data points. Table

XXVII gives a summary of the data

from Tables III-XXVI.

Table III. The rate in 0.189 M LiOH at 20.0°c

 

 

 

 

 

Initial Concentrations (MLX 105) kr Percent

_ 2_ 2_ __, _ _1 _1 standard
R1104 M1104 R1104 Mn04 (fl sec 0 ) deViation
3.49 3.87 0.00 0.04 536* 0.45
4.66 2.90 0.00 0.03 558 0.33
5.82 1.94 0.00 0.02 568 0.87
2.33 4.84 0.00 0.05 533 0.42
3.49 3.87 0.00 0.04 534 0.42
4.66 2.90 0.00 0.03 561 0.66

**
548114

7(-
Rate data plotted in Figure 2.

**
Standard deviation Of the mean.

 

34

 

 

 

 

 

 

 

 

 

 

Table Iv. The rate in 0.379 M LiOH at 20.0°c
Initial Concentrations (M.X 105) kr Percent
_ 2_ 2_ _ _1 _1 standard
Ru04 Mn04 Ru04 Mn04 (M; sec. ) deviation
3.44 4.21 0.04 0.00 643 0.67
2.29 5.26 0.03 0.00 637 0.79
3.44 4.21 0.04 0.00 680 0.92
4.59 3.15 0.06 0.00 713 0.39
670i29*
*Standard deviation of the mean.
Table V. The rate in 0.946 M_LiOH at 20.0°c
Initial Concentrations (M_x 105) kr Percent
_ 2_ 2_ _ _1 _1 standard
Ru04 MnO4 RuO4 MnO4 (M_ sec. ) deviation
4.96 3.49 0.30 0.00 1004 0.45
6.62 2.62 0.40 0.00 1036 1.15
3.31 4.37 0.20 0.00 801 0.41
4.96 3.49 0.30 0.00 969 1.38
953:86*

7(-
Standard deviation

 

Of the mean.

 

35

 

 

 

 

Table VI. The rate in 0.101 M NaOH at 20.0°c
InitiEl Concentrations (M'x 10‘5) kr Percent
_ 2- 2_ _ _1 _1 standard
Ru04 Mn04 Ru04 Mn04 (M_ sec. ) deVIation
3.57 6.53 0.00 0.56 472 1.55
5.36 5.22 0.00 0.45 508 1.23
7.14 3.92 0.00 0.34 527 0.75
8.93 2.61 0.00 0.23 523 1.11
8.93 2.61 0.00 0.23 501 0.63
3.57 6.53 0.00 0.56 426 1.34
2.17 7.82 0.00 0.48 466 0.67
3.26 6.26 0.00 0.38 457 2.10
5.43 3.13 0.00 0.19 442 0.85
4.34 4.69 0.00 0.29 451 0.60
477:33*

*-
Standard deviation

of the mean.

 

 

36

 

 

 

 

Table VII. The rate in 0.202 M NaOH at 20.0°c
Initial Concentrations (M.x 105) kr Percent
- 2_ 2_”‘r’* _ _1 _1 standard
Ru04 Mn04 Ru04 Mn04 (ML sec. ) deVIation
3.56 8.10 0.00 0.14 577 0.46
5.34 6.48 0.00 0.11 590 0.76
7.11 4.86 0.00 0.09 589 0.92
8.89 3.24 0.00 0.06 623 0.33
7.11 4.86 0.00 0.09 598 0.43
5.34 6.48 0.00 0.11 605 1.25
1.87 2.06 0.21 0.00 530 0.75
1.24 2.58 0.14 0.00 515 2.68
2.49 1.55 0.29 0.00 565 1.59
3.11 1.03 0.36 0.00 605 1.24
2.49 1.55 0.29 0.00 552 1.02
1.87 2.06 0.21 0.00 537 1.20
573:33*

*
Standard deviation of the mean.

 

 

37

Table VIII. The rate in 0.299 M NaOH at 20.0°c

 

 

 

 

 

Initial Concentrations (M_x 105) kr Percent

_ 2_ 2_ _ _1 _1 standard
Ru04 Mn04 Ru04 Mn04 (M_ sec. ) deviation
4.23 2.71 0.00 0.01 714* 0.46
5.64 2.03 0.00 0.01 735 1.32
2.82 3.39 0.00 0.01 683 0.37
3.15 3.70 0.10 0.00 737 0.43
3.15 3.70 0.10 0.00 742 0.51

**
722i26

*-
Rate data plotted in Figure 2.

*7?
Standard deviation of the mean.

 

Table IX. The rate in 0.405 M NaOH at 20°C

 

 

 

 

 

Initial Concentrations (M_x 105) kr gigfigggd
Ru04- Mnoi- RuOi- MnO4- (Mrlsecjl) deviation
2.06 5.38 0.08 0.00 761 1.41
3.09 4.30 0.12 0.00 772 0.64
4.12 3.23 0.16 0.00 778 0.72
5.15 2.15 0.20 0.00 780 0.56
4.12 3.23 0.16 0.00 759 0.64
3.09 4.30 0.12 0.00 758 0.48
766:9*

*-
Standard deviation Of the mean.

38

 

 

 

 

 

 

 

 

 

Table X. The rate in 0.608 M NaOH at 20°C
Initial Concentrations (M.x 105) kr Percent

_ 2_ 2_ _ _1 _1 standard
Ru04 MnO4 Ru04 Mn04 (M_ sec. ) deviation
2.09 4.85 0.12 0.06 874 1.55
3.13 3.88 0.18 0.06 903 0.62
4.17 2.91 0.24 0.04 932 1.01
5.22 1.94 0.29 0.03 972 0.32
4.17 2.91 0.24 0.04 963 0.81
3.13 3.88 0.18 0.05 950 0.29

*
932134

*Standard deviation of the mean.
Table XI. The rate in 0.697 M NaOH at 20.0°c
Initial Concentrations (M.x 105) kr Percent

_ 2_ 2_ _ _1 _1 standard
Ru04 MnO4 RuO4 Mn04 (M_ sec ) deviation
1.14 3.60 0.96 0.00 900 1.20
1.52 2.70 1.28 0.00 1051 1.51
1.89 1.80 1.60 0.00 1060 0.39
2.27 0.90 1.92 0.00 1231 2.61

 

1061:110*

*
Standard deviation Of the mean.

 

39

 

 

 

 

 

 

Table XII. The rate in 1.01 M NaOH at 20.0°c
Initial Concentrations (M,x 105) k Percent
_ 2_ 2_ _ _1 r _ standard
RuO4 Mn04 RuO4 MnO4 (M. sec. ) deviation
1.87 4.38 1.01 0.03 1085 0.94
2.50 3.29 1.34 0.02 1077 1.05
3.12 2.19 1.68 0.01 1164 1.69
2.50 3.29 1.34 0.02 1084 2.51
1.87 4.38 1.01 0.03 1044 2.31
109li4o*

*
Standard deviation Of the mean.

 

 

 

 

 

 

 

Table XIII. The rate in 0.199 M NaOH + 0.100 M Na2SO4 at
20.0°C
Initial Concentrations (M.X 105) kr Percent
_ 2- 2_ _ _ _1 standard
Ru04 Mn04 Ru04 MnO4 (M_ sec. ) deviation
1.91 3.50 0.06 0.03 681 0.69
1.91 3.50 0.06 0.03 670 0.95
2.54 2.62 0.08 0.03 684 1.09
2.54 2.62 0.08 0.03 688 0.97
3.18 1.75 0.10 0.02 698 1.08
1.27 4.37 0.04 0.04 668 0.92
682:20*

*-
Standard deviation of the mean.

 

40

 

 

 

 

 

Table XIV. The rate in 0.199 M NaOH + 0.200 M NaZSO4 at
20. 0°C , w n _ -
Initial Concentrations (M_x 105) kr Percent
_ 2_ 2_ _ _1 _1 standard
Ru04 Mn04 - RuO4 MnO4 (M. sec. ) deviation
1.89 3.13 0.04 0.03 912 0.74
2.52 2.35 0.05 0.02 870 1.32
3.15 1.56 0.06 0.01 961 0.55
1.26 3.91 0.02 0.03 908 0.77
1.89 3.13 0.04 0.03 908 1.07
2.52 2.35 0.05 0.02 948 0.89
917i3o*

*
Standard deviation of the mean.

 

 

 

 

 

 

Table XV. The rate in 0.199 M NaOH + 0.300 M Na2804 at
20. 0°C

Initial Concentrations (M.x 105) k Percent

_ 2_ _1 _1 standard
RuO4 MnO4 RuO4 MnO4 M, sec ) deviation
1.90 3.33 i 0.05 0.03 977 0.45
2.53 2.50 0.06 0.02 1058 1.68
1.90 3.33 0.05 0.03 1000 2.05
2.53 2.50 0.06 0.02 1063 0.82
3.16 1.67 0.08 0.01 1074 1.53
1.27 4.17 0.03 0.04 1001 2.71

1029:37*

*
Standard deviation

of the mean.

 

41

Table XVI. The gate in 0.199 M NaOH + 0.200 MNaapo4 at
20.0 C

 

 

 

 

 

Initial Concentrations (M.x 105) kr Percent
_ 2_ 2_ _ _1 _1 standard
Ru04 MnO4 RuO4 Mn04 (M, sec. ) deviation
1.92 3.12 0.04 0.00 865 1.41
2.56 2.34 0.05 0.00 926 0.59
3.19 1.56 0.07 0.00 920 1.24
1.28 3.90 0.03 0.00 860 1.54
1.92 3.12 0.04 0.00 918 1.20
2.56 2.34 0.05 0.00 938 0.62
904:30*

*
Standard deviation of the mean.

 

Table XVII. The rate in 0.199 M NaOH + 0.600 M NaN03 at

 

 

 

 

 

20.0°c

Initial Concentrations (M’X 105) kr Percent

_ 2_ 2_ _ _1 _1 standard
R1104 M1104 R1104 Mn04 (fl SEC . ) deviation
3.59 2.75 0.02 0.01 1014 1.41
2.69 3.67 0.02 0.02 979 0.93
3.59 2.75 0.02 0.01 1001 0.94

998:20*

*-
Standard deviation Of the mean.

 

Table XVIII.

42

The rate in 0.199 M NaOH + 0.600 M NaClO4 at

 

 

 

 

 

 

 

 

 

 

 

 

20.0°c
Initial Concentrations (M x 105) kr Percent
_ 2_ 2_'_ _ _ _1 standard
RuO4 Mn04 Ru04 Mn04 (M_ sec. ) deviation
3.61 3.10 0.03 0.00 1047 1.21
2.71 4.14 0.03 0.00 1002 0.59
3.61 3.10 0.03 0.00 1038 0.75
1029:20*
*Standard deviation Of the mean.
Table XIX. The rate in 0.090 M KOH at 20.0°c
Initial Concentrations (M_x 105) kr Percent
_ 2_ 2_ _ _1 _1 standard
RuO4 MnO4 RuO4 Mn04 (M, sec ) deviation
6.18 2.85 0.00 0.21 612 0.85
4.95 4.28 0.00 0.32 616 0.97
3.71 5.71 0.00 0.42 612 0.92
2.47 7.14 0.00 0.53 609 0.09
4.95 4.28 0.00 0.32 620 1.43
6.18 2.85 0.00 0.21 622 1.96
615i4*

*
Standard deviation

of the mean.

 

 

 

 

 

Table XX. The rate in 0.180 M KOH at 20.0°c.
Initial Concentrations (Mix 105) kr Percent
- 2- 2- - -1 -1 standard
Ru04 Mn04 Ru04 Mn04 (M sec. ) dev1ation
2.48 7.27 0.01 0.10 807 3.02
3.71 5.81 0.01 0.08 809 1.04
2.48 7.27 0.01 0.10 786 0.34
4.95 4.36 0.01 0.06 794 0.89
6.19 2.91 0.01 0.04 794 1.07
4.95 4.36 0.01 0.06 765 1.45
4.95 4.36 0.01 0.06 794 0.91
793i14*

 

X-
Standard deviation of the mean.

 

44

Table XXI. The rate in 0.360 M KOH at 20.0°c

 

 

 

 

 

Initial Concentrations (M x 105) kr Percent
_ 2_ 2_'. _ _1 _1 standard
RuO4 MnO4 RuO4 Mn04 (M. sec. ) deVIation
3.18 6.30 0.07 0.03 1018 1.01
4.24 4.73 0.10 0.03 1011 0.98
5.30 3.15 0.12 0.02 1081 0.39
4.45 4.41 0.10 0.02 1036 0.80
4.24 4.73 0.10 0.03 1031 0.82
1035:22*

*-
Standard deviation of the mean.

 

Table XXII. The rate in 0.720 M KOH at 20.0°c

 

 

 

 

 

Initial Concentrations (M x 105) kr Percent
_ 2_ 2_ =L—— _ _1 _1 standard
RuO4 MnO4 RuO4 MnO4 (M sec. ) deviation
2.87 4.58 0.35 0.00 1413 1.21
3.82 3.43 0.47 0.00 1618 0.40
2.87 4.58 0.35 0.00 1453 0.65
3.57 3.74 0.44 0.00 1579 1.15
1.91 5.72 0.23 0.00 1480 0.48
3.82 3.43 0.47 0.00 1586 1.68
1521i7si

9(-
Standard deviation Of the mean.

 

45

Table XXIII. The rate in 0.199 M NaOH + 0.05 M RbZSO4 at

 

 

 

 

 

20.0°c

Initial Concentrations (M,x 105) kr Percent

_ 2_ 2_ _ _1 _1 Standard
RuO4 MnO4 RuO4 Mn04 (M_ sec. ) deviation
2.765 2.295 0.355 0.022 835 0.95
2.21 3.44 0.284 0.033 831 0.87
2.765 2.295 0.355 0.022 837 0.86

834 i 3

*-
Standard deviation of the mean.

 

Table XXIV. The rate in 0.199 M NaOH + 0.10 M Rb2804 at

 

 

 

 

 

20.0°c

Initial Concentrations (M'x 105) kr Percent

— 2- 2- ' _ _ -1 standard
Ru04 Mn04 RUO4 M1104 (£4 sec 0 ) deViation
2.835 1.805 0.284 0.015 1093* 0.79
2.27 2.71 0.227 0.022 983 0.78
2.27 2.71 0.227 0.022 989 0.75

‘X’ ‘X’
1022i51

*-
Rate data plotted in Figure 2.

16*
Standard deviation of the mean.

 

46

Table XXV. The rate in 0.199 M NaOH + 0.050 M_CSZSO4 at

 

 

 

 

20.0°c
Initial Concentrations (M x 105) kr Percent
_ 2_ 2_ _ _ _1 standard
Ru04 Mn04 Ru04 ~ Mn04 (M’ sec. ) deviation
2.78 2.22 0.317 0.02 1075 1.80
2.22 3.33 0.254 0.03 1118 0.64

 

1097r22*

*
Standard deviation Of the mean.

 

Table XXVI. The gate in 0.199 M NaOH + 0.100 M Cszso4 at
20.0 C

 

 

 

 

Initial Concentrations (M_x 105) kr Percent
_ 2_ 2_ _ _1 _1 standard
RuO4 Mn04~ RuO4 MnO4 (M. sec. ) deviation
2.78 2.405 0.308 0.01 1451 0.83
2.22 3.61 0.246 0.015 1462 0.77
2.78 2.405 0.308 0.01 1469 0.71
1461i8*

*-
Standard deviation of the mean.

 

47
Table XXVII. Summary of the rate at 20.0°c

 

 

 

 

Concentrations (moles/liter) kr

Cation Hydroxide Anion (Mrlsec.
0.189 Li+ 0.189 -— "548:14
0.379 Li+ 0.379 -- 670:29
0.946 Li+ 0.946 -— 953:86
0.101 Na+ 0.101 -— 477:33
0.202 Na+ 0.202 —— 573:33
0.299 Na+ 0.299 -— 722:26
0.405 Na+ 0.405 —- 766: 9
0.608 Na+ 0.608 -- 932:34
0.697 Na+ 0.697 —— 1061:110
1.01 Na+ 1.01 -— 1091:40
0.399 Na+ 0.199 0.100 502’ 682:10
0.599 Na+ 0.199 0.200 soi' 917:30
0.799 Na+ 0.199 0.300 903‘ 1029:37
0.799 Na+ 0.199 0.200 902‘ 904:30
0.799 Na+ 0.199 0.600 N03- 998:20
0.799 Na+ 0.199 0.600 C104- 1029:20
0.090 K+ 0.090 —- 615: 4
0.180 x+ 0.180 -— 794:14
0.360 x+ 0.360 -— 1035:22
0.720 K+ 0.720 -— 1521:22
3:133 ES: 0 199 0.050 302' 834: 3
0.199 Na+ 2-
o 200 Rb+ 0.199 0.100 so4 1022:51
0.199 Na+ 2-
0.100 CS+ 0.199 0.050 so4 1097:22
°°199 Na: 0 199 0 100 302‘ 1461: 8
0.200 Cs ° ' 4

 

48
C. Dependence of the Rate on Ionic Strength

The rate of reaction was more sensitive tO the concen-
tration Of the cation than to ionic strength. Marcus'

treatment (Section III-B) indicates that a plot of In kr yg.
e-Kr should be linear and that the rate should increase with

increasing ionic strength for a positive charge product,

elez. Examination of the data in Table XXVIII shows there

 

is, if anything, a slight decrease in rate with an increase
in ionic strength when the concentration of cation is held
constant. The accuracy of the rate data does not show

whether or not the decrease is significant.

Table XXVII. Dependence of the rate on ionic strength in
sodium hydroxide solutions at 20.0°c

 

 

 

 

Concentrations (moles/liter) kr
Hydroxide Anion Na+ u (Mflsectl)
0.405 —- 0.405 0.405 766: 9
0.199 0.100 30:" 0.399 0.499 682:10
0.608 -— 0.608 0.608 932:34
0.199 0.200 303‘ 0.599 0.799 917:30
0.199 0.600 N03“ 0.799 0.799 998:20
0.199 0.600 C104" 0.799 0.799 1029:20
0.199 0.300 303' 0.799 1.099 1029:37
0.199 0.200 poi" 0.799 1.399 904:30

 

49

D. Dependence of the Equilibrium Constant on Temperature

The equilibrium constant depends markedly on temperature.
The equilibrium data are given in Table XXIX. It is possible
to determine the enthalpy of reaction, AHo, from the

relationship:
-AHO
eq RT

 

ln K + constant [33]

if one assumes that AHO is constant over the temperature
range. The data are plotted in Figure 3, AH° = 3950 cal/mole,

and A30 can be calculated from

AGO = AHO - TASO [34]
. 0:-
where. AG RTaneq
AGO = - 850 cal/mole
and AS° = —10.6 e.u. at 20.0°c.

E. Dependence of the rate on Temperature

The temperature dependence Of the rate was studied in
only one medium, 0.30 M_NaOH. The data Obtained are given

in Table XXX. The activation energy, Ea’ can be obtained

from the relationship:
E

— _§
In kr RT + constant [35]

and Ba = 7.65 kcal/mole (Figure 4). The data can be inter—

preted by the transition state equation (18):

kr = (kT/h)exp[As*/R - AHi/RT] [36]

rate constant

where: k

k = Boltzmann's constant

Table XXIX.

temperature

50

Dependence Of the equilibrium constant on

 

 

Initial concentrations (M'X 105)

 

.K

 

Ru04- Mnoi- Ruoi- Mn04 T(°C) eq
3.13 3.685 0.130 0.018 14.3 5.26
3.13 3.685 0.130 0.018 14.3 5.18
From Table II 20.0 4.32:0.25
3.15 3.70 0.104 0.00 24.7 3.90
3.93 2.46 0.130 0.00 24.7 4.22
3.15 3.70 0.104 0.00 24.7 4.11
3.14 3.67 0.124 0.018 32.0 3.54
3.92 2.45 0.155 0.012 32.0 3.36
3.14 3:67 0.124 0.018 32.0 3.57

 

51

 

 

 

 

 

I.
U
a, “T
X
C
l.4'-
Li-
].2 O l 1 l 1
3.25 3.30 335 3.40 - 3.46
'03/ T

Figure 3. Temperature dependence of the equilibrium
constant in 0.299 M NaOH.

Table XXX.

52

Dependence Of the rate on temperature in
0.299 M NaOH

 

 

 

 

Initial Concentrations (M_X 105) kr
RuO4- MnOi- Ruoi' Mno4' T ( 0c) (M_lsec-.'1)
3.13 3.685 0.130 0.018 14.3 572
3.92 2.455 0.163 0.012 14.3 587
3.13 3.685 0.130 0.018 14.3 573
3.92 2.455 0.163 0.012 14.3 576

See Table VIII 20.0 722126
3.15 3.70 0.104 0.00 24.7 902
3.93 2.46 0.130 0.00 24.7 905
3.15 3.70 0.104 0.00 24.7 904
3.92 2.45 0.155 0.012 32.0 1227
3.14 3.67 0.124 0.018 32.0 1301

 

In k,

53

 

7.3L-

 

 

 

 

325 3.30 3.35 3.40 3.45

Figure 4. Temperature dependence of the rate
constant in 0.299 M NaOH.

54

h = Planck's constant

H
II

absolute temperature

[>
U)

4+
ll

entrOpy of activation per mole

AH I enthalpy of activation per mole

:0
ll

gas constant

I?!
ll

activation energy per mole

AH = Ea - RT (for reactions in solution)

AG$ ' AHi - TASi .

From the above relationships, AHi = 7.07 kcal/mole,

AS* = — 10.7 e.u., and AG* = 10.2 kcal/mole.

VI. DISCUSSION

The values Obtained for AGO, AHO, and AS° were not

 

anticipated. The entropy change for the reaction

RuO4- + MnOi-

 

> Ruoi‘ + Mno4‘ [37]

would be expected to be near zero. The value AS0 = 1.7 e.u.
for the above reaction is calculated from the empirical

formula (40):

S°(MOr-IZ) = 40.2 + g- R In A - 9%0 [38]

where:

n = number Of "bare oxygen atoms

Z = charge on the anion

A = molecular weight Of the anion

r0 = M-O distance + 1.40 X.
The experimental result Of A§2_= — 10.6 e.u. is much tOO
different from the calculated value Of fig: = 1.7 e.u. to
attribute to experimental error. It was suggested to the

author that one or more Of the anions could possibly have

associated hydroxide ion (41). Hydroxide ion assoc1ation

can be represented by the following equilibrium:

_. _ +1...
MOE + OH ———> MO4OH(X )

< [39]
where M is Ru or Mn and M is 1 or 2, depending on the
oxidation state. The negative value of A80 for reaction

[37] suggests that the equilibrium constants for reaction

[39] are larger for ruthenate and permanganate than

y—.

L)

LT‘

56
perruthenate and manganate because reaction [39] would have
a large negative entropy. The equilibrium constant for re-
action [39] should also be larger for permanganate than
ruthenate because of size and charge contribution to electro—
static repulsion.

Comparison of the experimental rate constant with the
rate constants calculated from Marcus‘ equations is of
interest. A summary of the necessary calculations may be
found in the Theoretical section of this thesis. From
Marcus' equations (for reaction in solution of 0.20 ionic E

strength):

 

k 7.8 x 104 Mflsec.

r 5.76 2, crystal radii)

H
II

10.14 2, water molecule

6.2 x 107 Mflsec. (r
interposed).

k
r

The experimentally determined rate constant for reaction in
0.20 fl_sodium hydroxide solution was (Table XXVII):

kr = 5.7 x 102 fl-lsec._1
The agreement between the experimental value and the cal-
culated value for £_= 5.76 R is as good as can be expected.
The estimate of the rearrangement energy is undoubtedly low,
especially in view of the possible hydroxide ion association
with one or more of the anions. The increase in rate by

a factor of 1.10 predicted from Marcus' equations for a
change in ionic strength from 0.405 to 0.499 was not observed

(Table XXVIII). In fact, there may be a slight decrease

in rate with increasing ionic strength at constant sodium

57

and hydroxide concentrations. The increase in the rate with
size and concentration of the alkali-metal cation can prob-
ably be attributed to the ion-pairing abilities of the
larger cations; the larger cations shield the anions from
each other. The observed rate of reaction is thus affected
by both ion—pairing and association of the anions with
hydroxide. One cannot assess the contribution to the rate
made by these factors at present.

A comparison of the results from this investigation
with those obtained from the manganate-permanganate (7)
and ruthenate-perruthenate (Appendix) system is worthwhile.
In the manganate-permanganate exchange reaction Sheppard
and Wahl found for 0°C and 0.16 g sodium hydroxide:
-1

kr = 710 gflsec.

In the ruthenate—perruthenate exchange reaction, a value of

-1 ...1
kr > 104 M_ sec.

for 0°C and 0.10 g sodium hydroxide has been estimated.
For the "mixed" system of manganate-perruthenate a value
of

—1 _1

kr = 220 M. sec.

is calculated for 00C and 0.20 fl_sodium hydroxide from the
rate at 20.0°c and Ea = 7.65 kcal/mole. We note that the
manganate—perruthenate reaction is slower than either of
the two exchange reactions. The Q factor in the Marcus

theory would suggest a higher rate for the manganate—per—

ruthenate reaction since the value of AG0 is negative,

58

whereas the value of égP for the exchange systems is about
zero. On the other hand, the manganate-perruthenate reac-
tion may have a higher energy of rearrangement which would
predict a lower rate of reaction. In addition, the elec-
tronic vibrational levels of the ruthenium and manganese
species do not coincide so that the transmission probability
for the electron within the activated complex for manganate-
perruthenate is probably lower than the transmission prOb-
ability in either ruthenate-perruthenate or manganate-
permanganate° The lower rate in the manganate-permanganate
system in comparison to the ruthenate-perruthenate system
might be attributed to the association of permanganate with
hydroxide. Hydroxide association is consistent with the
negative value found for égo in the manganate-perruthenate
system.

The values of the activation energy and the entropy
and free energy of activation for the manganate—permanganate
reaction were determined by Sheppard and Wahl (7) to be

Ea = 10.5 kcal.

AS:t = -9 e.u.

AF: = 12.4 kcal/mole
for 0°C and 0.16 M sodium hydroxide solution. For the man—

ganate-perruthenate system

E = 7.6 kcal.
a
AS = -10.7 e.u.
at ,
AF = 10.2 kcal/mole

59

for 20.0°c and 0.30 M sodium hydroxide solution. The dif-
ferences can be attributed, at least in part, to experimental
error and to the different concentrations of sodium hydroxide.
One would expect, however, that the entropy of activation
would be more negative for the manganate—perruthenate sys-
tem, as is observed.

A comparison of the cation effect in the manganate—
permanganate and manganate-perruthenate reactions shows that
the former is more sensitive to the size and concentration
of the cation. For example, increasing the sodium ion con-
centration from 0.16 glto 0.99 g increases the rate of the
manganate-permanganate reaction by a factor of 2.4. In
the manganate-perruthenate reaction, a similar increase in
sodium ion concentration (0.20 g to 1.0 5) increases the
rate of reaction by a factor of 2.1. Similarly, the reac-
tion rate in manganate-permanganate is nearly doubled by
changing from 0.57 g sodium to 0.57 g potassium ion. The
rates of reaction for similar concentrations, interpolated
from the rate data (Table XXVII), indicate that potassium
ion is only 40% more effective than sodium ion in the man—
ganate-perruthenate reaction.

In the manganate-perruthenate reaction the entropy of
reaction, 駰 = -10.6 e.u., is essentially the same as the
entropy of activation, ég¢ = -10.7 e.u. Considering experi-
mental error, it is possible to estimate the difference
between the two entropies as high as 2 e.u. Thus the major

part of the entropy of activation is the entropy of reaction

60
which is, perhaps, not unreasonable when one considers that
the reaction is slower than predicted by Marcus' equations.
The major factor in the lower rate of reaction could then

be the entropy of reaction.

10.

11.

12.

13.
14.
15.
16.
17.

18.

19.

LITERATURE CITED

Lewis, J., and R. G. Wilkins, ed. "Modern Coordination
Chemistry," Chap. 2, by D. R. Stranks, p. 78-173.
Interscience, New York, 1960.

Halpern, J., Quart. Rev., 15, 207 (1961).

Frazer, R. T. M., Rev. Pure Appl. Chem. (Australia),
11, 64 (1961).

Sutin, N., Ann. Rev. Nuclear Sci., 13, 285 (1962).

Albery, W. J., Ann. Rep. Prog. Chem. (Chem. Soc. ),
60,40 (1963).

Brubaker, C. H., Record Chem. Progr., 24, 181 (1963).

Sheppard, J. C. and A. C. Wahl, J. Am. Chem. Soc., 12,
1020 (1957).

Hush, N. 8., Trans. Faraday Soc., 51, 557 (1961).

Laidler, K. J., Can. J. Chem., 37, 138 (1959).

Sacher, E. and K. J. Laidler, Trans. Faraday Soc.,
‘59, 396 (1962).

Marcus, R. J., B. Zwolinski, and H. Eyring, J. Phys.
Chem., §§, 432 (1954).

 

Marcus, R. A., J. Chem. Phys., 24, 966 1956
J. Chem. Phys., 26, 867 1957
J. Chem. Phys., gg, 872 1957

Marcus, R. , J. Chem. Phys., 43, 679 (1965).

Marcus, R. , J. Phys. Chem., 61, 853 (1963).

Can. J. Chem., 37, 155 (1959).

Marcus, R.

w 3’ P 3’

Marcus, R. ., Ann. Rev. Phys. Chem., 15” 155 (1964).
Strehlow, H., Ann. Rev. Phys. Chem., 16, 167 (1965).

Frost, A. A., and R. G. Pearson, "Kinetics and Mechan-
isms," 2nd Ed., Wiley, New York, 1961.

Benson, S. W., "The Foundations of Chemical Kinetics,"
McGraw-Hill, New York, 1960, p. 29.

61

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.
34.

35.

36.

37.

38.

62

Rasmussen, P. G., and C. H. Brubaker, Inorg. Chem.,
§J 977 (1964).

Herzberg, G., ”Infrared and Raman Spectra of Poly—

atomic Molecules," D. Van Nostrand, New York,
1945, p. 100.

Mooney, R. C. L., Phys. Rev., 31” 1306 (1931).

Silverman, M.'D., and H. A. Levy, J. Am. Chem. Soc., 16,
3317 (1954).

Pauling, L., "Nature of the Chemical Bond," Cornell
University Press, Ithaca, New York, 1960.

Badger, R. M., J. Chem. Phys., g“ 710 (1935).

Sidgwick, N. V., "The Chemical Elements and Their
Compounds," Clarendon Press, Oxford, 1950, p. 1481.

Larsen, R. P. and L. E. Ross, Anal. Chem., 31, 176(1959).

Nowogrocki, G., and G. Tridot, Bull. Soc. Chim. France,
684 (1965).

Connick, R. E., and C. R. Hurley, J. Am. Chem. Soc., 14,
5012 (1952).

Stoner, G. A., Anal. Chem. 219 1186 (1955).

Welcher, F. J., (editor), "Standard Methods of Chemical
Analysis," Vol. II, Part A, D. Van Nostrand, New
York, 1963, p. 874.

Bennett, R. M., and O. G. Holmes, Can. J. Chem., 41,
108 (1963).

Symons, M. C. R., J. Chem. Soc., 3676 (1954).

Carrington, A., and M. C. R. Symons, J. Chem. Soc.,
284 (1960).

Jezowska—Trzebiatowska, B., and J. Kalecinski, Bull.

Acad. Polon. Sci., Ser. Sci. Chim., Geol., Geogr.,
VII, 405 (1959).

Ibid., p. 411.
Ibid., p. 417.

Issa, J. M., S. E. Khalafalla, and R. M. Issa, J. Am.
Chem. Soc., 11, 5503 (1955).

39.

40.

41.

42.

43.

44.

63

Latimer, W. M., "The Oxidation States of the Elements
and Their Potentials in Aqueous Solutions",
Prentice-Hall, New York, 1952, p. 230 and 239.

Couture, A. M., and K. J. Laidler, Can. J. Chem., 35,
202 (1957).

Dye, J. L., private communication.

"Tables of SpectrOphotometric Absorption Data of Com-
pounds Used for the Determination of Elements",
International Union of Pure and Applied Chemistry,
Butterworths, London, 1963, p. 337-8.

Carrington, A., and M. C. R. Symons, J. Chem. Soc.,
3373 (1956).

Pode, J. S. F., and W. A. Waters, J. Chem. Soc., 717
(1956).

APPENDIX

THE ELECTRON EXCHANGE BETWEEN PERRUTHENATE AND RUTHENATE

IN ALKALINE AQUEOUS SOLUTION

64

A preliminary study of the electron exchange between
ruthenate and perruthenate showed that the exchange was too
fast to measure by the available techniques.

Stock solutions were prepared as described in Section
IV-A of this thesis. The 106Ru tracer was obtained as
Ru-106-Rh-106, carrier free, from Oak Ridge National Labora-
tory as RuCl3 in 61M HCl. It was added to one sample of
Ru(III) in 3 M_H2804 before the sodium bismuthate oxidation.
The concentrations of ruthenate and perruthenate in stock
solutions were determined spectrophotometrically as described
above (Section IV-B).

The experiments, in which perruthenate was separated
from the exchanging mixture, perruthenate solutions were
added to ruthenate, both in 0.10 M_NaOH, at 0°C and the
mixture was mechanically stirred. A quench solution con-
sisting of 4.00 ml of 0.1 M tetraphenylarsonium chloride in
0.1 M_perrhenate (ReO4-, a non-isotopic carrier) was added.
The precipitate was removed by suction and the supernatant
liquid was reserved for counting. When it had been learned
that exhange was very rapid, several experiments were car-
ried out with the quench solution added before the per-
ruthenate and the solution was stirred vigorously during
the addition.

In an effort to determine that the fast exchange was
not due to separation induced exchange, a second series of

experiments was carried out in which ruthenate was

65

66
precipitated. In these experiments ruthenate was added to
stirred perruthenate at 0°C in 0.1 M NaOH. .A quendh solu-
tion was prepared with 4.00 ml of saturated Ba(OH)a plus
5.00 ml of 0.01 a Naaso4 and was added rapidly to the ex-
change mdxture. The BaRuO4-Baso4 was filtered off and the
filtrate was reserved for counting.

Two-milliliter samples of the various supernatant
liquids were placed in one dram, screw-cap vials and were
counted in an integral, well-type, scintillation counter.
The energetic gamma rays (0.51-2.4 M.e.V.) from the 1°°Rh
daughter were counted after the solutions reached radio-
active equilibrium (a few minutes are required).

In all experiments conducted, even those with the
quench added before the reagents were mixed, complete ex-
change was Observed in the time of mixing and separating,
which is estimated to be 5-15 seconds for precipitation and
another 10-40 seconds for the filtration. Thus the exchange
must be complete in less than 5 seconds, if there is no
exchange between precipitates and the supernatant liquids.

In experiments in which perruthenate was precipitated,
the solutions were 2.5 x 10"5 M in Ruo‘a', 4.9 x 10'3 g in
Ru04', and 0.10 §(in Neon. Thus a second order rate con-
stant of 1.7 x 108 grlsectl is a lower limit. By similar
experimental procedures, Sheppard and wahl (7) measured half-
times as short as 0.25 seconds in the manganate-permanganate
exchange reaction. Thus is seems the exchange would be even

_1 ..
faster and a rate constant of 3.3 x 104 M; sec.1 is suggested.

67
In experiments in which ruthenate was precipitated,
concentrations were 2.8 x 10'5 g in RuO42-, 2.95 x 10‘5 g
in RuO4—, and 0.10 Mgin NaOH. These figures suggest a

1 -1
sec. for a 5

second order rate constant of 2.5 x 103 MI
second half-time and 4.8 x 104 Mflsectl for 0.25 second.
Electron spin resonance measurements were made on solu-
tions of 2.0 x 10"2 g RuO'42- in 2.0 g; NaOH and 1.0 x 10"2 g
RuO4- in 1.0 M NaOH in the hope that signals could be
detected which were suitable for measuring the exchange by
line broadening techniques. A very weak signal, probably
peroxide was found in the perruthenate solution and no
other signal was detected.
The exchange rate constant calculated from the equa-
tions of Marcus given in Section III-B of this thesis for
a Ru-Ru distance of 5.618 from crystalline potassium per-
ruthenate (23) is 5 x 102 firlsectl If we estimate that a
water molecule intervenes between the oxygens of the two
Ru-O units, 1.6 x 107‘Mflsec71 is calculated. The latter

figure is more-or-less in agreement with the estimates from

the experiments.