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PARTITIONING 0F ZINC BETWEEN SOLID AND LIQUID

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RICHARD CLEVELAND ZIELKE

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PARTITIONING OF ZINC BETWEEN SOLID AND LIQUID

IN SYNTHETIC AND SOIL MATERIALS

By

Richard Cleveland Zielke

A DISSERTATION
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Crop and Soil Sciences

1986

“r or» L. a» s» 1

ABSTRACT

PARTITIONING OF ZINC BETWEEN SOLID AND LIQUID
IN SYNTHETIC AND SOIL MATERIALS

By

Richard Cleveland Zielke

Metal activities in soil solutions and natural waters are
primarily a function of partitioning ‘between colloidal and aqueous

phases. For Zn2+

, solution activity is likely controlled by adsorption-
desorption rather than precipitation-dissolution reactions. Frequently
adsorption is irreversible and the resulting solution activity is much
lower than analytical detection limits. A batch equilibrium technique
based on isotopic dilution and mass balance was developed to study
adsorption and desorption of trace Zn2+ by Ca smectite (montmorillonite
# 25, Upton, Wyoming). The method was verified analytically and hence

applicable to the study of desorption in clay minerals. Desorption

hysteresis commonly occurred when <1% of the CEC was occupied by Zn.

Three isotherms (Linear, Freundlich and Langmuir) were tested to
determine their utility in characterizing Zn desorption. The Freundlich
equation proved most useful and enabled adsorption to be viewed over

2+

several decades of Zn activity. Comparison of model ion exchangers

(Ca. Dowex BOW-X8, Ca. Chelex-lOO) wit}: Ca. smectite and. Charity" clay

Richard Cleveland Zielke

(aeric. 'haplaquept) allowed. insight. to mechanisms operating in
adsorption, desorption and hysteresis. For smectite, reversibility was
attributed to an ion exchange mechanism while hysteresis was attributed
to strong bonding at broken edge OH. Hysteresis was ubiquitous in
Charity clay and was attributed to broken edge OH, A1 and Fe oxides,

free carbonates and organic matter.

The pH dependency of hysteresis at broken edge OH was
investigated. Only at pH 3.5 was adsorption by Ca smectite completely
reversible. As the pH increased, adsorption and hysteresis increased,
however reversibility at high surface occupancy of Zn verified that

smectites can mask precipitation in alkaline solution.

The effect of initial exchange ion on hysteresis was also
investigated using homoionic Na, K, Rb and Cs smectites. Adsorption
followed the lyotropic series, however adsorption and desorption by Rb
and Cs smectites was sterically inhibited at interlayer exchange sites
because Rb+ and Cs+ have a demonstrated ability to reduce swelling of
smectite minerals thus reducing the rate of Zn diffusion into and out of
the interlayer positions. Hysteresis in this case was merely an

artifact of nonequilibrium.

DEDICATION

TO MY MOTHER, BROTHERS, THEIR WIVES AND CHILDREN

ii

ACKNOWLEDGEMENTS

Deepest appreciation is extended to my nmjor professor Dr. Boyd
Ellis for his invaluable assistance in preparing this manuscript and the

friendship provided throughout the course of study.

Also gratefully acknowledged are Drs. M.M. Mortland, S.A. Boyd and

T.J. Pinnavaia who served on the graduate committee.

The friendship, expertise and unselfish dedication of Calvin
Bricker was also invaluable throughout the course of my studies and

hence warrants special thanks.

Appreciation is also extended to the People of the State of
Michigan who through taxation support the Michigan Agriculture

Experiment Station which provided financial support for this project.

iii

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES.

INTRODUCTION .

CHAPTER

I.

II.

III.

IV.

VI.

LITERATURE REVIEW .

ADSORPTION AND DESORPTION OF ZINC BY
SMECTITE: COMPARISON OF RADIOTRACER AND
ANALYTICAL METHODS .

Introduction .

Materials and Methods.
Results and Discussion .
Literature Cited .

DESORPTION OF ZINC FROM RESIN, SMECTITE
AND CHARITY CLAY .

Introduction .

Materials and Methods.
Results and Discussion .
Literature Cited .

EFFECT OF pH ON ADSORPTION AND DESORPTION
OF ZINC BY SMECTITE. . . . . . .

Introduction .
Materials and Methods.
Results and Discussion .
Literature Cited .

EFFECT OF INITIAL EXCHANGEABLE ION ON
ADSORPTION AND DESORPTION OF ZINC BY
SMECTITE .

Introduction .
Materials and Methods.
Results and Discussion .
Literature Cited .

SUMMARY AND CONCLUSIONS.

iv

. vi

. vii

l6

l6
18
2O
29

31
31
33
36
61
62

62

64

66
79

8O

8O
81
83
97

98

APPENDIX. . . . . . . . . . . . . . . . . . . . 102

LIST OF REFERENCES. . . . . . . . . . . . . . . 111

LIST OF TABLES
TABLE
CHAPTER II

1. Comparison of Freundlich and Linear isotherm
data at the lowest Zn level in the tracer
study.

CHAPTER III

1. Chemical properties and mass of adsorbent
used in batch adsorption experiments .

2. Summary+ of linear regression equations
for Zn adsorption by Ca chelex, Ca Dowex,
Ca smectite and charity clay .

3. Values of D 1 for adsorption of Zn2+ on
Ca Dowex, Cg Chelex, Ca smectite and
charity clay .

4. Equilibrium pH and Zn activity for Ca Chelex
adsorption isotherms . . . . . . . .

CHAPTER IV

1. Initial Zn2+ levels and equilibrium pH's for
Zn adsorption by Ca smectite . . . . .

CHAPTER V

1. Initial Zn2+ concentrations and equilibrium
pH's for the adsorption of Zn by
homoionic smectites. . .

2. Effect of interlayer cation on basal d(001)

spacings of Wyoming montmorillonite immersed
in water .

vi

PAGE

27

34

37

. 43

. 49

. 66

. 83

. 9O

LIST OF FIGURES
FIGURE PAGE
CHAPTER II

1. Comparative adsorption of Zn by Ca smectite
using analytical and radiotracer methods . . . 21

2. Desorption of Zn from Ca smectite as
measured by analytical methods . . . . . . . . 22

3. Desorption of Zn from Ca smectite as
measured by radiotracer methods. . . . . . . . 23

4. An illustration of the Linear equation data
variability for adsorption and desorption of
Zn as measured by radiotracer methods. . . . . 26

CHAPTER III

1. Adsorption and desorption of Zn by Ca Dowex
ion exchange resin fit to the Linear equation. 39

2. Adsorption and desorption of Zn from Ca Dowex
ion exchange resin fit to the Freundlich
equation . . . . . . . . . . . . . . . . . . . 4O

3. Adsorption and desorption of Zn by Dowex ion
exchange resin fit to the Langmuir equation. . 41

4. Desorption of trace amounts of Zn by Ca Dowex
ion exchange resin as measured by the Linear
equation . . . . . . . . . . . . . . . . . . . 42

5. Adsorption and desorption of Zn by Ca Chelex
ion exchange resin fit to the Linear equation. 45

6. Desorption of trace amounts of Zn by Ca Chelex
ion exchange resin as measured by the Linear
equation . . . . . . . . . . . . . . . . . . . 46

7. Adsorption and desorption of Zn from Ca Chelex

ion exchange resin fit to the Freundlich
equation. . . . . . . . . . . . . . . . . . . . 47

vii

Adsorption and desorption of Zn by Ca Chelex
ion exchange resin fit to the Langmuir

Adsorption and desorption of Zn by Ca smectite
at pH 6.6 fit to the Linear equation.

Adsorption and desorption of Zn by Ca smectite
at pH 6.6 fit to the Freundlich equation.

Adsorption and desorption of Zn by Ca smectite
at pH 6.6 fit to the Langmuir equation.

Desorption of trace amounts of Zn by Ca
smectite pH 6.5 as measured by the Linear

Adsorption of Zn by Ca smectite

desorption
fit to the

desorption
fit to the

desorption
fit to the

desorption
pH 3.5.

desorption
pH 4.5.

desorption
pH 5.9.

desorption
pH 6.5.

desorption
pH 7.0

desorption
pH 7.7

of Zn by a Charity
Linear equation .

of Zn by a Charity

Freundlich equation .

of Zn by a Charity
Langmuir equation.

of Zn by
of Zn by
of Zn by
of Zn by

of Zn

of Zn by

as a function

Effect of time on the adsorption of Zn by pH
4.5 Ca smectite at three initial Zn levels .

equation
9.
10.
11.
12.
equation
13. Adsorption and
clay at pH 7.4
14. Adsorption and
clay at pH 7.4
15. Adsorption and
clay at pH 7.4
CHAPTER IV
1. Adsorption and
Ca Smectite at
2. Adsorption and
Ca smectite at
3. Adsorption and
Ca smectite at
4. Adsorption and
Ca smectite at
5. Adsorption and
Ca smectite at
6. Adsorption and
Ca smectite at
7.
of time and pH .
8.
9.

Effect of time on adsorption and desorption
of Zn by Ca smectite at pH 4.5.

viii

. 48

. 51

52

53

54

56

57

58

67

69

70

71

72

73

75

76

. 77

CHAPTER V

Adsorption
Adsorption
Adsorption
Adsorption

Adsorption

smectites as a function of time .

Effect of time on
smectite at three

Effect of time on
smectite at three

Effect of time on
smectite at three

Effect of time on
smectite at three

the adsorption of

initial Zn levels .

the adsorption of

initial Zn levels .

the adsorption of

initial Zn levels .

the adsorption of

initial Zn Levels .

ix

and desorption of Zn by Na smectite.
and desorption of Zn by K smectite
and desorption of Zn by Rb smectite.
and desorption of Zn by Cs smectite.

of Zn by alkali metal saturated

Zn by Na
Zn by K
Zn by Rb

Zn by Cs

84

. 86

87

88

. 89

. 91

. 92

. 93

. 94

INTRODUCTION

Zinc retention by soils and soil materials has been the subject of
extensive research due to the fact that Zn is both an essential
micronutrient which has been deficient in many soils and a potential
environmental hazard” Several soil components have been isolated and
shown to effect removal of Zn from soil solution. These include Fe, A1
and Mn oxides, CaCO3, humic materials and clay minerals. In order to
elucidate the mechanism. of adsorption, studies using synthetic and
natural components ensued; however this approach has been criticized as
being environmentally unrealistic owing to the complex interaction of
soil colloids. Ironically, it was the comparison of single components

and whole soils that revealed these interactions.

Recently, there has been a resurgence of adsorption studies
utilizing whole soils and/or soils which are treated to selectively
remove individual fractions associated with Zn retention. In light of
the heterogenous nature of soil, it is not surprising to find
conflicting evidence for adsorption and precipitation. The
interrelationship ‘between surface area, structure and reactivity of
clays with metal emphasizes the importance of pure clay mineral studies.
The role of organic matter in adsorption, chelation and mobilization of
metals has also been demonstrated. The observation that metal retention
by some soils closely resembles the behavior exhibited by amorphous Fe
and Al oxides, and the subsequent role of surface hydroxyl groups in

"specific adsorption" has furthered the debate over the mechanism of Zn
1

retention in soils. Indeed, progress in this area of research can be
likened to Jenny's (1961) soil acidity merry-go-round in which each turn
produces a different though not unfamiliar view of what was termed the

soil chemistry landscape.

There can be little doubt that no single component controls Zn
retention and release in all environmental systems. Certainly, the
often reported failure of solubility principles to characterize Zn2+
reactivity in soil is reason enough to pursue an adsorption approach.
Reports that Zn is mainly associated with the mineral fraction in many
soils and sediments, combined with the recent interest in clay minerals

as sorbents for metallic and radioactive waste is the basis for

selecting smectite clay as the adsorbent phase in the present study.

Although adsorption of Zn by smectite minerals has been studied
and numerous fractionation and extraction schemes have been proposed,
few, if any contemporary studies have focused on true desorption over a
wide range of surface compositions. Many such studies have failed or
neglected to control pH or ionic strength, or have attempted desorption
using unrealistic concentrations of acids, competing ions or chelating

agents.

The objective of this study was to characterize Zn desorption in
response to pH and surface composition variables. More specifically,
the objectives were to (i) verify the applicability of the principles of
isotopic dilution to adsorption of trace amounts of Zn2+ by smectite,
(ii) determine the applicability of selected adsorption isotherms in
characterizing desorption phenomena for some model exchangers, (iii)

determine the effect of pH on adsorption and desorption of Zn2+ by Ca-

smectite, and (iv) determine the effect of initial exchange ion on Zn2+

adsorption and desorption by smectite. The results of these basic
studies will hopefully have application to waste disposal engineering as

well as conventional agriculture.

LITERATURE REVIEW

Mechanistically, removal of Zn2+ from solution by soils and clays
affords extreme ambiguity. In absence of microrganisms, living plant
roots and soluble organic ligands, two general processes are possible;
precipitation and adsorption. For the .purpose of this discussion,
adsorption is the general process whereby solute adheres to the surface
of a soil particle. Chemisorption. is adsorption resulting from a
specific chemical reaction, hence the term "specific adsorption". Ion
exchange is the adsorption process by which charged solutes exchange
with ions on a soil particle. Precipitation is a related process in
that it is generally preceded by adsorption; the difference being that
adsorption is a two dimensional process, while precipitation is a three

dimensional process (Corey, 1981).

The reactivity of solutes with soils and clays is generally
characterized by an adsorption isotherm. Because of their empirical
nature, adsorption isotherms fail to distinguish between the totality of
processes resulting in the attainment of equilibrium, and hence cannot
be used to distinguish the sorption mechanism (Veith and Sposito, 1977).
A detailed description of various adsorption isotherms and their use is
given by Travis and Etnier (1981). Of these, three have found extensive
use in describing the equilibrium between reactive solutes and soil

components. These are the Linear, Freundlich and Langmuir isotherms.

The Linear adsorption isotherm. is an empirical equation that
relates the quantity of solute adsorbed (X) per unit mass of adsorber

(m) to an equilibrium solution concentration or activity (C). Thus,
X/m - kC
where k is the distribution coefficient.

Few adsorption processes in soil obey this equation, but it has
been used in conjunction with transport equations to describe
radionuclide transport from geologic repositories (Burkholder, 1976) and

2+ in soil columns (Lai et al., 1978).

adsorption of Na+ and .Mg
Frequently the observed isotherm is nonlinear (Frost and Griffin, 1977;
Maquire et al., 1981; Brummer et al., 1983; Harter, 1983), depicting a
rapid rise in adsorption followed by a bending over or tailing off to a
constant value. One consequence of the asymptotic behavior at high
equilibrium solute levels is that it provides first-hand observation of
the adsorption capacity. Also the isotherm allows direct viewing of the
relationship between solute and solid. McLaren et a1. (1983) used this

fact to characterize Cu2+ desorption hysteresis from humic acid, Fe and

Mn oxides and montmorillonite.

Several researchers have described Zn adsorption using the

nonlinear equation proposed by Freundlich (1926),
X/m - KCl/n

where n and K are empirical constants. The equation may be linearized

by taking the log of both sides:

log(X/m) - l/n log(C) + log(K)

Thus a plot of log(X/m) vs log(C) yields a straight line if the
data conform to the Freundlich equation. The equation has one advantage
in that it can be used to view adsorption over several orders of
magnitude; however, like the Linear isotherm it fails to predict the
adsorption capacity. Furthermore, log-log plots tend to minimize data

variability and the two constants allow for easy curve fitting.

The Freundlich isotherm has been used to characterize desorption
hysteresis. Barney (1984) used the ratio of the Freundlich exponents
Ns/Nd (where Ns and Nd are the measured exponents for sorption and
desorption, respectively) as a measure of the magnitude of hysteresis in
radionuclide desorption from Columbia River basalt materials. Elrashidi
and O'Connor (1982) used the Freundlich equation to describe Zn sorption
and desorption from nine soils of varying physical and chemical
properties. Desorption of Zn from all soils was extremely hysteretic

even after five desorption cycles using .01 N CaClZ.

The Langmuir equation (1918), unlike the others, is derived from
the kinetic theory of gases. It's adaptation to solid-liquid adsorption
phenomena in soils was proposed by Boyd et a1. (1947). Of the many

forms derived, two have found frequent usage:
C/X/m - l/Kb + C/b
X/m - KbC/(1+KC)

where K is a measure of the bond strength, b is the adsorption maximum

and C is the ion activity.

In applying the Langmuir equation monolayer adsorption and uniform
bonding energy are assumed. Based on the heterogeny of soils and clays,
seldom are these assumptions met. NOnlinearity has been attributed to
sites of differing bonding energy, hence two surface isotherms have been
proposed (Shuman, 1975, 1977). This approach has been the subject of
recent controversy (Sposito, 1982; Posner and Bowden, 1980), and it was
suggested. that independent evidence for sites of different bonding
energy be provided before attempting to use the two surface equation.
Curvilinear isotherms have also been attributed to the a lack of
consideration of desorbed ions in exchange processes (Griffin and Au,
1977; and Harter and Baker, 1977). Since extreme variability can result
from the division of the measured quantities (C) and X/m, no attempts to

use the Langmuir equation to describe desorption have been reported.

Any discussion of Zn2+

adsorption by smectites should logically be
preceded by a brief description of their chemical nature in relation to
their properties. Smectites are layer lattice silicates formed through
weathering of igneous rocks such as granite and basalt. Their behavior
and abundance in soils and sediments make smectites an important class
of minerals from both an agricultural and environmental standpoint.
Among the most noted properties affecting ion adsorption are the

tremendous surface area (8 x 105 m2 kg'l) and high CEC (80-150 cmol(+)

kg'l).

Smectites are comprised of a central alumina octahedra sandwiched
between two silica tetrahedra. The tips of the two tetrahedra are
oriented such that apical O are shared with O of the alumina octahedra.

The result is a continuous two dimensional network extending in the a

and b dimension with individual 2:1 units stacked in the c dimension
(Grim, 1968). Depending upon the layer charge, 0 atoms of adjacent
structural 'units form.'bonds which. may 'be cleaved to allow lattice
expansion. The magnitude of the surface charge and occurrence of
exchangeable cations between structural units, in accordance with the
principal of electrical neutrality, is the result of localized electron
density due to substitution of A13+ for Si4+ in the tetrahedral and Mg2+
and Fe2+ for A13+ in the octahedral layers. This type of surface charge
is termed permanent CEC. Fbr the dioctahedral mineral montmorillonite
#25 used in this study, the CEC (90 cmol(+) kg'l) is mostly attributed
to octahedral substitution while the swelling properties are attributed
to the 'moderate surface charge. and. hydrated. nature of exchangeable

cations.

In addition to lattice substitution, cation exchange sites are
thought to arise from the existence of broken bonds in the a-b
dimension. Such broken 0 bonds and edge OH's are considered to undergo
ionization and exchange under alkaline conditions and hence are termed
pH dependent sites (Borchardt, 1977). Helfferich (1962) generalized ion
exchange on soil colloids as being an electrostatic phenomenon which is

diffusion controlled, stoichiometric and reversible.

There are several reports of non-reversible exchange of cations in
pure mineral studies involving both neutral salts and transition metals.
The inability to attain the same position of equilibrium when approached
from either direction has been termed hysteresis or fixation. Vanselow
(1932) observed hysteresis in Ca2+-NH4+ exchange on bentonite. Wiegner

(1935) attributed irreversibility to the existence of sites having

different geometries and. bonding energies. Based on electrostatic
principles, broken edge OH's, octahedral substitution and tetrahedral
substitution should provide for a range of sites with different bonding

energy.

Some researchers have attributed hysteresis to the imperfect
dispersion of flocculated clays and resulting inaccessibility of
exchange sites (Van Bladel and Laudelout, 1967; Tabikh et al., 1960).
Marshall (1964) attributed hysteresis to the possibility of attaining
minimum free energy at more than one substrate composition. More

recently, Maes and Cremers (1975) considered hysteresis in Zn2+

exchange
with smectite to be composition and pH dependent. Adsorption was
completely reversible at low surface occupancy and pH, but was neither
stoichiometric nor reversible at high surface occupancy. The reaction
could be made reversible by decreasing the pH. Due to the apparent role
of OH', hysteresis was attributed to specific bonding. The validity of
this work must be questioned since specific bonding , if it occurs, is

considered a high affinity phenomenon and hence is expected at low

surface occupancy.

The nonreversible sorption of Zn by bentonite was reported by
Elgabaly (1950). He proposed that Zn not removed by 1 M neutral
NH4(OAC) became fixed in alumina octahedra resulting in a permanent loss
of CEC. DeMumbrum and Jackson (1956) furthered this concept by
proposing specific adsorption. of Zn. by montmorillonite. Based on
perturbations of OH in IR studies, Zn retained in excess of the CEC was
thought to be associated with octahedral OH groups. Tiller and Hodgson

2+

(1962) proposed that Zn specifically adsorbed by nmmtmorillonite in

10

the presence of excess electrolyte (thereby‘ eliminating 'nonspecific
electrostatic sorption) was of two forms. One species exchangeable with
Cu2+, N12+, Mn2+ and Fe2+ was considered to be associated with broken
edge OH's, while the smaller nonexchangeable fraction was the result of

lattice penetration.

Specific adsorption (of Cu2+) on smectite has been challenged by
McBride and Mortland (1974). Using IR, XRD, ESR and thermal methods,
Cu2+ was shown to enter the hexagonal holes of the silicate structure
upon dehydration. Reduction in the CEC was attributed to further
penetration into the unoccupied hole in the octahedral layer. Upon

Cu2+

rehydration, in hexagonal positions was free to move, but

octahedral Cu2+

remained fixed, resulting in permanent loss of layer
charge. Since the temperature used by DeMumbrum and Jackson (1956) was
not sufficient for total dehydration of Cu2+, lattice penetration could
not have occurred. It was suggested that excess Cu retention was the
result of incomplete removal of' Cu(OAC)2 ‘While the IR. shift was
attributed to formation of K smectite during the preparation of a KBr

pellet. As a result, specific adsorption via this mechanism at

temperatures < 150 C seemed unlikely.

The reaction of silicic acid with montmorillonite is also thought
to result in the formation of specific adsorption sites for transition
metals (Hingston et al.,l972), although this interaction is considered
to be a surface adsorbed layer rather than lattice penetration (Tiller,

1967).

2+

Several factors have been shown to affect adsorption of Zn and

other metals by smectite. Nelson and Melsted (1955) observed that the

11

2+ Ca2+

relative adsorption of different cations in clays was H+ > Zn >

>Mg2+ > KI, and suggested that retention of applied Zn may be affected
by ions on the sorption complex. It is likely that the H+ was really
Al3+ in their experiments due to clay lattice breakdown. Garcia-
Miragaya and Page (1977) determined the effect of initial exchangeable
ion on sorption of Cd by montmorillonite. Sorption was related to ion
size and polarizability factors and decreased along the series Na+ > K+
> Ca2+ >A13+. Increasing ionic strength has also been shown to reduce
metal sorption through complexation with inorganic ligands. In
addition, solution composition was shown to affect adsorption since some
ligands (eg. 8042') have a larger tendency to form ion pairs in solution
(Garcia-Miragaya and Page, 1976; Mattigod et al., 1979). Mattigod and
Sposito (1977) compiled. experimental association constants for

complexation of Zn2+

with several inorganic ligands. Such data allow
prediction of solution species available for adsorption or transport

based on the ionic strength and solution composition.

Since the mechanism of adsorption cannot be determined from
adsorption isotherms, indirect methods have been used. The fact that
Zn2+ adsorption was complete in 15 minutes suggested a ion exchange
mechanism (Bourg and Filby, 1974). In a later study this hypothesis was

2+ in solution was in kinetic

confirmed by demonstrating that Zn
equilibrium with Zn adsorbed on the surface of montmorillonite (Bourg
and Filby, 1976). Bingham et a1. (1964) also suggested an ion exchange

mechanism since Zn retained by H-montmorillonite did not exceed the CEC

if the solution pH was low enough to prevent Zn(0H)2 formation.

12

Singhal and Kumar (1977) used the exchange isotherm approach of
Gaines and Thomas (1953) to calculate thermodynamic parameters for Zn2+
exchange on Mg-bentonite. Zinc exchange was found to be endothermic,
however the use of thermodynamic approaches has been questioned since

exchange is not always stoichiometric or reversible for metals which

form hydroxy salts (Maes and Cremers, 1975).

Farrah and Pickering (1978) used selective extraction procedures
to characterize nonexchangeable Zn on montmorillonite, illite and
kaolinite. Solvents were classified as acid, protonated, ligand and

competing species, and their efficiency at removing Zn2+

previously
sorbed at pH 5 and 7 was evaluated. While EDTA could completely remove
sorbed Zn at both pH's, competing species exhibited a pH dependence. At
pH 5 where exchange mechanisms have been proposed, sorbed Zn could be
removed completely with 0.1 M NaNO3 or 0.05 M CaC12. At more dilute
concentrations extraction was incomplete, but the fact that some
reagents resulted in total recovery is evidence of minimum
irreversibility.‘ The pH dependence of extraction suggests that clays

are polyfunctional, containing mostly traditional exchange sites with

some sites exhibiting affinities for protons and metal ions.

The pH dependency of Zn2+

reactions in clays has received
considerable attention. While clays appear to act as nucleation centers
for Zn-hydroxy species (Farrah and Pickering,1976), there is no known
physical evidence for a precipitated solid phase. Much of the evidence

is based on solubility principles wherein thermodynamic data is either

unavailable or inaccurate due to analytical limitations.

13

In pure clay studies marked uptake of Zn2+

increased when the pH
exceeded the formation constant of Zn(OH)2 (Farrah and Pickering, 1977.
In other studies adsorption in excess of the CEC has been attributed to
the formation of ZnOH+ in bulk solution (Hodgson et al., 1964), but
based on calculations of the Zn2+/ZnOH+ ratio, this explanation assumes

preference for the 'hydrolyzed. species 'which seems unlikely from an

electrostatic viewpoint (Bingham et al., 1964).

Frost and Griffin (1977) suggested that Zn2+

adsorption from
landfill leachate occurred by ion exchange at pH's < 6, while
precipitation as Zn(OH)2 resulted at higher pH's. Farrah and Pickering
(1976) observed precipitation of Zn(OH)2 in pure solution at pH's > 6.5
followed by dissolution and formation of the zincate anion at pH's >
10.5. In the presence of montmorillonite the pH required for
precipitation was reduced by 0.5 units. Furthermore, since
deprotonation and dissociation did not occur at high pH, chemisorption,
not simple precipitation was implied. It should be noted that the

conclusions in both these studies were based solely on comparisons of

isotherms obtained in the presence and absence of clays in solution.

Up to this point the discussion has focused on reactions of Zn2+

involving pure clay minerals. Even in such homogeneous materials there
is a general lack of distinction between adsorption and precipitation
processes. Furthermore the occurrence of hysteresis, specific bonding
and the debate over the role of surface OH's in Zn retention has not
been fully resolved. The behavior of Zn2+ in the presence of whole
soils and soil clays, though not completely different, is unique enough

to present a brief review for contrast and comparison. More extensive

14

reviews are given by Lindsay (1972), Nicholas and Egan (1975) and Shuman

(1980).

Zinc retention in soils has been attributed to a variety of
components besides clay minerals. Some studies have reported
significant correlations with the CEC (Shuman, 1975), while others have
not (Harter, 1983). Many researchers have emphasized the importance of
organic matter (Tyler and McBride, 1982; Kuo and Baker, 1980).
Retention of Zn2+ by acid subsoils indicates that Al, Fe and Mn oxides
may control Zn adsorption (Kalbasi et al., 1979; Shuman, 1976, 1977;
Kinniburg and Jackson, 1982; McBride and Blasiac, 1979). Adsorption of
Zn on Ca and Mg—carbonates has also been reported (Jurniak and Bauer,
1956). Tiller et a1. (1984) fractionated several soils and identified
different magnitudes of influence for Zn adsorption by organic matter,
A1 and Fe oxides and clays. All these materials are presumed to sorb
Zn2+ through different mechanisms (Cavallaro and McBride, 1984).

Regardless of the mechanism of adsorption, soils exhibit a definite pH

effect (Kurdi and Donner, 1983; Bar-Yosef, 1979; Harter, 1983).

There is general agreement among researchers that Zn retention in
acid soils occurs on a variety of soil components and that Zn2+ in the
soil solution is controlled by adsorption-desorption reactions.
Conversely, there is sufficient evidence for Zn precipitation in

alkaline soils. Among the various Zn2+

controlling ’solid phases
suggested are Zn-carbonate (Udo et al., 1970), Zn-phosphate (Kalbasi et
al., 1978), Zn-silicate (Tiller and Pickering, 1974), ZnS (Kittrick,

1976) and Zn(OH)2 (Saeed and Fox, 1977). Lindsay (1979) reported that

15

2+

many of these compounds were too soluble to control Zn activity, and

proposed the existence of the unknown compound "soil Zn".

While precipitation of Zn undoubtedly occurs in some soils,
distinction between the adsorption-precipitation boundary is difficult.
Recently Brummer et a1. (1983) investigated this problem, and concluded
that Zn2+ in equilibrium with whole soils below pH 7 was controlled
exclusively by adsorption-desorption processes. In neutral to alkaline
soils precipitation is likely only if sufficient Zn2+ is added to ensure
complete saturation of the adsorption complex. Such observations
emphasize the importance of clays, A1 and Fe oxides, carbonates, humus
and soluble ligands in masking precipitation reactions in soils, and
further imputes a need to understand adsorption and particularly

desorption phenomenon in soils and clays.

CHAPTER II
ADSORPTION AND DESORPTION OF ZINC BY SMECTITE:

COMPARISON OF RADIOTRACER AND ANALYTICAL METHODS

Introduction

Much of the evidence for removal of Zn2+

and other heavy metals
from solutions by soils and clay is expressed in the form of an
equilibrium adsorption isotherm. Failure to attain the same position of
equilibrium when approached from the opposite direction is termed
hysteresis, and there is extensive chemical evidence for hysteresis
when heavy metals are adsorbed by soils (Kuo and Mikkelsen, 1979;
Elrashidi and O'Connor, 1982) and pure clay minerals (Tabikh et al.,

1960; Van Bladel and Laudelout, 1967; McLaren et al., 1973: Maes and

Cremers, 1975).

Because of the large surface area and high CEC, smectite clays are
considered to contribute to Zn retention in many soils. Among the
mechanisms proposed for Zn retention by smectites are ion exchange
(Bourg and Filby, 1976; Bingham et al., 1964), specific adsorption
(Brummer et al., 1983), and precipitation (Frost and Griffin, 1977).
Generally, cation exchange is suggested if the reaction is rapid,
stoichiometric and most importantly, reversible (Helfferich, 1962).
Hysteresis is usually associated with non-reversibility in the low end

16

17

of the adsorption isotherm where precipitation seems unlikely (Tiller
and Hodgson, 1960; Tiller et al., 1984). As a result such hysteresis

has been termed "specific adsorption".

Demumbrum and Jackson (1956) proposed that specific adsorption of

2+ 2+

Cu and Zn was the result of lattice penetration, but McBride and
Mortland (1974) have demonstrated using IR, ESR and thermal methods that
temperatures exceeding 150 C were required for this process. While
these physical methods 'have proven useful in studying the surface
chemistry of clays, they are not sensitive enough or not applicable to

the study of Zn2+

at low surface occupancy where hysteresis is often
observed. Similarly, the ability of clays to effect almost complete

removal of metal ions from solution poses some unique analytical

problems to characterization of hysteresis using chemical methods.

In the present study 652n was used as a tracer to enable
characterization of adsorption and desorption of Zn2+ by smectite in the
trace region. In light of reports of irreversible sorption,
precipitation and specific adsorption, there is no guarantee that
isotopic equilibria will occur at all substrate levels. The objectives
of this study were to determine if the principles of isotopic dilution
are valid over a wide range of surface compositions, and to develop
techniques to further study adsorption and desorption of trace amounts
of Zn2+ by Ca smectite. To accomplish these objectives, batch
adsorption experiments using 65Zn as a tracer were compared to results

2+

obtained over an analytical range in which Zn could be determined by

standard AA methods.

18

Materials and Methods

Preparation of Ca,smectite

A given weight of smectite (Montmorillonite # 25, Upton, Wyoming)
was dispersed in distilled, deionized H20 by stirring for 24 hr. The
colloidal portion was obtained by repeated sedimentation and decantation
of the < 2uM fraction. Ca smectite was prepared by equilibrating this
fraction with 1 M Ca012 (pH 6.0) for a period of 24 hr. At the end of 5
equilibrations the Ca clay was dialyzed against distilled, deionized H20
until a negative test for 01' was obtained using AgNO3. The resulting
clay was suspended in 0.01 M CaC12 and stored until ready for use. The
CEC of the clay was determined to be 90 i 2 cmol (+) kg'1 using the
NHAOAC-NaOAC method of Jackson (1958), and the pH was measured to be 6.5

i 0.2 using a standard reference electrode. XRD was conducted but

revealed no other detectable minerals.

Adsorption isotherms

Batch adsorption experiments were initiated by pipetting 25 mL of
the rapidly stirred clay suspension into tared 50 mL Oak Ridge
centrifuge tubes. The clays were centrifuged at 3000 RPM for 5 min and
the mass of clay used ( 3.3 i 0.1 x 10'4 kg) and solvent entrained ( 3.6
i 0.1 x 10'3 kg) were determined gravimetrically on 6 randomly selected

tubes by drying at 105 C for 48 hr.

In the nonradioactive study each of the 12 treatments were
duplicated and received 21.4 mL 0.01 M CaC12 containing from 13.2 uM to

12.8 mM Zn2+ as ZnC12 + 1 mL supporting electrolyte. Three replications

2+

were run in the tracer study, and 16 initial Zn concentrations ranged

19

from 9.3 nM to 12.8 mM. In addition, each tube received 1 mL lmCi 65Zn
L'l' The initial Zn2+ concentrations were calculated on a 26 mL basis.
All treatments were dispersed on a Vortex mixer and equilibrated for 1
wk at 27 i 1 C on a wrist action shaker. The samples were separated by
centrifugation as previously described, and 4ml was removed for

analysis.

For the analytical study Zn2+

in the equilibrium solution was
determined by standard AA methods using a Varian AA6 with an air-
acetylene flame. Radiometric data were obtained.<n1 a Packard Tri-Carb

spectrometer equipped with a gamma counter by comparing sample

radioactivity with that obtained for known 65Zn standards of the same

geometry. Equilibrium ‘values were calculated using principles of
isotopic dilution. In both cases Zn adsorbed was calculated by
difference from the initial concentration . Where appropriate , Zn2+

activity was calculated from the extended De Bye—Huckel equation using

an ionic strength of 0.03.

Desorption isotherms

Desorption was accomplished by replacing the 4 mL sample with 0.01
M CaC12 and re-equilibrating for 1 wk. At the end of this period
radiometric and AA analyses were repeated. In this fashion 6 desorption
cycles were accomplished. Data for adsorption and desorption isotherms
were calculated using a mass balance approach. For a more detailed
description of this calculation the reader is referred to the BASIC

computer programs "ZNCALC" and "NUCALC" listed in the appendix.

20

Results and Discussion

The comparative adsorption of Zn2+

as measured by radiotracer or
analytical methods is presented as a Freundlich isotherm (Figure 1).
Except for the lowest analytically determined Zn2+ level, relatively
good agreement was obtained between the two methods. Bourg and Filby

(1976) also reported that 65

Zn was isotopically exchangeable with Zn
adsorbed by smectite, however Tiller et a1. (1972) reported that 65Zn in
alkaline soils did not undergo complete isotopic exchange, possibly due
to fixation. lkumn et a1. (1963) attributed lower rates of isotopic
exchange to high bond energies of P in a Mn phtalate precipitate. Such
results suggest isotopic exchange may be useful in studying high

affinity adsorption in clay minerals since the existence of such sites

could result in non attainment of isotopic equilibria.

Another point to note in figure 1 is that data do not conform to
the Freundlich equation. Similar behavior for Zn2+ adsorption in soils
has been attributed to multiple bonding mechanisms or adsorption at
sites of different energies (Kuo and Mikkelsen, 1979; Elrashidi and

O'Connor, 1982).

Freundlich desorption isotherms are presented for both methods in
figures 2 and 3. Desorption appears to be dependent on the extent of
surface coverage. Based on calculations using the CEC, 1 symmetry of
Zn2+ - 450 uM g'1 (or log (X/m) - 2.65). The highest fractional loading
of Zn observed in this study was .65 x CEC. In both studies desorption
hysteresis begins to occur at log (X/m) = 0.5 or 3.2 uM Zn/g. Thus
desorption hysteresis occurs when < 1% of the surface is occupied by Zn.

At higher surface occupancies the reaction is completely reversible as

21

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23

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Eggggmogquuofiflg .mwnsmflm

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an 2 m:

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24

indicated by the proximity of the desorption points to the adsorption
isotherm. The resulting hysteresis may be interpreted as evidence of
sites of higher bonding energy at low surface coverage. Tiller et a1.
(1962) also reported non-reversible adsorption of Zn by smectite at low
surface coverage, however Maes and Cremers (1975) observed hysteresis at
high surface occupancy. In the later case, smectite was pretreated at

pH 3.5 which may have resulted in formation of hydroxy-A1 compounds.

There are several interesting points to note in Figure 3. First
is the fact that hysteresis begins around the inflection point of the
nonlinear isotherm. This again. may be an indication of multiple
adsorption mechanisms or sites with different bonding energy, however in
absence of independent mechanistic evidence, this explanation remains
unconfirmed (Veith and Sposito, 1977). Secondly, at intermediate Zn2+
levels, sequential dilution of the solution phase produced a horizontal
line in the direction of the ordinate (i.e. hysteresis). Desorption
points below log (X/m) - -1 depict an increase in solution concentration

with no subsequent decrease in solid phase composition, a result which

is physically impossible.

Two explanations for this behavior are offered” First, is the
probability of experimental error at very low solution levels and the
insensitivity of log-log plots to reflect changes in the solid phase
composition as a result of minute changes in the solution phase. This
fact is evident in both the linear and log transformed data (Table 1).
Comparison of figures 3 and 4 further illustrate the insensitivity of

the Freundlich equation to depict data variability.

25

coco

.8958 885688 E 3388 ma 5
no 83808 as Sag you hang
33 833mm 33 «5 mo Bflgafl ca . a. magma

323 33:8 EN

 

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. t _ . P t _ . r L\o
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26

Second, and more importantly, is the possibility of non-attainment
of isotopic equilibria. Experimentally desorption is accomplished by
removing and diluting the solution phase. The new position of
equilibrium is calculated based on measured changes of 65Zn in solution
and mass balance principles. Thus small errors may be compounded in
subsequent calculations. Furthermore, if isotopic dilution cannot be
assumed then mass balance calculations are not valid. Unfortunately
isotopic equilibrium in such dilute solutions cannot be verified
analytically since the detection limit of Zn by AA methods was

determined to be 0.2 uM (.015 ppm).

27

Table 1. Comparison of Freundlich and linear isotherm
data at the lowest Zn level in the tracer study.

 

 

 

 

 

 

 

 

 

 

 

FREUNDLICH LINEAR
# Log [Zn] Log uM/g (Zn) uM/L uM/g
REP l
1 -3.25609 -2.13917 0.000303 0.00726
2 ~2.96962 -2.13949 0.000586 0.00725
3 -2.82611 -2.14226 0.000815 0.00721
4 -3.00788 -2.l4093 0.000536 0.00723
5 -3.00788 -2.14165 0.000536 0.00722
6 -2.98833 -2.14258 0.000561 0.00720
7 -2.98833 -2.14333 0.000561 0.00719
REP 2
1 -3.27080 -2.13950 0.000293 0.00725
2 -3.18973 -2.13754 0.000353 0.00729
3 -3.14833 -2.13831 0.000388 0.00727
4 -3.l8326 -2.13856 0.000358 0.00727
5 -3.21660 -2.13881 0.000332 0.00726
6 -3.ll784 -2.13998 0.000416 0.00724
7 -3.08082 -2.l4086 0.000453 0.00723
REP 3
1 -3.26287 -2.l36l6 0.000298 0.00731
2 -3.l3473 -2.13743 0.000400 0.00729
3 -3.13092 -2.13799 0.000404 0.00728
4 -3.l9629 -2.13804 0.000348 0.00728
5 -3.08082 -2.13942 0.000453 0.00725
6 -3.04671 ~2.14034 0.000490 0.00724
7 -3.09108 -2.14058 0.000443 0.00723

 

In the present study a radiotracer method was developed to study
trace desorption of Zn from smectite. Two important conclusions may be
drawn from this preliminary study. First the principles of isotopic
dilution appear to be valid over the adsorption range compared. Since
the data in Table 1 reveal that desorption is occuring to some extent,
the anomaly in the desorption behavior below Log (X/m) = -1 is

attributed to compounded experimental error and insensitivity of log-log

28

plots. Secondly, the extent of non-reversible adsorption is dependent
on the surface occupancy. At high occupancy adsorption is perfectly
reverible. At Zn occupancies < 1% of the CEC, desorption hysteresis

becomes extreme. Interestingly, soil Zn seldom exceeds 1% of the CEC.
Hysteresis on clay minerals may therefore contribute to Zn deficiency in
plants although the complexity of natural soil systems compared to
aqueous solution studies with pure clay minerals is acknowledged.
Regardless, the reversibility at high occupancy suggests that pure clays
may not be as useful in immobilizing heavy metals in a waste disposal

scenario.

29

Literature Cited

Bingham, F.T., A.L. Page, and J.R. Sims. 1964. Retention of Cu and Zn by
H-montmorillonite. Soil Sci. Soc. Am. J. 28:351-354.

Bourg, A.C.M., and R.H. Filby. 1976. Isotopic exchange of Zn65 with
stable Zn adsorbed on reference clay minerals. Geochim. Cosmochim.
Acta. 40:1573-1574.

Brummer, G., K.G. Tiller, V. Herms, and P.M. Clayton. 1983. Adsorption-
desorption and/or precipitation-dissolution processes of zinc in
soils. Geoderma. 31:337-354.

DeMumbrum, L.E. , and M.L. Jackson. 1956. Infrared adsorption evidence
on ecxhange reaction mechanism of copper and zinc with layer
silicate clays and peats. Soil Sci. Soc. Am. J. 20:334-337.

Elrashidi, M.A., and G.A. O'Connor. 1982. Influence of solution
composition on sorption of zinc by soils. Soil Sci. Soc. Am. J.
46:1153-1158.

Frost, R.R., and R.A. Griffin. 1977. Effect of pH on adsorption of
copper, zinc and cadmium from landfill leachate by clay minerals.
J. Environ. Sci. Health, Part A. 12:139-156.

Helfferich, F. 1962. Ion exchange, McGraw-Hill. New York.
Jackson, M.L., 1958. Soil chemical analysis. Prentice-Hall. New Jersy.

Kuo, S., and D.S. Mikkelsen. 1979. Zinc adsorption by two alkaline
soils. Soil Sci. 128:274-279.

Lamm, C.G., E.H. Hansen, and J.A. Jorgensen. 1963. Isotopic exchange in
soil fertility studies. Soil Sci. 94:16-23.

Maes, A., and A. Cremers. 1975. Cation-exchange hysteresis in
montmorillonite: a pH dependent effect. Soil Sci. 119:198-202.

McBride, 14.3., and M.M Mortland. 1974. Copper (11) interactions with
montmorillonite: evidence from physical nethods. Soil Sci. Soc.
Am. J. 38:408-414.

McLaren, R.G., and J.G. Williams, and R.S. Swift. 1983. Some
observations on the desorption and distribution behavior of copper
with soil components. J. Soil Sci. 134:325-331.

Tabikh, A.A., I. Barshad, and R. Overstreet. 1960. Cation exchange
hysteresis in clay minerals. Soil Sci. 104:219—226.

Tiller, R.G., J. Gerth, and G. Brummer. 1984. The relative affinities of
Cd, Ni, and Zn for different soil clay fractions and goethite.
Geoderma. 34:17-35.

30

Tiller, K.G., and J.F. Hogdson. 1962. The specific adsorption of cobalt
and zinc by layer silicates. p393-403. In Proceedings of the 9th
(1960) National Conference on Clays and Clay Minerals. Pergamon
Press. New York.

Tiller, K.G., J.L. Honeysett, and M.P.C. de Vries. 1972. Soil zinc and
its uptake by plants. I. Isotopic exchange equilibria and the
application of tracer techniques. Aust. J. Soil Res. 10:151-164

Van Bladel, R., and H. Laudelout. 1967. Apparent irreveribility of ion-
exchange reactions in clay suspensions. Soil Sci 104:134-137.

Veith, J.A., and G. Sposito. 1977. On the use of the Langmuir equation
in the interprtation of "adsorption phenomenon. Soil Sci. Soc. Am.

J. 41:697-702.

CHAPTER III
DESORPTION OF ZINC FROM RESIN, SMECTITE AND CHARITY CLAY
Introduction

The use of solubility product principles to describe reactivity
of Zn2+ with soil components has met with limited success. It is more

likely that Zn2+

is controlled by adsorption-desorption reactions rather
than precipitation-dissolution reactions (Krauskopf, 1972; Brummer et
a1. 1983). In describing adsorption of heavy metals in soils and clays,
extensive use has been made of three models; the Linear, Freundlich and

Langmuir equations. However, there are few reports of their use in

modeling desorption.

There are no known published reports on the use of the langmuir
equation to nwdel desorption from soil components, however McLaren et
al. (1983) used. the linear equation. to ‘model Cu2+ desorption from
smectite. Barney (1984) used the Freundlich equation to model
desorption of radionuclides from basalt materials. Elrashidi and
O'Connor (1982) also used the Freundlich equation to model desorption of
Zn2+ from nine soils of varying chemical and physical properties. An
equilibrium dialysis approach was used by Maes and Cremers (1975) to

2+ and Zn2+ from smectite. In all cases

model desorption of Co
desorption hysteresis was reported and some nonlinear isotherms were

observed.

31

32

Historically, nonlinear adsorption isotherms have been attributed
to sites of different bonding energy or multiple adsorption mechanisms
(Shuman, 1976). It is well recognized that whole soils have an
extremely large number of sites which may provide for different
adsorption mechanisms or bonding energies. Smectites are considered to
have two different types of sites, those resulting from isomorphic
substitution, and pH dependent sites resulting from broken edge OH's.
Ion exchange resins on the other hand, are considered to have only one
type of functional group and bonding mechanism. Comparative studies
using simple, well characterized adsorbents could be used to determine
the utility of different models to characterize adsorption and
desorption in more complex systems such as pure clay minerals and whole

soils.

The objective of the present study was to investigate the use of
the Linear, Freundlich and Langmuir equations in modeling adsorption and
desorption from Ca smectite, a Charity clay, a weak acid cation
exchange-chelating resin (Chelex) and a strong acid cation exchange
resin (Dowex). The later materials were chosen for their well
characterized adsorption mechanism and possible conformity to the

assumptions of uniform bonding energy and monolayer adsorption.

33

Materials and Methods
Preparation of adsorbents

Ca smectite (montmorillonite #25, Upton, Wyoming) was prepared by
sedimentation and decantation of the <2uM fraction in distilled H20
followed by repeated saturation with 1M CaC12 (pH 6.0). The flocculated
Ca-clay was dialyzed against distilled H2O until a negative test for C1-
was obtained using AgNO3. The resulting Ca-clay was stored in 0.01 M
CaC12 until ready for use. The Charity clay (aeric haplaquept) was
collected from the top 20 cm, air dried, ground to pass a 20 mesh sieve

and stored until ready for use.

Ca Dowex (Dowex 50W-X8) and Ca Chelex (Chelex-100) were prepared
from their Na forms by column elution with 0.1 M CaC12 (pH 6.0) until
the pH stabilized and Na+ could no longer be detected in the effluent.
The resins were then eluted with 5 bed volumes of distilled H20, 5 bed
volumes of 0.01 M CaC12 (pH 6.0), vacuum filtered and stored in sealed

containers until ready for use.

Physical and chemical analyses

Table 1 contains results of chemical analyses conducted on the
adsorbents. The CEC of the smectite and Charity soil were determined by
the NHAOAC-NaOAC method of Jackson (1958). The CEC of the resins were
determined by summation of cations (Ca2+ + Na+) eluted with 5 .020 L
washings with 0.1 M HCl. The pH was determined on the equilibrium
solutions described below using a combination electrode. The
equilibrium pH's for Ca Chelex changed drastically upon Zn2+ adsorption

and are presented in the discussion section. For the Charity clay, the

34

texture was determined by the hydrometer method and the soil was found
to contain 15 % sand, 39.3 % silt and 45.7 % clay. XRD peak intensity,
d(001) spacings and CEC determinations after various treatments revealed
the clay fraction contained mostly vermiculite with smaller amounts of
smectite, chlorite, kaolinite and illite. Organic C was 1.53 i .08% as

determined by a modified Walkley-Black method.

Table 1. Chemical properties and mass of adsorbent used
in batch adsorption experiments.

 

 

 

Adsorbent pH CEC mass
cmol(+) kg-l kg x 103

Ca Dowex 5.9 i .2 186 i 5 .1

Ca Chelex —- 161 i 3 .1

Ca smectite 6.6 i .2 90 i 2 .226

Charity clay 7.4 i .2 29 i 1 2.35

 

Batch adsorption experiments

Duplicate batch adsorption experiments were conducted in 50 mL Oak
Ridge centrifuge tubes. Adsorption was initiated by adding 28 mL 0.01 M

Ca012 containing 8 levels of Zn2+

as ZnC12 ranging from 0.46 uM to 14.7
mM (Table 3) to a given mass of adsorbent (Table 1). Each sample was
radiolabeled with 1 mL, lmCi 65Zn L'l, and equilibrated on a wrist
action shaker for 24 hr at 26 i_2 (L At the end of this period the

samples were centrifuged at 3000 rpm for 5 min and 4 mL was removed for

35

analysis. Three desorption cycles were accomplished by replacing the 4

mL portion with 0.01 M CaC12 and equilibrating as described above.

Radiometric data were obtained on a Packard Tri-Carb spectrometer
equiped with a gamma counter by comparing sample radioactivity with that
observed for known 65Zn standards of the same geometry. Equilibrium
Zn2+ concentrations or activities were calculated from principles of

isotopic dilution and mass balence. In all cases the amount of Zn

adsorbed was calculated by difference from the initial concentration.

Adsgrption-desorptiop isothegms

Adsorption-desorption data were calculated and isotherms
constructed for the three adsorption equations given below. A detailed
description of these equations is not intended, however an excellent

review is presented by Travis and Etnier (1981).
1.) Linear equation

X/m - KC

2+ adsorbed, m - mass of adsorber, K - a

where X - amount of Zn
distribution coefficient and C - the Zn2+ activity calculated from the
extended Debye-Huckel equation. For purposes of this discussion, this
model will be distinguished from the linear equation (y -1m<-+ b) by

capitalization (eg. Linear equation).

36

2.) Freundlich equation
log (X/m) - log(K) + l/n log(C)

where X and m are defined as before, K and n are empirical

2+

constants and C is the equilibrium Zn concentration.

3.) Langmuir equation
C/X/m - l/(Kb) + C/b

where K and b are the bonding coefficient and adsorption capacity,

2+

respectively, and C is the equilibrium Zn activity.

Results and Discussion

Conformity of adsorption data to a particular equation is
typically determined by fitting the data to the linearized form of the
equation via a linear regression approach. The value of the regression
coefficient (r2) is taken as a measure of fit of the data to the
adsorption model (Table 2). A graphical approach is clearly more useful
for characterizing desorption, since the proximity of the desorption
points to the adsorption isotherm is a measure of reversibility even
when nonlinear isotherms are observed (McLaren et al. 1983, Elrashidi

and O'Connor, 1982).

37

Tagle 2. Summary of linear regression equations for
Zn + adsorption by Ca Chelex, Ca Dowex, Ca smectite
and Charity clay.

 

 

 

 

Adsorbent Equation Regression Capacity
Coefficient
1 r2 cmol (+) kg.1
nea
Ca Dowex Y - 7.32 x 10'2x + 21.2 .97 -
Ca Chelex Y - 7.86 x 10'2x + 133 .61 -
Ca smectite Y - 3.42 x 10'2X + 11.0 .97 -
Charity clay Y - 1.93 x 10'2x + 7.68 .89 -
W1
Ca Dowex Y - .939X - .972 .99 -
Ca Chelex Y - .458X + 1.36 .86 -
Ca smectite Y - .582X - .182 .98 -
Charity clay Y - .660X - .211 .94 -
Langmuir1
Ca Dowex Y - 1.08 x 10‘3x + 5.99 .98 185
Ca Chelex Y - 1.60 x 10'3x + .114 .99 130
Ca smectite Y - 3.32 x 10'3x + 7.26 .76 60
Charity clay Y - 1.13 x 10‘3x + 1.64 .98 17.8
1

Adsorption model.

38

Adsorption of Zn2+

by Dowex is clearly nonlinear for the linear
(Figure 1) and Langmuir (Figure 3) adsorption models, despite the fact
that the regression coefficients indicate a good fit to the model (r2 -
.97 and .98, respectively, Table 2). The Freundlich equation is linear

over 5 decades of Zn2+

in. solution. (Figure 2). More importantly,
adsorption appears to be completely reversible at all surface
occupancies observed. The Freundlich equation has one advantage in that
it can be used to view adsorption and desorption phenomena over several

orders of' magnitude at a single glance, 'however log-log plots are

generally insensitive and tend to minimize data variability.

Unlike the Freundlich equation, the Linear model does not mask
data variability since the relationship between solid and solution Zn is
viewed directly. As such, it appears useful in characterizing
desorption (Figure 1), although scale expansion in necessary to view

adsorption and desorption of trace amounts of Zn (Figure 4).

That the adsorption data did not conform to the Langmuir equation
appears unusual at first glance, since Ca Dowex is expected to fulfill
the assumptions of monolayer adsorption and uniform bonding energy.
This anomaly may be explained in terms of the ion exchange distribution

coefficient Dg where

Dg - (ion conc. in resin/ion conc. in soln) — (X/m)/C

Typically Dg decreases as the fractional loading of a particular

ion increases, while in dilute solution. D8 is constant (Fritz and

Schenk, 1979). The adsorption data for Dowex exhibit this behavior.

1

Only at the 2 highest Zn levels does Dg- change (column 2, Table 3).

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Furthermore, variability of C/X/m may become extreme in the Langmuir
model since analytical errors are associated with both C and X/m. As a
result, the Langmuir equation appears to be of little use in
characterizing either adsorption or desorption of Zn2+ by Ca Dowex
despite the fact that the predicted adsorption capacity (185 cmol (+)
kg'l, Table 2) corresponds nicely with the CEC (186 cmol (+) kg'l, Table
1).

Table 3. Values of D '1 for adsorption of Zn2+

on Ca Dowex, Ca Chelex,
Ca smectite and CharIty clay.

 

Initial Zn Ca Dowex Ca Chelex Ca smectite Charity

 

 

 

uM L‘1 L g'1
0.46 6.20 0.00358 0.0527 0.573
5.81 0.00182 0.0778 0.576
15.0 5.38 0.00556 2.29 0.492
5.84 0.00284 2.28 0.492
73.0 5.95 0.00358 6.86 0.345
6.06 0.00380 6.54 0.352
147 5.95 0.00424 8.68 0.476
6.22 0.00270 8.79 0.495
728 6.77 0.0252 12.4 1.26
6.25 0.0293 12.6 1.11
1470 6.45 0.461 12.9 2.82
6.58 0.484 13.9 2.87
3705 7.75 2.39 16.4 11.4
8.62 2.55 18.3 11.2
14670 13.4 11.1 28.6 49.0

 

44

Adsorption of Zn2+ by Ca chelex did not conform to the Linear
model as indicated by graphical methods (Figure 5) or linear regression
methods (r2 - 0.61, Table 2). Adsorption is completely reversible above
200 uM Zn g'l, however desorption hysteresis becomes extreme below 50 uM
Zn g'1 (Figure 6). Adsorption of Zn2+ by Chelex also did not conform to
the Freundlich model (Figure 7). In fact, there are two linear portions
with very different slopes. In soils and clays this behavior has been
attributed to sites of uniquely different bonding energies, but in the
present case it was assumed that there was only one type of exchange
site present. That adsorption conformed to the Langmuir equation
(Figure 8, r2 - 0.99, Table 2) is further evidence to support this

assumption.

The "two surface" result may be related to reduced selectivity for

Zn2+ resulting from changes in the pH as the degree of fractional
loading increased (Table 4). Hydrogen ions were released into the
solution as Zn was adsorbed. Comparison of the Zn adsorption capacity

determined from the Langmuir equation (b - 130 cmol (+) kg'l, Table 2)
with the CEC( 161 cmol (+) kg'l, Table 1) may be an indication of a

mixed H+-Ca2+

resin. Hendrickson et al. (1982) also reported that Ca
Chelex retained considerable H+ in the pH range 5.5 - 6.0. More
importantly, they Observed. and. quantified. the pH dependence of the

selectivity coefficient using the following equation:
log Kd - 0.815pH - 2.37 (r - .986)

While this equation may explain the unusual "two surface"
behavior, it does not account for the occurrence of desorption

hysteresis in very dilute solution. Furthermore, these results are in

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contrast to previous reports that Chelex can act as a solid phase buffer
to maintain pH and constant metal activity below analytical detection
limits (Turner et al. 1984; Hendrickson et al. 1982; Hendrickson and

Corey, 1983)

One possible explaination for this behavior may be that the
driving force resulting from diluting the solution phase after a sample
is removed may not be enough to effect desorption, or that the extent of

desorption is so small that it cannot be measured accurately.

Table 4. Equilibrium pH and Zn activity
for Ca Chelex adsorption isotherms.

 

 

 

Zn activity DH
uM L-l
.000476 5.9
.000243 6.0
.0241 5.7
.0124 5.8
.0756 5.9
.0802 5.8
.180 6.0
.114 6.0
5.26 4.9
6.10 4.8
157 4.0
164 4.0
1130 3.8
1160 3 8
6860 3.7

6820 3.7

 

50

Adsorption of Zn2+ by Ca smectite did not conform to the Linear
(Figure 9), Freundlich (Figure 10), or Langmuir models (Figure 11) over
the range of surface occupancy studied, even though regression
coefficients indicate a reasonable fit of the data to the first two
equations (r2 - 0.97 and 0.98 respectively, Table 2). Adsorption
appears to be completely reversible down to 3 uM Zn g'l, however extreme

1 or when < 1% of the CEC is

desorption hysteresis occurs at 1.2 uM g'
occupied by Zn (Figure 12). In contrast, Maes and Cremers (1975)
reported reversibility at low surface coverage and desorption hysteresis
of Zn at high occupancy. This behavior was attributed to specific

adsorption involving structural OH groups or Al-hydroxy species which

might have formed during acid pretreatment.

The fact that adsorption was completely reversible for all
compositions of a pure ion exchanger (Figure 2) is further evidence that

ion exchange is the mechanism operating above 1.2 uM g'1

(Figure 12).
Desorption. beIOW’ this value behaved more like the chelating resin
(Figure 6) which is known to have a high bonding energy (12-15 kcal mol'
05.5

1) and a large selectivity for Zn over Ca of approximately 1 times
(Gamble and Schnitzer, 1973). It is doubtful that hysteresis is due to
inadequate driving force since McLaren et a1. (1983) observed hysteresis
for Cu2+ desorption from smectite at a level 5 times higher (6.3 uM Cu2+
g'l) even though a larger displacement from equilibrium was used by
removing and replacing the entire solution phase before re-
equilibration. As a result, desorption hysteresis must be attributed to

some type of unusually strong bonding, irreversible bonding or a

reaction with a high activation energy (chemisorption).

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Adsorption and desorption of Zn2+ by Charity clay using the Linear
(Figure 13), Freundlich (Figure 14), and Langmuir models (Figure 15)
produced nonlinear adsorption isotherms in spite of the apparent good
fit of the data to the models as indicated by the regression
coefficients (r2 - 0.89, 0.94, 0.98 respectively, Table 2). Desorption
hysteresis is extreme at all surface occupancies studied (Figure 14).
Elrashidi and O'Connor (1982) also reported extreme hysteresis for Zn
desorption from 9 soils of varying physical and chemical composition,
though their work did not cover the desorption range investigated in

these studies.

The Charity clay is an alkaline soil (Table 1) with free

carbonates and was expected to adsorb a significant amount of Zn2+.

Using the Arrhenius equation, Kuo and Mikkelsen (1979) determined the

activation energy for Zn2+

adsorption by two alkaline soils. Since this
value was considered too high to be due to electrostatic attraction, the
stability of adsorbed Zn was attributed to chemisorption. Similar
behavior in alkaline soils has been attributed to precipitation of Zn0H2
(Saeed and Fbx, 1977), however recent evidence suggests that
precipitation-dissolution reactions are masked by the presence of a wide
2+

variety of other sites, and hence will occur only when sufficient Zn

is added to ensure complete saturation of the exchange complex (Brummer

et al., 1983).

In the present study the highest surface occupancy attained was 80

1 or 16 cmol (+) kg'1 (Figure 13) which was not enough to

saturate the CEC (29 cmol kg'l, Table 1). Regardless, even Zn0H2 is

uM Zn 5'

expected to dissolve in response to changes in the solution activity of

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59

Zn2+ (Lindsay, 1979). As such, strong retention of Zn by the Charity
clay cannot be attributed to precipitation. Chemisorption seems to be a

more realistic possibility.

Two important points regarding the use of the Langmuir equation in
modeling adsorption-desorption reactions in soils should be mentioned.

First is the fact that desorption isotherms appear to be linear at the

two 'highest Zn levels for the Charity clay (Figure 15). Similar
behavior' was observed for Chelex (Figure 8). In the later case,
adsorption was truly reversible over a certain range. In Figure 13 it

is easy to see that dividing an evenly spaced variable (C) by a constant
(X/m) will result in a straight line with a slope similar to the
adsorption isotherm. Secondly, the adsorption maximum predicted by the
Langmuir equation (17.8 cmol (+) kg'l, Table 2) was very close to the
highest surface occupancy observed in the Linear adsorption isotherm (16
mmol (+) kg'l, Figure 13). Significant errors can result if the
adsorption capacity is calculated from adsorption data which does not
approach the true adsorption maximum, in which case the Linear equation
is just as useful. One must therefore conclude that the Langmuir

equation is of limited use in describing either adsorption or desorption

of heavy metals in soils.

In summary, a number of important observations should be
emphasised. None of the adsorption models investigated quantitatively
described adsorption or desorption of Zn2+ by Ca smectite or a Charity
clay. Adsorption—desorption data for Dowex 50W—X8 did obey the
Freundlich equation, while the Langmuir equation could adequately

describe adsorption and desorption from Chelex-100. The Langmuir

60

equation proved to be of little use in describing adsorption-desorption
reactions by soil materials, however the utility of the Linear and
Freundlich equations should not be discounted even though nonlinear
adsorption isotherms were obtained. Both equations provide a useful

approach to viewing adsorption-desorption phenomena.

Comparison of the smectite and Charity clay data to model systems

provided some interesting empirical insights regarding adsorption and

desorption mechanisms. Adsorption of Zn2+ was completely reversible on
smectite, except when < 1% of the CEC was occupied by Zn. This
reversibility was attributed to an exchange mechanism. Conversely,

extreme hysteresis was observed at all levels of Zn on a Charity clay.
Retention in both cases was similar to that for a chelation reaction

2+ was added

which had a strong preference for Zn. Since insufficient Zn
to saturate the exchange complex of either soil material, precipitation
seemed unlikely. Desorption hysteresis is likely the result of some

form of chemisorption.

61

Literature Cited

Barney, G.S., 1984. Geochemical behavior of disposed radioactive waste.
ACS Symposium Series No. 244:3-23. American. Chemical Society,
Washington D.C.

Brummer, G., K.G. Tiller, V. Herms, and P.M. Clayton. 1983. Adsorption-
desorption and/or precipitation-dissolution processes of zinc in
soils. Geoderma. 31:337-354.

Elrashidi, M.A., and G.A. O'Connor. 1982. Influence of solution
composition on sorption of zinc by soils. Soil Sci. Soc. Am. J.
46:1153-1158.

Fritz, J.S., and G.H Schenk. 1979. Quantitative analytical chemistry.
Allyn an Bacon, Boston.

Gamble, D.S., and M. Schnitzer. 1973. Trace metals and metal organic
interactions in natural waters. Ann Arbor Science, Ann Arbor

Grim, R.B. 1968. Clay mineralogy. 2nd ed. McGraw-Hill, New York.

Hendrickson, L.L., and R.B. Corey. 1983. A chelating resin method for
characterizing soluble metal complexes. Soil Sci. Soc. Am. J.
47:467-474.

Hendrickson, L.L., M.A. Turner, and R.B. Corey. 1982. Use of Chelex-100
to maintain constant metal activity and its application to
characterization of metal complexation. Anal. Chem. 54:1633-1637.

Maes, .A., and A. Cremers. 1975. Cation-exchange hysteresis in
montmorillonite: a pH dependent effect. Soil Sci. 119:198-202.

McLaren, R.G., J.G Williams, and R.S. Swift. 1983. Some observations on
the desorption and distribution of copper with some soil
components. J. Soil Sci. 134:325-331.

Shuman, LHM. 1976. Zinc adsorption isotherms for soil clays with and
without iron oxides removed. Soil Sci. Soc. Am. J. 40:349-352.

Travis, C.C., and E.L. Etnier. 1981. A survey of sorption relationships
for reactive solutes in soil. J. Environ. Qual. 10:8-17.

Turner, M.A., L.L. Hendrickson, and R.B. Corey. 1984. Use of chelating
resins in metal adsorption studies. Soil Sci. Soc. Am. J. 48:763-
769.

CHAPTER IV

EFFECT OF pH ON ADSORPTION AND DESORPTION

OF ZINC BY SMECTITE

Introduction

Among the prOperties known to affect Zn2+

and other metal sorption
by soil materials, none has been more intensely studied or more poorly
understood than pH. Even in pure clay mineral studies there is a
general lack of distinction between adsorption and precipitation.
Several researchers have reported marked uptake of metals by smectites
when the pH exceeds that required for formation of hydroxy species in

pure solution. For Zn2+

, precipitation in the presence of smectite has
been reported in the pH range 6.0-6.5 (Farrah and Pickering, 1976; Frost
and Griffin, 1977). Conversely, recent evidence by Brummer et a1.
(1983) suggests that Zn2+ is controlled exclusively 'by adsorption-
desorption reactions unless sufficient Zn2+ has been added to ensure
complete saturation of the exchange complex. The ability of chelating

ligands to mask precipitation has also been reported (Maquire et al.

1983).

Irreversible adsorption of metals below the pH required for
precipitation and the pH dependence of such adsorption. has been
attributed to Chemisorption or specific bonding. Maes and Cremers
(1975) attributed irreversible Zn2+ adsorption by Na smectite at high
surface occupancies to strong pH dependent bonding at broken edge OH's

62

63

or Al-OH compounds which may have resulted from dissolution of the clay
during acid pretreatment. However, this behavior is unusual since

specific adsorption is expected to occur at low surface occupancies.

Smectites are not considered to have extensive pH dependent
charge, but their ability to irreversibly sorb Al-OH compounds is well
documented (Keren, 1980). Irreversible pH dependent adsorption of Cu2+
and Zn2+ by soil clays which contain coatings of A1 and Fe oxide has
been attributed to chemisorption (Cavallaro and McBride, 1984). Using

ESR, Cu2+ adsorption on a Al-OH-montmorillonite complex was shown to be

both physi-(electrostatic) and chemi-sorbed (Harsh and Donner, 1984).

While these results may explain Zn2+

retention by soils and clays
which contain microcrystalline and noncrystalline oxides, they do not
account for desorption hysteresis of Zn on smectite observed in earlier
studies by this laboratory (Zielke, Chapter III). In these studies,
extreme desorption hysteresis occurred in the trace region while
adsorption of Zn by smectite at moderate to high surface occupancy was
completely reversible even at pH's where precipitation has been reported
by others. In light of these differences, the objective of the present
2+

study was to investigate the effect of pH on the reversibility of Zn

adsorption by Ca smectite over a wide range of surface coverage.

64

Materials and Methods

Preparation of adsorbents

Ca smectite (montmorillonite # 25, Upton, Wyoming) was prepared by
sedimentation and decantation of the <2um fraction in distilled H20
followed by repeated saturation with 1M CaClZ. The flocculated Ca clay
was dialyzed against distilled H20 until a negative test for C1' was
obtained using AgNO3. The resulting clay was diluted with 0.01 M CaC12
to give a 1% w/w suspension, split into several portions and the pH was
adjusted twice a day with 0.01 M HCl or saturated Ca(OH)2 until a stable
reading (1 0.05 pH units) was obtained for 3 consecutive days. This
process required approximately three weeks. The CEC was determined on

unadjusted Ca clay and was found to be 90 i 2 cmol (+) kg-l.

Adsorption isgtherms

Batch adsorption experiments were conducted in duplicate at each
of 6 pH levels by adding 3 mL of the rapidly stirred clay suspensions to
5 mL RIA polypropylene test tubes. Each tube received 0.2 mL of an
appropriate Zn solution (Table 1) and 0.2 mL of a 65Zn solution
containing 1 mCi 65Zn L'l. The mass of clay used at each pH level was
determined gravimetrically. The tubes were then sealed, dispersed on a
vortex mixer and equilibrated on a wrist action shaker at 26 i 2 C for 2
wks. At the end of this time the samples were separated by
centrifugation at 3000 rpm for 5 min, and a 1 mL aliquot was removed for
radioassay. Six desorption cycles were accomplished by replacing the 1

mL sample with 0.01 M CaC12 and re-equilibrating for 24 hr.

65

Radiometric data were obtained on a Packard Tri-Carb spectrometer
equipped with a gamma counter by comparing sample radioactivity with
that observed for known 652n standards of the same geometry.

Equilibrium 2112+

concentrations were calculated from principles of
isotopic dilution and mass balance. In all cases the amount of Zn
adsorbed was calculated by difference from the initial concentration.

The equilibrium pH was determined on the 1 mL aliquot using a

combination pH electrode.

The rate of Zn adsorption at the lowest Zn2+ level was
investigated by equilibrating duplicate samples for periods of .5, l, 2,
4, 8, and 20 hr, and determining the amount of Zn adsorbed as described
above. The effect of equilibration time on adsorption and desorption
was investigated at the 3 lowest Zn2+ levels by equilibrating duplicate
samples for 24, 72, 168 and 672 hr. Three desorption cycles were

conducted as described earlier.

66

Table 1. Initial Zn2+ levels and equilibrium pH's for
Zn adsorption by Ca smectite.

 

Initial Zn2+ Equilibrium le

 

uM L'1

.0097 3.47 4.44 5.88 6.51 6.94 7.70

.430 3.45 4.45 5.92 6.57 7.03 7.73
4.47 3.45 4.49 5.91 6.57 7.02 7.74
44.9 3.45 4.50 5.86 6.53 6.98 7.76
426 3.44 4.47 5.76 6.43 6.80 7.76
4380 3.44 4.40 5.56 6.23 6.59 6.94

 

1 Means of duplicate samples

Results and Discussion

The equilibrium pH for adsorption by the 6 different clay
suspensions is presented in Table 1. In all cases the pH in subsequent
desorption cycles did not change by more than i 0.1 pH units. There was
a tendency for the pH to decrease at the higher initial Zn2+ levels
(column 4,5, 6, and 7, Table 1). This decrease is most likely the

result of hydrolysis via the reaction:
2n2+ + H20 - ZnOH+ + H+

Adsorption of Zn by smectite at pH 3.5 conformed to the Freundlich
equation and was completely reversible at all Zn2+ levels as indicated
by the proximity of the desorption points to the initial adsorption

isotherm (Figure 1). At this pH, smectite is most likely a mixed Al-Ca-

67

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68

Zn clay (Pionke and Corey, 1967), and any pH dependent sites capable of

strong bonding remain undissociated or are associated with A13+. Zinc
adsorption appears completely reversible under these conditions because
it is competing with Ca2+ for sites which do not lead to specific

bonding.

At pH 4.5 Zn adsorption still conforms to the Freundlich equation
over the entire range observed. (Figure 2), but. moderate desorption
hysteresis occurs below log (X/m) - -0.5. Three explanations are
offered for this behavior. First, at this pH smectite may be subject to
acidic dissolution, however exchangeable A1 is probably very low and Al-
OH complexes which contribute to hysteresis might be forming on the
surface (Harsh and Donner, 1984). Secondly, is the possibility that
desorption hysteresis is the result of strong bonding at broken edge
OH's, and that these sites dissociate at a lower pH than originally
thought. Still another possibility is that some other type of pH

dependent site capable of effecting desorption hysteresis is present.

At pH 5.9 and above, data no longer conform to the Freundlich
equation and nonlinear isotherms are observed (Figures 3,4,5 and 6).
Adsorption appears to be completely reversible above log (X/m) - 0, but
hysteresis becomes extreme below this value (Figure 3). Irreversible
adsorption, on pH dependent sites such as broken. edge OH's may ‘be
responsible since Zn adsorbed on the surface at this level represents <1

% of the CEC.

As the pH is increased further, more Zn was adsorbed in the range
where hysteresis was observed, while adsorption at the high end remained

relatively constant. For example, log [Zn] where hysteresis begins at

69

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74

pH 5.9 (Figure 3) is approximately 0. At pH 6.5, log [Zn] - -.75
(Figure 4), and at pH 7.0, log [Zn] is approximately -1 (Figure 5). At
pH 7.7 this value shifts to log [Zn] - -1.5, and hysteresis is observed
at the next highest initial Zn2+1evel (Figure 6). In contrast,
adsorption at the highest initial Zn level was completely reversible and
occurs uniformly at log (X/m) - 2 and log [Zn] - 3.5. Mathematically,
these results contribute to increasing nonlinearity of the Freundlich
isotherm. Mechanistically, they confirm that hysteresis is occurring on
pH dependent sites while complete reversibility is exhibited at the

permanently charged sites.

Maes and Cremers (1975) first suggested that hysteresis was a pH
dependent phenomenon, however the results presented here are in no way
similar to those previously presented, since desorption hysteresis was
observed in the high end of the adsorption envelope. One explanation
offered for this observation was the formation of Al-OH complexes which

selectively retained Zn.

Harsh and Donner (1984) studied specific adsorption of Cu2+

on Al-
OHI complexes which. were precipitated on smectite. Adsorption *was
extremely energetic and time dependent. After 168 hr only 0.6% of the
Cu adsorbed could be removed with 0.25 M Ba(NO3)2. In the present
study, adsorption at the lowest Zn2+ level was nearly complete in less
than 24 hr at all pH's (Figure 7). Rapid adsorption was observed at
higher Zn levels as well (Figure 8). More importantly, there was no
significant effect of time on the desorbability of Zn at 72 and 672 hr
(Figure 9). While results are shown only for pH 4.5, similar behavior

was observed throughout the pH range investigated.

75

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Two important conclusions can be drawn from these time dependent
studies. First, it is unlikely that precipitation occurred at any pH or
Zn level since equilibria was attained in <24 hrs. Secondly, hysteresis
cannot be accounted for by chemisorption on aluminum polymers as was
suggested in data by Harsh and Donner (1984) since these types of
reactions exhibit strong time dependence. Furthermore the smectite used
in this study was prepared to exclude the formation of aluminum

polymers.

In conclusion, adsorption of Zn was observed to be pH dependent.
At. high surface occupancy, adsorption.*was completely reversible as
expected for an ion exchange reaction. Desorption hysteresis in the
trace region did not behave like chemisorption on AJ-OH polymers and
hence must be attributed to the presence of some other pH dependent
site. One possibility would be broken edge OH's; however, moderate
desorption hysteresis was observed even at pH 4.5, which is below the pH
where such sites are expected to be ionized. One fact is known for
certain; smectite clays have a demonstrated ability to mask Zn
precipitation even in alkaline solution. This observation raises
serious doubt as to the effectiveness of pH control as a means to
immobilize heavy metals in waste disposal processes that utilize
smectite clays. If the sites contributing to 'hysteresis could. be
identified and optimized, smectites would have greater appeal as an

adsorbent for heavy metals.

79

Literature Cited

Brummer, G., K.G. Tiller, V. Herms, and P.M. Clayton. 1983. Adsorption-
desorption and/or precipitation-dissolution processes of zinc in
soils. Geoderma. 31:337-354.

Cavallaro, N., and M.B. McBride. 1984. Zinc and copper sorption and
fixation by an acid soil clay: effect of selective dissolutions.
Soil Sci. Soc. Am. J. 48:1050-1054.

Farrah, R., and W.F. Pickering. 1976. The sorption of zinc species by
clay minerals. Aust. J. Chem. 29:1649-1656.

Frost, R.R., and R.A. Griffin. 1977. Effect of pH on adsorption of
copper, zinc and cadmium from landfill leachate by clay minerals.
J. Environ. Sci. Health, Part A. 12:139-156.

Harsh, J.B, and H.E. Donner. 1984. Specific adsorption of copper on an
hydroxy-aluminum-montmorillonite complex. Soil Sci. Soc. Am. J.
48:1034-1039.

Keren, R. 1980. Effects of hydroxy aluminum precipitation on the
exchange capacity reduction and aggregate size distribution of
montmorillonite hydroxy-aluminum complexes. Soil Sci. Soc. Am J.
44:1209-1212.

Maes, A., and A. Cremers. 1975. Cationyexchange hysteresis in
montmorillonite: a pH dependent effect. Soil Sci. 119:198-202.

Maquire, M., J. Slavek, I. Vimpany, F.R. Higginson, and W.F. Pickering.
1981. Influence of pH on copper and zinc uptake by soil clays.
Aust. J. Soils Res. 19:217-229.

Pionke, R.B. and R.B. Corey. 1967. Relations between acidic aluminum
and soil pH, clay and organic matter. Soil Sci. Soc. Am. Proc.
31:749-752.

CHAPTER V
EFFECT OF INITIAL EXCHANGEABLE ION ON ADSORPTION

AND DESORPTION OF ZINC FROM SMECTITE
Introduction

Several. ‘researchers ‘have studied. the effect of solution
composition. on. metal adsorption. by soils and clays (Elrashidi and
O'Connor, 1982; Egozy, 1980). However, there are few reports of the
effect of initial exchange ion on adsorption. Furthermore, there are no
known studies where metal desorption is systematically studied relative

to the initial exchange ion.

Logically, most of the studies conducted have been on soil
materials saturated with ions of agricultural importance. Nelson and
Melsted (1955) reported the relative order of affinity of different
cations by clay minerals was H+(A13+) > Zn2+ > Ca2+ > Mgz+ > K+.

Garcia-Miragaya and Page (1977) reported that Cd2+

sorption by different
homoionic montmorillonites followed the order Na > K > Ca > A1. Shukla
et a1. (1980) found that Zn adsorption. by ‘whole soils which. were
saturated with different cations followed the order H(A1) < Ca < Mg < K
,Na. Adsorption of alkali metal cation on smectite followed the order

Li < Na < K < Rb < Cs. The free energy of adsorption was related to ion

size parameters and polarizability factors (Gast, 1969).

Although the cation composition of soils varies widely, there can

be little doubt: the initial exchange ion and. associated adsorption

8O

81

energy will affect the position of equilibria in heavy metal adsorption-
desorption studies and in natural systems. Since different cations
affect the basal spacings of smectite minerals, these effects may be

steric as well as electrostatic (MacEwan and Wilson, 1980).

The objective in the present study was to determine the effect of
initial exchange ion on adsorption and desorption of Zn by a smectite
clay. Homoionic alkali metal smectites were prepared in an attempt to
systematically vary the hydrated ion size and adsorption energy of the
initial exchange ion. In this fashion, the periodic nature of homoionic

2+

clays and their reactivity toward Zn could be investigated.

Materials and Methods

Preparation of adsorbents

Sodium and K saturated smectites (montmorillonite # 25, Upton,
Wyoming) were prepared by repeated saturation with the appropriate 1 M
MCl salt at pH 5.0. Rubidium and Cs smectites were prepared by repeated
saturation with a 0.1 M_MC1 salt. In all cases, smectites were prepared
from the < 2 um fraction. which. was recycled from previous Ca-Zn
adsorption. experiments. The saturated. alkali metal smectites were
dialyzed against distilled H20 until a negative test for C1" was
obtained using Ag(NO3)2. The resulting clay was diluted with the

appropriate 0.03 MCl salt solution and stored until ready for use.

82

Adsorption isotherms

Batch adsorption experiments were conducted in duplicate for each
of the alkali metal saturated clays by pipetting 3 mL of the rapidly
stirred clay suspensions into 5 mL RIA polypropylene test tubes. Each
tube received 0.2 mL of an appropriate Zn solution (Table 1) and 0.2 mL
of a 652n solution containing lmCi 65Zn L'l. The mass of each clay used
was determined gravimetrically. The tubes were then sealed, dispersed
on a vortex mixer and equilibrated on a wrist action shaker at 26 i 2 C
for 2 wks. At the end of this period the samples were separated by
centrifugation at 3000 rpm for 5 min, and a 1 mL aliquot was removed for
radioassqy. Eight incremental desorption cycles were accomplished by
replacing the 1 mL sample with the appropriate 0.03 M MCl solution and

re-equilibrating for 24 hrs.

Radiometric data were obtained on a Packard Tri—Carb spectrometer
equipped with a gamma counter by comparing sample radioactivity with
that obtained for known 65Zn standards of the smae geometry.
Equilibrium Zn concentrations were calculated from principles of
isotopic dilution and mass balance. the amount of Zn adsorbed was
calculated from the initial concentration. The equilibrium pH was

determined on the 1 mL aliquot using a combination electrode.

The rate of Zn adsorption at the lowest Zn2+ level was
investigated by equilibrating duplicate samples for periods of 1, 2, a,
8 and 16 hr. Adsorbed Zn was determined as described above. The effect
of longer equilibration times on adsorption was investigated at the 3

2+

lowest Zn levels by equilibrating duplicate samples for 24, 72, 168

and 672 hrs.

83

Table 1. Initial Zn2+ concentrations and equilibrium pH's
for the adsorption of Zn by homoionic smectites

 

 

 

Initial Zn2+ Equilibrium le
Na K Rb Cs
uM L’1

.0097 5.49 5.66 5.73 5.45
.147 5.48 5.69 5.74 5.43
1.45 5.50 5.62 5.73 5.53
146 5.49 5.65 5.72 5.40
1450 l 5.13 5.21 5.36 5.18

 

i Means of duplicate samples

Results and Discussion

In this study an attempt was made to maintain the pH at a constant
value so that adsorption-desorption effects could be attributed to the
exchangeable ion rather than to differences in the equilibrium pH. This
objective was attained as the pH in subsequent desorption cycles did not
change by mnore than i 0.1 unit, however the equilibrium pH's at the
highest Zn level were lower, possibly due to hydrolysis in the bulk

solution.

Adsorption data for the different homoionic clays are presented as
Freundlich isotherms. For Na smectite, adsorption obeyed the Freundlich
equation over 6 orders of magnitude and appears to be completely
reversible over the entire range studied (Figure 1). Conformity to the

Freundlich equation and. complete reversibility ‘was observed for Zn

84

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adsorption on K smectite as well (Figure 2). Adsorption of Zn by Rb
smectite obeyed the Freundlich equation to a degree, but more
importantly, desorption hysteresis was observed at log (X/m) ==() and
below (Figure 3). Am: higher surface occupancies of' Zn, adsorption
appeared to be completely reversible as is expected in normal exchange
reactions. For Cs smectite, desorption hysteresis was extreme
throughout the entire adsorption range (Figure 4). Furthermore, the

adsorption data did not conform to the Freundlich equation.

For' Na, the desorption. points are tightly grouped. around the
adsorption points, indicating that Na does not displace adsorbed Zn very
effectively. As we proceed along the series Na, K, Rb, and Cs, there is
a trend for the desorption points to spread out over a larger
concentration range. This is an indication of the increasing ability of
these cations to displace adsorbed Zn, and is in line with the free
energy of adsorption of these cation on Wyoming montmorillonite as
measured ‘by Cast (1969). These observations are also in general
agreement with data presented by Nelson and Melsted (1955), Garcia-
Miragaya. and Page (1977) and Shukla et al. (1980); (i.e that the
smaller, more electropositive ion is adsorbed to a greater extent).
That desorption hysteresis of Zn occurs on the smectites saturated with
the smaller, more competative Rb and Cs ions seems to be a contradiction
to the commonly observed lyotropic series. However, these observations

can be explained from a kinetic viewpoint.

At the lowest Zn2+ level, adsorption as a function of time by the
different clays follows the order Na > K > Rb > Cs (Figure 5). This

order was observed at higher initial Zn2+ levels as well. Zn adsorption

86

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by Na (Figure 6) and K smectite (Figure 7) was > 99% complete in less
than. 24 hrs. This rapid equilibrium. is characteristic of an ion
exchange reaction (Helfferich, 1962). Adsorption equilibria of Zn for

Rb (Figure 8) and Cs smectites (Figure 9) was not attained even after

672 hrs.

The different adsorption rates of Zn can be attributed to the
hydrated nature of the individual alkali metal ions and their effect on
the basal spacings of smectites (Wyoming montmorillonite) in H20 (Table
2). Sodium and K spacings were large and indeterminate, and while data
were not available for Rb, the value is expected to be slightly higher

than that reported for Cs.

Table 2. Effect of interlayer cation
on basal d(001) spacings of Wyoming
montmorillonite immersed in water.

 

Interlayer cation d(001) spacing1

 

10‘3m
Na >>
K >>
Rb --
Cs 12.5
Mg 19.5
Ca 19.0
Sr 19.0
Ba 18.8

 

l MacEwan and Wilson (1980) p. 203

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Interestingly, the values reported for alkaline earth ions are
relatively constant. The value for Zn is expected to be very similar
since its crystal radii and aqueous chemistry is similar to that for Mg
(Cotton and Wilkinson, 1980). This would account for the fact that
equilibrium.‘was attained. quite rapidly for Ca-Zn exchange (Zielke,
Chapter IV). Conversely, desorption hysteresis was shown to be
concentration and pH dependent in these earlier studies, and was
attributed to strong bonding, possibly at broken edge OH's. In the
present study, similar hysteresis would be expected on Na (and K)
smectites since these ions could not compete for specific adsorption
sites in other studies (Harsh and Doner, 1984). One possible
explaination for this behavior was that Zn remained fixed at broken

edges when Ca-Zn clays were recycled for use in this experiment.

Regardless, migration of Zn into interlamelar exchange sites on Rb
and Cs smectites appear to 'be sterically inhibited. by the limited
swelling as indicated by the nonattainment of equilibria. Similarly,
once adsorbed at interlayer positions, migration into the bulk solution
would be equally inhibited. As a result, the occurrence of hysteresis
on Rb and Cs smectites appears to be a consequence of non equilibrium
rather than strong irreversible bonding at specific adsorption sites.
While this was a testable hypothesis, similar desorption kinetic
experiments at the lowest Zn level failed to confirm this under these
experimental conditions because the rate of «J urption proceeded faster

than the rate of desorption even after 8 wks.

In summary, Zn adsorption by homoionic alkali metal smectites

followed the order Na > K > Rb > Cs. Data obtained in kinetic

96

experiments revealed that both adsorption and desorption of Zn was
sterically inhibited by the limited swelling of Rb and Cs smectites.
Desorption. hysteresis was therefore attributed. to ‘nonattainment of
equilibria rather than to specific bonding as was reported in earlier
Ca-Zn adsorption-desorption experiments. Failure to consider the
initial exchanger composition. and its effect on the attainment of
equilibrium, and the ability of some homoionic smectites (eg Cs) to
produce nonlinear isotherms ‘may result in erroneous conclusions as
regards desorption hysteresis or adsorption at sites with different

bonding energies.

97

Literature Cited

Cotton, F.A. and G. Wilkinsen. 1980. Advanced inorganic chemistry. (4th
ed). Interscience Publishers. John Wiley & Sons. New York

Egozy, Y. 1980. Adsorption of cadimum and cobalt on montmorillonite as
a function of solution composition. Clays and Clay Miner.
28:311-318.

Elrashidi, M.A., and G.A. O'Connor. 1982. Influence of solution
composition on sorption of zinc by soils. Soil Sci. Soc. Am. J.
46:1153-1158.

Garcia-Miragaya, J . , and A. L. Page . 1977 . Influence of exchangeable
cation on the adsorption of trace amounts of cadmium by
montmorillonite. Soil Sci. Soc. Am. J. 41:718-721.

Gast, R.G. 1969. Standard free energies of exchange for alkali metal
cations on Wyoming bentonite. Soil Sci.l Soc. Am. Proc. 33:37-
41.

Helfferich, F. 1962. Ion exchange. McGraw-Hill. New York.

Harsh, J.G. and H.E. Doner. 1984. Specific adsorption of copper on an
hydroxy-aluminum-montmorillonite complex. Soil Sci. Soc. Am. J.
48:1034-1039.

MacEwan, D.M.C. and M.J. Wilson. 1980. Interlayer and intercalation
complexes of clay minerals. p. 197-248. In G.W. Brindley and G.
Brown (ed.). Crystal structures of clay minerals and other X-ray
identification. Mineralogical Society Monograph No. 5. Miner.
Soc., London.

Nelson, J.L., and S.W. Melsted. 1955. The chemistry of added zinc to
soils and clays. Soil Sci. Soc. Am. J. 19:323-326.

Shukla, V.C., S.B. Mittal, and R.K. Gupta. 1980. Zinc adsorption in
some soils as affected by exchangeable cations. Soil Sci.
129:366-370.

CHAPTER VI
SUMMARY AND CONCLUSIONS

A batch equilibrium technique based on principles of isotopic
dilution and mass balance was developed to study adsorption and
desorption of trace amounts of Zn by Ca smectite (montmorillonite # 25,
Upton, Wyoming) The technique was tested by comparison with results
obtained using conventional atomic adsorption for Zn analysis. Based on
these comparisons it was concluded that 65Zn in solution was in kinetic
equilibrium with 65Zn adsorbed on the surface of Ca smectite, and hence
the technique was applicable to the study of desorption hysteresis in
clay minerals. Desorption hysteresis occurred when <1% of the CEC was
occupied by Zn but at higher occupancies Zn adsorption was completely

reversible.

Three isotherms (Linear, Freundlich and Langmuir) were tested to
determine their utility in characterizing desorption. Data were
obtained for Zn adsorption-desorption with Ca smectite, Charity clay
(aeric haplaquept), a strong acid cation exchange resin (Ca Dowex 50W-

X8), and a weak acid cation exchange-chelating resin (Ca Chelex).

None of the equations could quantitatively describe Zn adsorption
or desorption by and from Ca smectite or Charity clay since nonlinear
isotherms were observed, but the Linear and Freundlich equations were

better than the Langmuir. The Freundlich equation was a convenient

98

99

2+

method to view adsorption over several decades of Zn activity, even

though log-log plots tend to minimize data variability.

Adsorption. of Zn. by Ca. Dowex. was completely reversible. and
quantitatively described by the Freundlich equation. A two surface
Freundlich isotherm was obtained for Chelex, and hysteresis was observed
in the high affinity region. The "two surface" behavior was attributed
to reduced selectivity of the resin for Zn in acid solutions.

Hysteresis was attributed to strong bonding by the chelating resin.

Comparison of the behavior of the model ion exchangers with the
smectite and Charity clay Freundlich isotherms allowed insight to the
mechanisms operating in adsorption, desorption and hysteresis. For
smectite the reaction was completely reversible at high surface
occupancies, but hysteresis was observed. at low surface occupancy.
Reversibility was attributed to an ion exchange mechanism. For Charity
clay, extreme hysteresis occurred at all Zn levels. Hysteresis on both
materials resembled the behavior of the Chelex resin in the high
affinity region. For smectite, hysteresis was attributed to strong
bonding at broken edge OH's, while Zn retention on the Charity clay
could be due to strong bonding on broken edges of clay minerals, Al and

Fe oxides, free carbonates or organic matter.

There was a strong interaction between pH and hysteresis in Zn
adsorption-desorption on Ca smectite. At pH 3.5, a linear Freundlich
isotherm was observed and adsorption was reduced probably because of
competition with Al3+ that resulted from acidic dissolution of the clay
mineral. However, the reaction was completely reversible at all Zn

levels. In general, as the pH increased, adsorption and hysteresis

100

increased. At the highest initial Zn2+ level, adsorption was relatively
constant at all pH's and was completely reversible. Fhrthermore, the
ability' of smectite clay to mask 'precipitation. was observed since
adsorption of large amounts of Zn was reversible even in alkaline
solution. Thus hysteresis was shown to be pH dependent while adsorption
in the higher end of the isotherm could be attributed to ion exchange on
permanently charged sites. In combination these factors contributed to
nonlinear Freundlich isotherms. The pH dependency of hysteresis must be
attributed to strong bonding at broken edge OH sites since these sites
are considered to be the only source of pH dependent charge in the

system.

The effect of the initial exchange ion on Zn adsorption was also
investigated using homoionic Na, K, Rb and Cs smectites. Hysteresis was
not observed on Na an K smectites as was expected from the occurrence of
hysteresis in previous Ca-Zn studies. This anomaly was attributed to
incomplete removal of Zn from hysteretic sites because the smectites
were 'prepared from clays recycled from previous Ca-Zn experiments.
Regardless, the extent of Zn adsorption followed the lyotropic series Na
> K > Rb > Cs. The ability of these ions to compete with Zn2+ for
permanently charged exchange sites also followed this order and was
observed as a spreading out of the desorption points along the lyotropic

series.

Extreme hysteresis was observed for Rb and Cs smectites, and while
this appeared to be contradictory to their highly competitive nature,
kinetic studies revealed hysteresis was an artifact of nonequilibrium.

Adsorption and desorption was sterically inhibited at interlayer

101

exchange sites because Rb and Cs ions have a demonstrated ability to
reduce swelling in smectite minerals thus reducing the rate of diffusion

of Zn into and out of interlayer positions.

APPENDIX

APPENDIX

NUCALC

10 REM NUCALC BAS CALCULATES PPM ZN IN SOLUTION FROM RADIACTIVE CPM AND
PRINCIPLES OF ISOTOPIC DILUTION VIA A MASS BALANCE APPROACH AND PRODUCES
A HARD COPY OF THE MODEL PARAMETERS AND INPUT AND OUTPUT FILES

20 REM NUCALC.BAS ALSO CALCULATES VALUES FOR CONSTRUCTION OF
GENERAL,FREUNDLICH AND LANGMUIR ISOTHERMS

30 REM NUCALC.BAS WAS WRITEN BY' RICHARD CLEVELAND ZIELKE GRADUATE
ASSISTANT IN SOIL CHEMISTRY MICHIGAN STATE UNIVERSITY CROP AND SOIL
SCIENCES DEPARTMENT JULY 23 1986

40 LPRINT CHR$(27) "N"CHR$(6)

50 LPRINT CHR$(27) "M";

60 LPRINT CHR$(27) "P" CHR$(15);

7o WIDTH "LPTl:",150

80 LPRINT CHR$(27) "1"CHR$(10);

9O LPRINT CHR$(27) "Q"CHR$(140);

100 DEFDBL Z,G,F,L

110 OPTION BASE 1

120 INPUT "WHAT IS THE NUMBER OF TREATMENTS?",N

130 INPUT "WHAT IS THE NUMBER OF ADSORPTION/DESORPTION CYCLES?",D

140 DIM CSTD(N,D),CSAM(N,D),ZI(N,D),ZF(N,D),ZREM(N,D)

150 DIM ZADS(N,D),ZINI(N,D),ZSOL(N,D),CORR(N,D)

160 DIM GX(N,D),GY(N,D),FX(N,D),FY(N,D),LX(N,D),LY(N,D)

170 REM CSTD-STANDARD CPM CORRECTED FOR COUNTING GEOMETRY CSAM-SAMPLE
CPM ZI-INITIAL PPM ZN ZF-FINAL PPM ZN ZREM-MG ZN REMAINING IN
SYSTEM AFTER EQUIL ZADS-MG ZN ADSORBED ZINI-MG ZN IN SYSTEM BEFORE
EQUIL ZSOL-MG ZN IN SOLUTION AT EQUIL

180 REM CORR-SAMPLE COUNT ADJUSTED FOR COUNTING GEOMETRY

19o REM GX-ZN ACTIVITY (uM/L) GY-X/M (uM/G) FX-LOG [ZN] FY-LOG X/M LX=ZN
ACTIVITY LY-C/X/M (uM/L/uM/G)

200 INPUT "WHAT IS MESSAGE?",A$

210 INPUT "WHAT IS THE SAMPLE VOLUME IN MLS?",VS

22o INPUT "WHAT IS THE ANALYTE VOLUME IN MLS?",VA

230 INPUT "WHAT IS IONIC STRENGTH IN M/L?",U

240 INPUT "WHAT IS THE SAMPLE WEIGHT IN GRAMS? ",w

250 K—10‘(-.5085*4*U‘.5/(1+1.969*U‘.5)) :REM EXTENDED DE BYE HUCKEL EQN
TO CALCULATE ZN ACTIVITY COEFFICIENT

260 INPUT "WHAT IS THE AVERAGE BACKGROUND COUNT?",CBKGD

27o INPUT "WHAT Is THE AVERAGE STANDARD COUNT?",CSTD

280 STD-CSTD-CBKGD

2 90 LPRI NT n *************************PROGRAM I S
NUCALC.BAS************************* ":LPRINT "IDENTIFYING MESSAGE:
”;:LPRINT AS

300 LPRINT " *****INPUT PARAMETERS FOR SPECIFIED
FILENAME***** "

102

103

310 LPRINT "SAMPLE VOLUME IN MLS-";VS

320 LPRINT "ANALYTE VOLUME IN MLS-";VA

330 LPRINT "IONIC STRENGTH-":U

340 LPRINT "ZN ACTIVITY COEFFICIENT- ";K

350 LPRINT "SAMPLE WEIGHT IN GRAMS-";W

360 LPRINT "BACKGROUND COUNT IN CPM-";CBKGD

370 LPRINT "UNCORRECTED STANDARD COUNT IN CPM-";CSTD

380 CLS:FILES "A:*.DAT"

390 INPUT "WHAT IS FILENAME CONTAINING CPM DATA (OMIT EXTENSION)?",F$
400 S$-F$+".DAT"

410 LPRINT ”INPUT FILENAME-";S$:LPRINT

420 OPEN "I",#1,S$

430 FOR I-l TO NzFOR J-l TO D:INPUT#1,CSAM(I,J):NEXTzNEXT

440 LPRINT S$;:LPRINT "(UNCORRECTED FOR BACKGROUND CPM)"

450 FOR I-l TO NzFOR. J-l TO DzLPRINT CSAM(I,J);" ";:NEXT:LPRINT,"
":NEXTzLPRINT

460 CLOSE #1

470 T$-F$+".COR"

480 FOR I-l TO N:FOR J-l TO D:CSAM(I,J)-CSAM(I,J)-CBKGD:NEXT:NEXT

490 OPEN "O",#2,T$

500 FOR I-l TO NzFOR J-l TO D:PRINT#2,CSAM(I,J);" ";:NEXT:PRINT#2,"
":NEXT

510 LPRINT T$;:LPRINT "(CORRECTED FOR BACKGROUND CPM)"

520 FOR I-l TO NzFOR J-l TO DzLPRINT CSAM(I,J);" ":tNEXTzLPRINT," ":NEXT
530 LPRINT:

540 CLOSE #2

550 OPEN T$ FOR INPUT AS #3

560 FOR I-l TO N:FOR J-l TO D:INPUT#3,CSAM(I,J):NEXTzNEXT

570 LPRINT "INITIAL PPM ZN FINAL PPM ZN INITIAL MG ZN MG ZN
REMAININ MG ZN ADSORBED"
530 '*************************START DATA

CALCULATIONS **************************

590 FOR I-1 TO N

600 FOR J-l TO D

610 IF J-l THEN CSTD(I,J)-STD*VS/VA

620 IF J>1 THEN CSTD(I,J)-CSTD(I,J-1)-CSAM(I,J-1)

630 CORR(I,J)-CSAM(I,J)*VS/VA

640 IF J-l THEN INPUT "WHAT IS THE INITIAL PPM ZN?",ZI(I,J)
650 IF J>1 THEN ZI(I,J)-ZF(I,J-1)*(VS-VA)/VS

660 IF J-l THEN ZINI(I,J)-ZI(I,J)*VS/1000

670 IF J>l THEN ZINI(I,J)-ZREM(I,J-l)

680 ZSOL(I,J)-CORR(I,J)*ZINI(I,J)/CSTD(I,J)

690 ZF(I,J)-ZSOL(I,J)*lOOO/VS

700 ZREM(I,J)-ZINI(I,J)-ZF(I,J)*VA/1000

710 ZADS(I,J)-ZINI(I,J)-ZSOL(I,J)

720 GX(I,J)—ZF(I,J)*K/.06537

730 IF J-l THEN GY(I,J)-(ZI(I,J)-ZF(I,J))*VS*1000/(65370!*W)
740 IF J>l THEN GY(I,J)-GY(I,J-1)+(ZI(I,J)-ZF(I,J))*VS*1000/(65370!*W)
750 FY(I,J)-LOG(GY(I,J))/2.30256

760 FX(I,J)-LOG(ZF(I,J)/.06537)/2.30256

77o LX(I,J)-GX(I,J)

780 LY(I,J)-LX(I,J)/GY(I,J)

104

790 LPRINT USING" M.M ###.######### ###.#########
M.M

M.M" ;ZI(I,J) ,ZF(I,J) ,ZINI(I,J) ,ZREM(I,J) ,ZADS(I,J)

800 NEXT J

810 LPRINT

820 NEXT I

830 '**************************END DATA
CALCULATIONS***************************

840 CLOSE #3

850 KILL T$

860 U$-F$+".OUT"

870 OPEN "O",#3,U$

880 FOR. I-l TO 1N:FOR. J-l TO D:PRINT#3,USING "###.#######
";ZI(I,J);ZF(I,J);:NEXT:PRINT#3,:NEXT

890 ‘LPRINT ‘U$;:LPRINT "(ADJACENT COLUMNS ARE INITIAL .AND FINAL ZN
REMAINING IN SOLUTION AT EQUILIBRIUM. THE # OF COLUMNS/2 -# OF
DESORPTION CYCLES. ADJACENT ROWS ARE REPS.)”

900 Ks-"INI PPM ZN":L$-"FIN PPM ZN"

910 LPRINT USING "\ \";K$,L$

920 FOR I-l TO N:FOR J-l TO DzLPRINT USING "###.#######
';ZI(I,J);ZF(I,J);:NEXTzLPRINTzNEXT

930 CLOSE #3

940 GOSUB 1490

950 REM SUBROUTINE TO PRINT AND FILE GENERAL,FREUNDLICH AND LANGMUIR
ISOTHERMS

960 H$-"G"+F$+".SDF"

970 I$-"F"+F$+".SDF"

980 J$-"L"+F$+".SDF"

990 OPEN "O",#1,H$

1000 OPEN "O",#2,I$

1010 OPEN "O",#3,J$

1020 FOR I-I TO N:FOR. J-l TO D:PRINT#1,USING "####.#######
";GX(I,J);GY(I,J);:NEXT:PRINT#1,:NEXT

1030 LPRINTzLPRINT H$;:LPRINT " GENERAL ADSORPTION ISOTHERM DATA"

1040 GOSUB 1250

1050 M$-"X(uM ZN/L)":N$-"Y(uM ZN/G)"

1060 LPRINT USING "\ \";M$,N$

1070 FOR I-l TO NzFOR. J-l TO DzLPRINT USING "####.#######
";GX(I,J);GY(I,J);:NEXT:LPRINT:NEXT:LPRINT

1080 FOR I-l TO NzFOR J-l TO D:PRINT#2,USING "##.#####
";FX(I,J);FY(I,J);:NEXT:PRINT#2,:NEXT

1090 LPRINT I$;:LPRINT " FREUNDLICH ADSORPTION ISOTHERM DATA"

1100 GOSUB 1330

1110 OS-"x LOG[ZN]":P$-"Y LOG X/M"

1120 LPRINT USING "\ \";O$,P$

1130 FOR I-1 TO N:FOR J-I T0 D LPRINT USING "##.#####
”;FX(I,J);FY(I,J);:NEXT:LPRINT:NEXT:LPRINT

1140 FOR I-1 TO NzFOR. J-l TO D:PRINT#3,USING "####.#######
";LX(I,J);LY(I,J);:NEXT:PRINT#3,:NEXT

1150 LPRINT J$; :LPRINT " LANGMUIR ADSORPTION ISOTHERM DATA"

1160 GOSUB 1410

1170 Q$-"X(uM ZN/L)":R$-"Y(uM ZN/L/uM/G)"

1180 LPRINT USING "\ \";Q$,R$

1190

105

FOR I-l TO NzFOR J-l TO D:LPRINT USING "####.#######

";LX(I,J);LY(I,J);:NEXTzLPRINTzNEXTzLPRINT

1200
1210
1220
1230
1240
1250
1260
1270

CLOSE #1:CLOSE #2: CLOSE #3

LPRINT CHR$(27) "@"

WIDTH "LPTl:",8O

END

REM *****SUBROUTINE TO PRINT REGRESSION EQUATIONS
LPRINT "FOR THE GENERAL ISOTHERM (ZN) VS X/M "
LPRINT "B-";B9;TAB(25),"A-";A3;TAB(4S);"R92-";R9
YS-B9*GX(1,1)+A3

1280 Y6-B9*GX(N,1)+A3

1290 LPRINT "X5-";GX(1,1);TAB(40),"Y5-";Y5

1300 LPRINT "X6-";GX(N,1);TAB(40),”Y6-";Y6

1310 LPRINT "Y-";B9;"X+";A3

1320 RETURN

1330 LPRINT ”FOR THE FREUNDLICH EQUATION LOG [ZN] VS LOG X/M"
1340 LPRINT "B-";B3;TAB(25),"A-";A1;TAB(45);"R“2-";R3
1350 Y1-B3*FX(1,1)+A1

1360 Y2-B3*FX(N,1)+A1

1370 LPRINT "X1-";FX(1,1);TAB(40),"Yl-";Y1

1380 LPRINT ”X2-";FX(N,1);TAB(40),"Y2-";Y2

1390 LPRINT "Y—";B3;"X+";A1

1400 RETURN

1410 LPRINT "FOR THE LANGMUIR ISOTHERM (ZN) VS C/X/M"
1420 LPRINT "B-";B12;TAB(25),"A-";A4;TAB(45),"R‘2-";R12
1430 Y7-B12*LX(1,1)+A4

1440 Y8-812*LX(N,1)+A4

1450 LPRINT "X7-";LX(1,1);TAB(40),"Y7-";Y7

1460 LPRINT ”X8—";LX(N,1);TAB(40),"Y8-";Y8

1470 LPRINT "Y-";B12;"X+";A4;TAB(40),"APPARENT ADSORPTION MAXIMUM=
";B14;” (uM Zn/G)"

1480 RETURN

1490 REM SUBROUTINE TO CALCULATE REGRESSION EQUATIONS
1500 LOXY-O

1510 PQXY-O

1520 PXXY-O

1530 XSUMLO-O

1540 YSUMLO-O

1550 XSUMPQ-O

1560 YSUMPQ-O

1570 XSUMPX-O

1580 YSUMPX-O

1590 XSSLO-O

1600 YSSLO-O

1610 XSSPQ-O

1620 YSSPQ-O

1630 XSSPX-O

1640 YSSPx-O

1650 FOR I-1 TO N

1660 REM *****GENERAL

1670 PXXY-PXXY+GX(I,1)*GY(I,1)

1680
1690
1700

XSUMPX-XSUMPX+GX(I,1)
YSUMPX-YSUMPX+GY(I,1)
XSSPx-XSSPX+GX(I,1)‘2

1710
1720
1730
1740
1750
1760
1770
1780
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100

10

106

YSSPx-YSSPx+GY(I,1)‘2

REM *****FREUNDLICH
LOXY-LOXY+FY(I,1)*FX(I,1)
XSUMLO-XSUMLO+FX(I,1)
YSUMLO-YSUMLO+FY(I,1)
XSSLO-XSSLO+FX(I,1)‘2
YSSLO-YSSLO+FY(I,1)“2

REM *****LANGMUIR
PQXY-PQXY+LX(I,1)*LY(I,1)
XSUMPQ-XSUMPQ+LX(I,1)
YSUMPQ-YSUMPQ+LY(I,1)
XSSPQ-XSSPQ+LX(I,1)‘2
YSSPQ-YSSPQ+LY(I,1)“2
NEXT I

REM *****TO CALCULATE GENERAL REGRESSION
B7-PXXY-XSUMPX*YSUMPX/N
BB-XSSPx-XSUMPx‘z/N
B9-B7/BS
A3-YSUMPX/N-B9*XSUMPX/N
R7-B7“2
R8-B8*(YSSPx-YSUMPX“2/N)
R9-R7/R8

REM *****T0 CALCULATE FREUNDLICH REGRESSION
B1-LOXY-XSUMLO*YSUMLO/N
32-XSSLO-XSUMLO‘2/N
B3-B1/B2
A1-YSUMLO/N-B3*XSUMLO/N
R1-B1“2
R2-Bz*(YSSLO-YSUML0“2/N)
R3-R1/R2

REM *****TO CALCULATE LANGMUIR REGRESSION
B10-PQXY-XSUMPQ*YSUMPQ/N
Bll-XSSPQ-XSUMPQAZ/N
B12-BlO/B11
A4-YSUMPQ/N-B12*XSUMPQ/N
R10-B10‘2
R11-BII*(YSSPQ-YSUMPq‘z/N)
R12-R10/R11

B14-B11/B10

RETURN

ZNCALC
REM ZNCALC.BAS

CALCULATES ‘VALUES

MEASURED BY AA SPECTROSCOPY

20 REM ZNCALC.BAS WAS WRITEN BY' RICHARD CLEVELAND ZIELKE GRADUATE
ASSISTANT IN SOIL CHEMISTRY MICHIGAN STATE UNIVERSITY CROP AND SOIL
SCIENCES DEPARTMENT

JULY 23 1986

30 LPRINT CHR$(27) "N"CHR$(6)
40 LPRINT CHR$(27) "M";
50 LPRINT CHR$(27) "P" CHR$(15);

CONSTRUCTION
GENERAL,FREUNDLICH AND LANGMUIR ISOTHERMS USING ZN(I,J) AND ZF(I,J) AS

107

60 WIDTH 'LPTl:",150

7o LPRINT CHR$(27) "1"CHR$(10);

80 LPRINT CHR$(27) "Q"CHR$(140);

90 DEFDBL z,G,F,L

100 OPTION BASE 1

110 INPUT "WHAT Is THE NUMBER OF TREATMENTS?",N

120 INPUT "WHAT IS THE NUMBER OF ADSORPTION/DESORPTION CYCLES?",D

130 DIM ZI(N,D),ZF(N,D),ZREM(N,D)

140 DIM ZADS(N,D),ZINI(N,D),ZSOL(N,D),ZDES(N,D)

150 DIM GX(N,D),GY(N,D),FX(N,D),FY(N,D),LX(N,D),LY(N,D)

16o ZI-INITIAL PPM ZN ZF-FINAL PPM ZN ZREM-MG ZN REMAINING IN SYSTEM
AFTER EQUIL ZADS-MG ZN ADSORBED ZINI-MG ZN IN SYSTEM BEFORE EQUIL
ZSOLPMG ZN IN SOLUTION AT EQUIL ZDEs-MG ZN DESORBED

17o REM GX-ZN ACTIVITY (uM/L) GY-X/M (uM/G) FX-LOG [ZN] FY=LOG X/M LX=ZN
ACTIVITY LY-C/X/M (uM/L/uM/G)

180 INPUT "WHAT IS MESSAGE?",A$

19o INPUT "WHAT IS THE SAMPLE VOLUME IN MLS?",VS

200 INPUT "WHAT IS THE ANALYTE VOLUME IN MLS?",VA

210 INPUT "WHAT IS IONIC STRENGTH IN M/L?",U

220 INPUT "WHAT IS THE SAMPLE WEIGHT IN GRAMS? ",W

230 K:10“(-.5085*4*U“.5/(1+1.969*U“.5)) :REM EXTENDED DE BYE HUCKEL EQN

TO CALCULATE ZN ACTIVITY COEFFICIENT

240 LPRINT n *************************PROGRAM IS
ZNCALC.BAS************************* ":LPRINT "IDENTIFYING MESSAGE:
":zLPRINT A$

250 LPRINT " *****INPUT PARAMETERS FOR SPECIFIED
FILENAME*****”

260 LPRINT "SAMPLE VOLUME IN MLS-";VS

270 LPRINT "ANALYTE VOLUME IN MLS-";VA

280 LPRINT "IONIC STRENGTH-";U

290 LPRINT "ZN ACTIVITY COEFFICIENT- ":K

300 LPRINT "SAMPLE WEIGHT IN GRAMS-";W

310 INPUT "WHAT IS FILENAME CONTAINING ZF(I,J) DATA (OMIT
EXTENSION)?",F$

320 S$-F$+".DAT"

330 LPRINT "INPUT FILENAME-";S$:LPRINT

340 OPEN "I",#1,S$

350 FOR I-1 TO NzFOR J-l TO D:INPUT#1,ZF(I,J):NEXTzNEXT

360 LPRINT "INITIAL PPM ZN FINAL PPM ZN INITIAL MG ZN MG ZN
REMAININ MG ZN ADSORBED MG ZN DESORBED"
37o '*************************START DATA

CALCULATI ONS **************************

380 FOR I-l TO N

390 FOR J-l TO D

400 IF J-l THEN INPUT ”WHAT IS THE INITIAL PPM ZN?",ZI(I,J)
410 IF J>l THEN ZI(I,J)-ZF(I,J-1)*(VS-VA)/VS

420 IF J-l THEN ZINI(I,J)-ZI(I,J)*VS/1000

430 IF J>l THEN ZINI(I,J)-ZREM(I,J-1)

440 ZSOL(I,J)-ZF(I,J)*VS/1000

450 ZREM(I,J)-ZINI(I,J)-ZF(I,J)*VA/1000

460 ZADS(I,J)-ZINI(I,J)-ZSOL(I,J)

470 IF J-l THEN ZDES(I,J)-O ELSE ZDES(I,J)-ZADS(I,J-I)-ZADS(I,J)
480 GX(I,J)-ZF(I,J)*K/.06537

490 IF J-l THEN GY(I,J)-(ZI(I,J)-ZF(I,J))*VS*1000/(65370!*W)

108

500 IF J>1 THEN GY(I,J)-GY(I,J-1)+(ZI(I,J)-ZF(I,J))*VS*1000/(6S370!*W)
510 FY(I,J)-LOG(GY(I,J))/2 30256

520 FX(I,J)-LOG(ZF(I,J)/.06537)/2.30256

530 LX(I,J)-GX(I,J)

540 LY(I,J)-LX(I,J)/GY(I,J)

550 LPRINT USING" ###.#########= ###.######### :###.#########
###.######### ###.#########
M.M";ZHLJ),ZF(I,J),ZINI(I,J),ZREM(I,J),ZADS(I,J),ZDES(I,J)
560 NEXT J

570 LPRINT

580 NEXT I

590 '**************************END DATA
CALCULATIONS***************************

600 CLOSE #1

610 U$-F$+".OUT"

620 OPEN "O",#3,U$

630 FOR I-l TO NzFOR J-l TO D:PRINT#3,USING "##4##”
";ZI(I,J);ZF(I,J);:NEXT:PRINT#3,:NEXT

640 LPRINT U$;:LPRINT "(ADJACENT COLUMNS ARE INITIAL .AND FINAL ZN
REMAINING IN SOLUTION AT EQUILIBRIUM. THE # OF COLUMNS/2 -# OF
DESORPTION CYCLES. ADJACENT Rows ARE REPS.)"

650 K$-"INI PPM ZN':L$-"FIN PPM ZN"

660 LPRINT USING "\ \";K$,L$

670 FOR I-I TO N:FOR J-l TO D:LPRINT USING "###.#######
";ZI(I,J);ZF(I,J);:NEXTzLPRINTzNEXT

680 CLOSE #3

690 GOSUB 1220

700 REM SUBROUTINE TO PRINT AND FILE GENERAL,FREUNDLICH AND LANGMUIR
ISOTHERMS

710 H$-"G"+F$+".SDF"

720 I$-"F"+F$+".SDF"

730 J$-"L"+F$+".SDF"

740 OPEN "O",#1,H$

750 OPEN "O",#2,I$

760 OPEN "O",#3,J$

770 FOR I—1 TO NzFOR J-l TO D:PRINT#1,USING "####.#######
":GX(I,J);GY(I,J);:NEXT:PRINT#1,:NEXT

780 LPRINT:LPRINT H$;:LPRINT " GENERAL ADSORPTION ISOTHERM DATA"

790 GOSUB 980

800 M$-"X(uM ZN/L)":N$-"Y(uM ZN/G)"

810 LPRINT USING "\ \";M$,N$

820 FOR I-1 TO NzFOR J-l TO D:LPRINT USING "####.#######
";GX(I,J);GY(I,J);:NEXT:LPRINT:NEXT:LPRINT

830 FOR I-1 TO N:FOR J-l TO D:PRINT#2,USING "##.#####
";FX(I,J);FY(I,J);:NEXT:PRINT#2,:NEXT

840 LPRINT Is; LPRINT " FREUNDLICH ADSORPTION ISOTHERM DATA"

850 GOSUB 1060

860 O$-"X LOG[ZN]":P$-"Y LOG X/M"

870 LPRINT USING "\ \";O$,P$

880 FOR I-1 TO NzFOR J-I TO D:LPRINT USING "##.#####
";FX(I,J);FY(I,J);:NEXT:LPRINT:NEXT:LPRINT

890 FOR I-l TO NzFOR J-1 TO D:PRINT#3,USING "####.#######
";LX(I,J);LY(I,J);:NEXT:PRINT#3,:NEXT

900 LPRINT J$;:LPRINT " LANGMUIR ADSORPTION ISOTHERM DATA"

109

910 GOSUB 1140
920 Q$-"X(uM ZN/L)":R$-"Y(uM ZN/L/uM/G)"

930 LPRINT USING "\
I-l

940

FOR

\";Q$.R$

TO N:FOR J-l TO D:LPRINT USING "####.#######

":LX(I,J);LY(I,J);:NEXTzLPRINTzNEXTzLPRINT
950 CLOSE #1:CLOSE #2: CLOSE #3

960 END
970 REM *****SUBROUTINE TO PRINT REGRESSION EQUATIONS
980 LPRINT "FOR THE GENERAL ISOTHERM (ZN) VS X/M "
990 LPRINT "B-";B9;TAB(25),"A-";A3;TAB(45);"R“2-";R9
Y5-B9*GX(1,1)+A3

Y6-B9*GX(N,1)+A3

1000
1010
1020
1030
1040
1050
1060
1070
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
1190
1200

LPRINT
LPRINT
LPRINT
RETURN
LPRINT
LPRINT

”X5-";GX(1,1);TAB(40),"Y5-";Y5
"X6-”;GX(N,1);TAB(40),"Y6-";Y6
"Y-";B9;"X+";A3

"FOR THE FREUNDLICH EQUATION LOG [ZN] VS LOG X/M"
"B-";B3;TAB(25),"A-";A1;TAB(45);"R“2-";R3

Y1-BB*FX(1,1)+A1
Y2-B3*FX(N,1)+A1

LPRINT
LPRINT
LPRINT
RETURN
LPRINT
LPRINT

"X1—";FX(1,1);TAB(40),”Y1—";Y1
"X2-";FX(N,1);TAB(40),"Y2-";Y2
”Y5";B3;"X+";A1

"FOR THE LANGMUIR ISOTHERM (ZN) VS C/X/M"
"B-";312;TAB(25),"A-";A4;TAB(45),"RA2-";R12

Y7-BlZ*LX(l,1)+A4
Y8-BlZ*LX(N,l)+A4
LPRINT "X7-";LX(1,1);TAB(40),"Y7-";Y7
LPRINT "X8-";LX(N,1);TAB(40),"Y8-";Y8

LPRINT

"Y-" ;812 ; "X+" ;A4 ; TAB(40) , "APPARENT ADSORPTION MAXIMUM=

";B14;" (uM Zn/G)"

1210
1220
1230
1240
1250
1260
1270
1280
1290
1300
1310

RETURN

REM SUBROUTINE TO CALCULATE REGRESSION EQUATIONS

LOXY-O
PQXY-O
PXXY-O

XSUMLO-O
YSUMLO-o
XSUMPQ-O
YSUMPQ-O
XSUMPX-o
YSUMPX-O

1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420

XSSLO-O

YSSLO-O

XSSPQ-O

YSSPQ-O

XSSPX-o

YSSPX-O

FOR I-1 TO N

REM *****GENERAL
PXXY-PXXY+GX(I,1)*GY(I,1)
XSUMPX-XSUMPX+GX(I,1)
YSUMPX-YSUMPX+GY(I,1)

1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1590
1600
1610
1620
1630
1640
1650
1660
1670
1680
1690
1700
1710
1720
1730
1740
1750
1760
1770
1780
1790
1800
1810
1820
1830

110

XSSPX-XSSPX+GX(I,1)‘2
YSSPX-YSSPX+GY(I,1)‘2
REM *****FREUNDLICH
LOXY-LOXY+FY(I,1)*FX(I,1)
XSUMLO-XSUMLO+FX(I,1)
YSUMLO-YSUMLO+FY(I,1)
XSSLO-XSSLO+FX(I,1)“2
YSSLO—YSSLO+FY(I,1)“2
REM *****LANGMUIR
PQXY-PQXY+LX(I,1)*LY(I,1)
XSUMPQ-XSUMPQ+LX(I,1)
YSUMPQ-YSUMPQ+LY(I,1)
XSSPQ-XSSPQ+LX(I,1)“2
YSSPQ-YSSPQ+LY(I,1)‘2
NEXT I

REM *****TO CALCULATE GENERAL REGRESSION
B7-PXXY-XSUMPX*YSUMPX/N
BB—XSSPX-XSUMPX‘z/N
B9-B7/BB
A3-YSUMPX/N-B9*XSUMPX/N
R7-B7“2
R8-BB*(YSSPX-YSUMPX“2/N)
R9-R7/R8

REM *****TO CALCULATE FREUNDLICH REGRESSION
B1-LOXY-XSUMLO*YSUMLO/N
Bz-XSSLO-XSUMLo‘z/N
B3-B1/B2
A1-YSUMLO/N-B3*XSUMLO/N
R1-BI‘2
R2-B2*(YSSLO-YSUML0“2/N)
R3-R1/R2

REM *****TO CALCULATE LANGMUIR REGRESSION
BlO-PQXY-XSUMPQ*YSUMPQ/N
B11-XSSPQ-XSUMPQ‘2/N
B12—B10/B11
A4-YSUMPQ/N-B12*XSUMPQ/N
R10-BIO‘2
R11-B11*(YSSPQ-YSUMPQ“2/N)
R12-R10/R11

B14-Bll/BlO

RETURN

LI ST OF REFERENCES

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