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Research: Science and Education

1348 Journal of Chemical Education Vol. 84 No. 8 August 2007 www.JCE.DivCHED.org

The main concern of chemists is the control of productyields and reaction rates, but the number of ways we can in-fluence the outcome of a particular reaction is surprisinglysmall. Moreover, the methods that are available have limitedapplicability owing to the physical properties of the systemunder study. Temperature, for example, is one of the mostcommonly controlled parameters, but the temperature range

available for monitoring is often severely limited by the sta-bility and phase of reacting substances. Changes in pressureare effective only in systems with at least one gaseous com-ponent. Other perturbations, including radiation, mechani-cal and acoustic actions, and so forth, have limitedapplicability and are specific to the process under investiga-tion. Any additional method that can be used to controlchemical reactivity is particularly welcome.

Solvent-control of chemical reactions is one method thathas gained popularity in recent years, since a judiciously se-lected solvent can alter the equilibrium or kinetics of a reac-tion, even changing its direction entirely. Also, since theoverwhelming majority of known chemical processes take

place in solution or liquid phase, solvent-control is a conve-nient means of influencing reactions. The comprehensivedevelopment of solution chemistry has allowed chemists toput forward and prove the idea that the solvent acts simulta-neously as a medium and a reactive agent in a chemical sys-tem (13).

A number of books (49)are devoted to detailing thepower that solvents have over the kinetics of chemical pro-cesses (10, 11)and the issue is also addressed in nearly everyphysical chemistry textbook. The influence of solvents onchemical equilibriaparticularly the role of solvent in alter-ing product yields and reaction branchinghas received lessattention (1218)and consequently is not included in manytextbooks. The didactic presentation of solvent effects onchemical equilibria given below is intended to provide thebasis for teaching physical chemistry of solutions. Followinga general review of equilibrium thermodynamics and quan-tification of the universal and specific solutesolvent inter-actions, the solvent-control is illustrated with examples fromhomo- and hetero-molecular associations and conformationalequilibria.

The material given in this article is appropriate for pre-sentation following a review of the general ideas underlyingchemical equilibrium and an introduction of different typesof solvent effects. The students should be familiar with theequilibrium constant and its relationship to the equilibriumfree energy (Gibbs energy at constant pressure and tempera-

ture); then the concepts of universal and specific solvationmay be introduced. Solvents such as hexane and carbon tet-rachloride are excellent examples of universal solvents, sincethey provide inert environments for carboxylic acid dimer-ization. The specific solvents such as water and dioxane arecapable of hydrogen bonding with the acid. The concept ofa dielectric medium that screens electrostatic solutesolvent

interactions should be discussed in terms of the dielectric con-stant.

Examples of nonpolar solvents with small dielectric con-stants, such as hexane, and polar solvents with large dielec-tric constants, such as acetonitrile and water, should beconsidered. The instructor may elect to quiz the students onchemical equilibrium and the types of solutesolvent inter-actions at this point. At this point, the discussion of solventeffects on chemical equilibrium may be terminated in a gen-eral chemistry curriculum. A physical chemistry class can fur-ther explore the detailed examples included below and in theSupplemental Material.WThese descriptions of homo- andhetero-molecular association and conformer equilibria could

be used to develop illustrative laboratory experiments. In suchcase, and especially if the laboratory experiment does not fol-low the lecture immediately, the instructor can provide a to-review list in the week preceding the lab. The to-review listshould be based on the lecture material and should give sev-eral examples of solutesolvent pairs and types of interactions.Finally, students should be required to hand in a completelaboratory report.

General Considerations

Chemical equilibrium (15)in solution can be representedin general as

BA (1)

where A are reactants and B are products formed from thereactants as a result of a chemical reaction. Consideration ofthe thermodynamic cycle gives the Gibbs energy of the reac-tion

! !G = GG GsolvAv" +GsolvB! ! (2)

where !GsolvA and!GsolvBare the Gibbs solvation energiesof reactants and products, respectively, and !Gvis theGibbsenergy of the reaction in vacuum.

The solutesolvent interactions can be separated intouniversal and specific components, giving a sum (19):

G G Gsolvuniv spec

= +( ) ( )! ! ! (3)

Control of Chemical Equilibrium by Solvent: WA Basis for Teaching Physical Chemistry of Solutions

Oleg V. Prezhdo* and Colleen F. Craig

Department of Chemistry, University of Washington, Seattle, WA 98195-1700; *[email protected]

Yuriy FialkovDepartment of Physical Chemistry, Ukrainian National Technical University, Kiev, Ukraine

Victor V. Prezhdo

Institute of Chemistry, Jan Kochanowski University, 25-020 Kielce, Poland
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www.JCE.DivCHED.org Vol. 84 No. 8 August 2007 Journal of Chemical Education 1349

In !G(univ) the solvent acts as an inert medium, whereas!G(spec) includes chemically active interactions such as hy-drogen bonding. Substituting eq 3 in eq 2 leads to a generalequation that describes the effect of a solvent on chemicalequilibrium:

G Gv

=! ! ++ "

+ "

)( )

()

!

!

G

G

(!GsolvA

univsolvB

univ

solvAspec(!GsolvBspec )) (4)

!Gv, of course, does not depend on the solvent. The differ-ence in the first bracket in eq 4 characterizes universal solva-tion, and the difference in the second bracket accounts forspecific solvation. Thus, the solvent effect on chemical equi-librium is determined by the solvation energies of each ofthe chemical species involved. Note that for universal, chemi-cally-inert solvents where !G(univ)>> !G(spec), we may re-write eq 4 as

( ) ( )= + "G G G G ! ! ! !v solvB

univsolvA

univ(5)

The equilibrium Gibbs energy is directly related to theequilibrium constant, K, at temperature T. As in eq 4 for theGibbs energy, one can distinguish between the universal andspecific contributions of a solvent to the magnitude of K

"=

+

K

G! v

ln

+

RT

"( ) ( )

! !G GsolvBuniv

solvAuniv

"( ) (

! !G GsolvBspec

solvAspec))

(6)

or

"=+ +

K G G G

RTln

! ! !v (spec) (univ)# #(6a)

As before (cf. eq 5), the equations simplify for universal sol-vents:

= "+

K

G

ln!

(univ)

v

R T

"( ) ( )

! !G GsolvBuniv

solvAuniv

(7)

or

" ! !

K G Guniv

v univ( )

=

+

ln #

(( )

R T(7a)

We can develop a practical representation for #!G(univ)

by considering the screening of the electrostatic solutesol-vent interactions in terms of solvent dielectric permittivity, $.Then eq 6a may be expressed (17)as

( )= + +"

"

"

=

KR T

G G

R T

1

1

ln ! !v solvspec solvB solvA #

% %

$

! !G Gv solvspec solv

+ +( )

# # %

$

(8)

where the %irepresent the main types of electrostatic inter-

actions, such as dipoledipole, iondipole, ionion interac-tions, and so forth. Equation 8 simplifies for the case of auniversal solvent to

" !KR T

Guniv v sol

= +( ) # %1ln vv

$(9)

where #%solvequals the universal solvation component ex-

trapolated to vacuum ($ =1), that is, #%solv= #!G$=1(univ)

. Inaddition to characterizing a solvent, the permittivity $pro-vides a convenient handle for hypothetically turning the sol-utesolvent interaction on and off. For instance, in the limitof perfect screening, $&'and the 1$interaction terms ineqs 8 and 9 disappear.

An analysis of eq 8 allows us to draw essential conclu-sions about the influence of solvent on the thermodynamiccharacteristics of chemical processes taking place in solution.It follows from eq 8 that at fixed temperature, the equilib-rium constant changes with solvent properties because of achange in either a specific interaction, #!Gsolv

(spec), or a uni-versal electrostatic interaction, #%solv. This leads to several sce-

narios for the functional dependence of ln K on 1$

,depending on the behavior of #!Gsolv(spec)and #%solv.

Generally, if both #!Gsolv(spec)and #%solvvary between the

solvents, ln K=f(1$) is a nonlinear function. Even in sol-vents where the specific interaction #!Gsolv

(spec) is constant,and only the universal interaction #%solv changes, ln K =f(1$) is still nonlinear in general. If both the #!Gsolv

(spec)

and #%solv, values are constant for different solvents, that is,in a conditionally universal medium (16),the ln K=f(1$)dependence becomes linear (cf. eq 9)

univ b

$= +( )K aln (10)

where aand bare the coefficients of the linear equilibriumequation. In the absence of specific solutesolvent interac-tions #!Gsolv

(spec)(0, the ln K=f(1$) dependence is alsolinear and is described by eq 10.

Extrapolation of the ln K=f(1$) dependence to $&', that is, putting the system in a hypothetical medium inwhich there are no electrostatic interactions, reduces eq 8 fora solvent with specific interactions to

vsolv

spec#$ = +& '

( )K

R TG G

1ln ! !" (11)

Similarly, eq 9 becomes

=& '( )K G

RTln $univ

v

!" (12)

from which we can find the vacuum component of the Gibbsenergy of a chemical equilibrium process:

= & '( )

G R T K ln $v univ

! " (12a)

Finally, we can determine the energy of specific solva-tion by comparing the equilibrium constants of chemical pro-cesses taking place in specific and universal solvents withapproximately the same dielectric constant $(spec)=$(univ):

R T Kln sppec univ( ) ( )" =ln K G# !

( )solv

spec" (13)
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Thus, analysis of the ln K=f(1$) dependence allows oneto characterize all three basic components of Gibbs energyof a chemical process in solution: !Gv, #!Gsolv

(spec), and#!G$=1

(univ).To compare the equilibrium constants of eq 1 in two

solvents S(1) and S(2), we start by writing eq 8 for each sol-vent:

=( )ln KR TS

11 )vsolvS(spec

(1)+G G#! ! )) solvS1

+ (#%$

" (14a)

S 2 =( )K

R T

1ln v

solvS

(spec)(2)+ +#G G! !

##%

$solvS 2( )" (14b)

Solving eqs 14a and 14b for 1$ and equating the results,we obtain

S I II S1 2const const( ) ( )= +K Kln ln (15)

where

connst Iv

solvS

spec

v

solvS

1

2

= +

" +

( )

( )

( )G G

G G

! !

! !

#

#sspec( )

RT1"

#%solvS 1( )

#%solvS 2( )

(15a)

IIsolvS

solvS

solvBconst

1

2

= =

"( )

( )

# %

# %

% %%

% %

solvA S

solvB solvA S

1

2

[ ]"[ ]

( )

( )(15b)

An examination of eq 15 leads to two important conclusions.First, the logarithm of the equilibrium constant of a chemi-cal process in one solvent, S(1), is linearly related to the loga-

rithm of the equilibrium constant of the same process inanother solvent, S(2), Figure 1. Second, if constII> 1, as rep-resented in Figure 1, the equilibrium constant in solvent S(1)

is increased relative to solvent S(2). Solvent S(1)shifts the equi-librium towards products, so it can be thought of as havinga differentiating effect with respect to solvent S(2). Con-versely, solvent S(2)has a leveling effect with respect to sol-vent S(1), since it tends to shift the equilibrium towards themiddle.

In this section we have shown that solvent contributionsto the equilibrium constant produce two major factors thataffect chemical equilibrium: the Gibbs energies of specificand universal solvation. The former occurs by a donorac-ceptor interaction between solute and solvent. The latter origi-nates due to universal electrostatic interactions between soluteand solvent molecules and is often taken into account by con-sidering dielectric permittivity of the solvent.

Several methodologically interesting examples of solventinfluence on chemical equilibrium are presented in the fol-lowing sections. The examples cover a wide range of phe-nomena, including homo- and hetero-molecular associationand conformational equilibrium.

Homo-Molecular Association Processes

Dimerization is the most common homo-molecular as-sociation process:

A22A (16)

The solvent dependence of the equilibrium constant for the

dimerization process (eq 16) can be obtained through appli-cation of eq 8:

=KR T

G1

ln dim d! iimv

solvAspec

solvAspec

solv A solv A

2

2

+ "

+

"

( ) ( )! !G G2

2% %

$

"

(17)

The solvent interaction factors %solvA2and %solvAcan be cal-culated using eq 5. For a dimerization process (eq 16) takingplace in a universal medium, we write eq 7a as:

= +K

R T

G G1

ln dim ! !

dim

v

dim

( )univ( )univ#"

(18)

We can specify the form of #!Gdim(univ)in terms of dielectric

permittivity as in eq 9

= +R T

G1

dim!v %% %

$

solv A solvA 2 " 2"Kln dim( )univ

(19)

obtaining a linear relationship

$= +a

bKln dim

( )univ(20)

where !Gdim*=RTaand !Gdim

(univ)=RTb$.Equation 20 agrees well with experimentally determined

Kdimvalues, as illustrated in Table 1 for solutions of carboxy-lic acids. The correlation coefficient rpresented in the tableis close to one. The linear correlation between the logarithm

Figure 1. Dependence of the equilibrium constants, K, of processestaking place in a solvent S(1) on the equilibrium constants of thesame processes taking place in another solvent S(2).

ehT.1elbaT a dna b gnibircseDstneiciffeoCK51.892tasdicAcilyxobraCfonoitaziremiD

dicA a b r

citecA 26.4 01.5 289.0

citecaorolhconoM 19.3 51.5 799.0

citecsorolhciD 53.3 79.5 899.0

citecaorolhcirT 06.5 53.4 899.0
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of the equilibrium constant and the polarity parameter (20,21)ET, which is directly related to the solvent dielectric per-mittivity $, gives reasonable estimates for Kdim in universalmedia (Figure 2).

Table 2 presents the vacuum and universal solvent in-teraction components of the equilibrium Gibbs energy of car-boxylic acid dimerization. The data show that in the seriesfrom acetic to trichloroacetic acid, the vacuum interaction

component !Gdim*decreases and the solvent interaction com-ponent #! Gdi m

(univ) increases. While the !Gdi m* an d

#!Gdim(univ) values are comparable in weakly-polar solvents

(small $), the #!Gdim(univ)component rapidly decreases with

increasing $; in chlorobenzene #!Gdim(univ)drops to about 20

30% of #!Gdim*. This trend is even more pronounced in the

highly-polar nitrobenzene. Thus, the dependence of ln K(or!G)on 1$in universal media provides important informa-tion about the thermodynamics of homo-molecular associa-tion.

The ln Kdim=f($,T) dependence for acetic acid dimer-ization (CH3COOH, Figure 3) in a mixture of the universalsolvents CCl4and C6H5Cl can be approximated (22)by thefollowing

KT

1 72 1817 1 0 92 15

$= " + " +dimln .

. . 553 4.

$ T

The dimer concentration (x, molL1) is related to initial con-centration of the monomer (c) and the equilibrium constant(Kdim) by

=

+ "4 1 8x

K c Kdim dim cc

K

+ 1

8 dim(21)

Equation 21 predicts that the concentration of the acetic acid

dimer in hexane (n-C6H14,, Kdim(1.5 103

) equals half thatof the monomer, whereas the dimer concentration in ni-trobenzene (C6H5NO2, Kdim(10

2) equals one third. Usingselected mixtures of the two solvents, one can adjust the ace-tic acid dimer content from 33 to 50%. Similarly, dissolvingphenol in mixtures of CCl4and C6H5NO2with varying com-position one can control the concentration of the phenoldimer within a 2-to-12% interval relative to the monomerconcentration. More examples can be found in refs 17, 2325.

In a specific medium, the interaction between some par-ticipants of a chemical equilibrium and solvent molecules canbe exceptionally strong. In such a case, homo-moleculardimerization is described by

A2 + (S)2AS (22)

which assumes that the dimer is solvated to a lesser degreethan the monomer. In order to relate the homo-moleculardimerization in the presence of specific solutesolvent inter-action (eq 22) to that in a universal solvent (eq 16), we mustconsider the solvation process

ASA + S (23)

sdicAcilyxobraCfonoitaziremiDfoseigrenEsbbiGfostnenopmoC.2elbaT

K51.892tastnevloSlasrevinUni

tnevloS $!G

mid)vinu( lomJk(/ "1)

citecAdica

-orolhconoMdicaciteca

-orolhcirTdicaciteca

-lyhtemirTdicaciteca

enaxeH 98.1 7.6 8.6 9.7 3.6

enahtemorolhcarteT 32.2 7.5 7.5 6.6 3.5

ediflusidnobraC 26.2 8.4 9.4 6.5 5.4

mroforolhC 27.4 7.2 7.2 1.3 8.2

enezneborolhC 26.5 2.2 3.2 6.2 1.2

eneznebortiN 8.43 63.0 73.0 34.0 43.0

muucaV 4.11 7.9 3.8 9.31

N ETO : sadesserpxesimuucavehtrofygrenesbbiGehT !Gmid

v lomJk(/ "1 .)

Figure 2. Dependence of the dimerization constants for acetic acid(solid line) and trichloroacetic acid (dashed line) on the polarityparameter (ET) of the following solvents: 1n-C6H14; 2CCl4; 3CS2; 4CHCl3; 5C6H5Cl; and 6C6H5NO2.

Figure 3. Molecular models of the acetic acid dimers: (A) cyclicdimer and (B) linear dimer.
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Comparing eqs 22 and 23 with eq 16 indicates thathomo-molecular association in a specific medium is compli-cated by the necessity to break the AS bond first. The en-ergy required to break the bond is subtracted from the energygained during dimerization, resulting in a decrease of Kdimcompared to the corresponding value in a universal mediumwith the same dielectric permittivity. Mathematically, thedecrease in Kdim follows from eq 17: the [!GsolvA2

(spec) "

2!GsolvA(spec)] term becomes negative in a specific medium,thereby lowering the total energy of the association processrelative to the Gibbs energy for a universal medium, eq 19.This analysis is supported by the experimental data presentedin Table 3, which shows a comparison of Kdim values fordimerization of acetic acid in various universal and specificsolvents.

The role of specific solvation is illustrated particularlywell through consideration of Kdimvalues in specific and uni-versal solvents with similar dielectric primitivities. We con-sider here the specific solvents benzene and 1,4-dioxane, andthe universal solvent CCl4, which all have $+2.5. The Kdimvalue for acetic acid dimerization in benzene is an order of

magnitude lower than in CCl4. The role of specific solvationis even more dramatic in 1,4-dioxane, where the equilibriumconstant is almost three orders of magnitude lower than itsvalue in CCl4. 1,4-Dioxane shows significantly stronger spe-cific solvation than benzene because it is much more basic.Equations 8 and 9 were used to calculate the energies of spe-cific solvation of acetic acid by benzene and 1,4-dioxane, giv-ing 5.8 and 16.6 kJ mol1, respectively.

In water, the Gibbs energies of both specific and uni-versal solvation of acetic acid are large. Owing to waters highdielectric permittivity, the Kdimvalue is insignificant.

Binary mixtures of universal and specific solvents allowone to control the degree of homo-molecular association overa wide range of concentrations (17).For instance, by vary-ing the composition of the n-hexane1,4-dioxane mixture itis possible to change the content of the acetic acid dimers

from 50% to 8%. The dimer concentration can be furtherdecreased below the 8% mark, all the way down to 0.5%, byusing a mixture of 1,4-dioxane and water.

It happens quite often that suitable solvent selection pro-vides the only practical mechanism for changing the degreeof molecular association.

Solvent Effect on Conformer Equilibrium

A conformational equilibrium process can be expressedin general as

conformer IIconformer I (24)

or for the special case of cistrans isomerization as

trans-isomercis-isomer (25)

The experimental approaches for determining conformer con-centrations are not always sufficiently accurate (17); as a rulethe difference in conformer energies is relatively small, rang-ing from 0.1 to 1012 kJmol. This is similar to the ener-gies of dipoledipole interaction and specific solvation inmoderately active solvents, so it is difficult to discriminatebetween the conformer equilibrium and other processes.

Since dipole moments are often very different betweenthe conformers (26),dielectric permittivity of the solvent

plays a crucial role in the equilibrium processes (22, 25).Theconformer transformation energies are inversely proportionalto permittivity in universal solvents

conG! ff A B

= +

$(26)

whereAand Bare the coefficients of the linear energy equa-tion. Correspondingly, ln Kconfdepends on 1$linearly

conf = +$

K a b

ln (27)

and the equilibrium constant shows an exponential depen-dence on 1$. Here, a=ART and b = BRT, cf. eq 6.These equations are sufficiently accurate to describe experi-mental data for conformation and isomerization equilibria.

We will illustrate the argument above with the isomer-ization of 1,2-disubstituted ethane: XCH2CH2Y. The po-tential energy of the molecule depends on a number ofgeometric parameters, the most important of which is the tor-sion angle ,(Figure 4). Stable conformers include the syn-clinal (sc) conformation characterized by ,sc and theanti-periplanar (ap) conformation characterized by ,ap, whichexactly equals 180owing to symmetry. The key parametersof the potential energy profile include the difference !Ginthe Gibbs free energies of the isomers and the heights of thetwo types of maxima !G#1and !G

#2. Given an explicit form

noitaziremiDrofstnatsnoCmuirbiliuqE.3elbaTK51.892tastnevloSsuoiraVnidicAcitecAfo

stnevloSlasrevinU $ Kmid

enaxeH 88.1 0521enahtemorolhcarteT 32.2 099

ediflusidnobraC 26.2 007

mroforolhC 27.4 092

enezneborolhC 26.5 042

eneznebortiN 8.43 011

stnevloScificepS

enezneB 3.2 59

enaxoiD-4,1 2.2 2.1

retaW 3.87 50.0

Figure 4. The potential energy (!G#1) of molecules of theXCH2CH2Y type (see main text for detailed explanation).
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for the shapes of the minima and the maxima, for instance, acosine function, one can uniquely determine the values of theangles ,scand ,ap. The Gibbs energy difference !Gbetweenthe stable rotamers follows the inverse dependence on solventdielectric permittivity. For example, eq 26 for 1-fluoro-2-chloroethane in mixtures of alkane and chloralkane solventsbecomes (27)

2 86 8.G! conf = " + ..

.

69

0 963

$

r =

Considering eq 5 in the context of eq 26, it is clear thatan increase in solvent dielectric permittivity decreases theabsolute value of the electrostatic components of the con-former transformation free energies in universal solvents. Thisstabilizes the isomerization equilibrium. For instance, the!Gconf for bromocyclohexanone in cyclohexane ($ = 2) is5.2 kJmol, while in acetonitrile ($=36) the energy equals0.3 kJmol.

The stabilization of polar conformers offered by solvents

with higher dielectric permittivity affects not only the finalequilibrium composition of the conformer mixture, but alsothe rate of approach to equilibrium. When the transition statebetween the conformers is more polar than the stable con-formersas is often the caseequilibration occurs faster inpolar solvents. We see this phenomenon, for instance, withthe rotation around the formally double CC bond in sub-stituted ethylenes

In this example, the isomerization transition state (II) is sig-nificantly more polar than the stable conformer (I) (28).

The influence of specific solvation on conformationalequilibrium is widely known for solvents capable of inter-molecular hydrogen bonding. A good illustration is given bythe tautomerization of imidazoletetrahydropyran (III), whichcan form a hydrogen bond or even abstract a proton (IV) insuch solvents as chloroform (28):

However, correlating specific solvation effects on con-formational equilibrium with the physical and chemical prop-erties of the solvent is extremely difficult. Attempts todetermine simple and reliable connections between !G andln Kconfvalues and the donor and acceptor energy levels donot succeed in general. Significantly better results have beenobtained with pairwise solutesolvent interaction parameters(29).

As in the molecular association example above, often-times the solvent effect is the only method available to effect

drastic change in the relative concentrations of different con-formational forms. Consider, for example, dichloro-acetaldehyde conformers in cyclohexane and DMSO solvents.At room temperature, the axial rotamer is favored in cyclo-hexane; the equilibrium constant for the formation of thisrotamer is Kconf = 0.79. However, the corresponding Kconfvalue in DMSO is just 0.075. To obtain a similar equilib-rium in cyclohexane, one would have to cool the solution to

64 K (209 C); this is entirely impossible experimentally,since cyclohexane freezes at +6.5 C. Similarly, to achieve Kconf=0.79 in DMSO, one would have to heat the solution to435 K (162 C).

Conclusions

We have presented a didactic description of solvent ef-fects on chemical equilibria, illustrated by several examplesof basic processes occurring in solution. This material is in-tended to provide the basis for teaching physical chemistryof solutions, assuming the students are familiar with the gen-eral ideas underlying chemical equilibrium: the equilibrium

constant and equilibrium free energy. The universal and spe-cific types of solvation have been introduced, followed bydetailed examples of homomolecular association and con-former equilibrium. Further examples involving hetero-molecular association may be found in the SupplementalMaterial.WThis article shows the students that solvent canbe used to influence chemical equilibrium, thereby alteringthe yield of reaction products.

To determine the influence of solvent on chemical equi-librium, it is necessary to consider the donoracceptor prop-erties of the solvent as well as its polarity (i.e., permittivityas a microscopic property or the dipole moment and polar-izability as a molecular property). Using mixed solvents al-

lows one to widely vary these properties.We have not considered chemical processes taking placein water, because they have been studied more extensivelythan those taking place in nonaqueous environments. More-over, owing to its singular physical-chemical properties, wa-ter in no way provides a representative system for the studyof nonwater solvents. It is certainly necessary to give atten-tion to mixtures of water and nonwater solvents, which findgreater application in research and in industry (dyeing, elec-trochemical processing of materials, etc.). However, areas ofscience and engineering based on nonwater solvents are ad-vancing no less intensely. Clearly the development presentedin this article is urgently needed and will provide a valuableaddition to the physical chemistry curriculum.

Acknowledgments

Financial support from the National Science Founda-tion of the United States and Petroleum Research Fund ofthe American Chemical Society is gratefully acknowledged.

WSupplemental Material

Mathematical derivation of the temperature dependenceof the Gibbs energy as well as a detailed example of the sol-vent effect on heteromolecular association are available in thisissue ofJCE Online.
http://www.jce.divched.org/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Aug/abs1348.htmlhttp://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/

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2. Noeres, C.; Kenig, E. Y.; Gorak, A. Chem. Eng. Process.2003,42,157.

3. Kapucu, N.; Guvenc, A.; Mehmetoglu, U.; Calimli, A. Rev.Chem. Eng.1999,15,233.

4. Amis, E. S.; Hinton, J. F. Solvent Effect on Chemical Phenom-ena;Academic Press: New York, 1973.

5. Entelis, S. G.; Tiger, R. P. Kinetic of Reactions in Liquids,Khimiya: Moscow, 1973; in Russian.

6. Palm, V. A. The Foundations of Quantitative Theory of OrganicReactions; Khimiya: Leningrad, 1977; in Russian.

7. Reichardt, C. Solvents and Solvent Effects in Organic Chemis-try;VCH: Weinheim, Germany, 1988.

8. Connors, K. A. Chemical Kinetics; VCH: New York, 1990.9. Pross, A. Theoretical and Physical Principles of Organic Reac-

tivity;John Willey & Sons, Inc.: NewYork, 1995.10. El Seoud, O. A.; Bazito, R. C.; Sumodlo, P. T.J. Chem. Educ.

1997,74,562.

11. Mazzacco, C. J.J. Chem. Educ. 1996,73,254.12. Pietro, W. J.J. Chem Educ. 1994,71,416.13. Leenson, I. A.J. Chem. Educ. 1986,63,437.14. Butler, J. N.J. Chem. Educ. 1984,61,784.15. Honig, J. M.; Amotz, D. B.J. Chem. Educ.2006,83,132.16. Fialkov, Yu. Solvent as an Agent of Chemical Process Control;

Khimiya: Leningrad, 1990; in Russian.

17. Fialkov, Y. Y.; Chumak, V. L.Mixed Solvents: in Handbook ofSolvents;Wypych, G., Ed.; ChemTec Publ., William AndrewPubl.: Toronto, 2001; pp 505564.

18. Smith, J. V.; Missen, R. W. Chemical Reaction EquilibriumAnalysis. Theory and Algorithms;Wiley Interscience: New York,1982.

19. Silla, E.; Arnau, A.; Tunon, I. Fundamental Principles SolventsUse. In Handbook of Solvents;Wypych, G., Ed.; ChemTec

Publ., William Andrew Publ.: Toronto, 2001; pp 736.20. Dimroth, K. Liebigs Ann. 1963,57, 576.21. Johnson, D. A.; Shaw, R.; Silversmith, E. F.; Ealy, J.J. Chem.

Educ.1994,71,517.22. Fialkov, Yu. Ya.; Barabash, V. A.; Bondarenko, E. S. Ukr. Khim.

Zh. 1987,53,490.23. Barcza, L.; Buvari-Barcza, A.J. Chem. Educ.2003,80,822.24. De Leon, D. G. L.; Guidote, A. M.J. Chem. Educ.2003,80,

436.25. Silverstein, T. P.J. Chem. Educ.1998,75,116.26. Minkin, V. I.; Osipov, O. A.; Zhdanov, Yu. A. Dipole Moments

in Organic Chemistry;Plenum Press: New York, 1970.27. Orville-Thomas, W. J.; Redshaw, M. Internal Rotation in Mol-

ecules;Wiley-Interscience: London, 1974.28. Vereshchagin, A. I.; Kataev, V. E.; Bredikhin, A. A.; Timosheva,

A. P.; Kovylyaeva, G. I.; Kazakova, E. H. Conformation Analysisof Hydrocarbons and Their Derivatives;Nauka: Moscow, 1990;in Russian.

29. Prezhdo, V. V.; Shevchenko, T. N.; Prezhdo, O. V.J. Mol. Str.1994,318,243.
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Control of Chemical Equilibrium by Solvent: A Basis for

Teaching Physical Chemistry of Solutions

Supplementary Material

Oleg V. Prezhdo

Department of Chemistry, University of Washington, Seattle, WA 98195-1700 USA;

E-mail: [email protected]; Tel: +1-206-221-3931; Fax: +1-206-685-8665

Colleen F. Craig

Department of Chemistry, University of Washington, Seattle, WA 98195-1700 USA;

E-mail: [email protected]; Tel: +1-206-543-2738

Yuriy Fialkov

Department of Physical Chemistry, Ukrainian National Technical University, Kiev, Ukraine

Victor V. Prezhdo

Institute of Chemistry, Jan Kochanowski University, 5 Chciska str., 25-020 Kielce, Poland

E-mail: [email protected]

Temperature Dependence of the Reaction Gibbs Energy.

The temperature dependence of the reaction Gibbs energy can be approximated

by a linear function

G = G0+ TG1. (S1)

Equation (S1) almost always gives a valid description, provided the temperature range is

such that the solvent remains liquid at normal pressure (1). In the ideal case, G0= H is

enthalpy of reaction and -G1= S is reaction entropy.Substituting (S1) into (6a) in the

main text gives the temperature dependence of the equilibrium constant

( ))(1

)(

0

)(

1

)(

010)/1(lnuniv

solv

univ

solv

spec

solv

spec

solv

vvGTGGTGGTGRTK +++++= . (S2)

The terms in (S2) either depend inversely on temperature or have no explicit temperature

dependence.

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A similar representation of the temperature dependence of the coefficients aand b

in equation (10)

a = a0+ a1/T, b = b0+ b1/T,

leads to a convenient approximate form for the lnK = f(T, ) functional dependence,

which is valid for conditionally-universal and universal media:

ln K = a0+ a1/T + b0/+b1/T. (S3)

The coefficients a0,a1,b0, andb1 in (S3) are taken to be independent of both and T. For

a specific medium or an equilibrium constant considered over a wide temperature

interval, the lnK = f(T, ) dependence takes a more general form:

=

+++=+++=+++++=n

nn

n fT

b

T

aa

b

T

b

T

aa

T

b

T

bb

T

aaK

1

010

0102

21010 )(

11ln

.

(S4)

Solvent Effect on the Processes of Heteromolecular Association

In universal media, equilibrium constants for heteromolecular adduct formation

mA + nB AmBBn (S5)

depend exponentially on solvent permittivity:

ln Kadd = a + b/, (S6)

cf. Eq (27) in the main text. In the case m, n= 1, the concentration cMof adductABmay

be related to equilibrium constant KABand initial concentration of the components by:0

Mc

( ) ABMABMABM KcKcKc 2/14122/100 ++= . (S7)

If at least one of the stoichiometric coefficients m, n is greater than one, the

expression gives an equation of higher degree than (S7):

nmBAK

( ) ( )mMBMn

MAMMBA mccncccK nm =0

,

0

,/ . (S8)

Let us consider, for example, the interaction between acetic acid (HAc) and

tributyl phosphate (TBP) to form the adduct lHAcTBP, where l = 1...4; the trend

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predicted by (S6) is nicely illustrated by lHAcTBPformation in universal solvents, such

as n-C6H14, CCl4, n-C4H9Cl, and C6H5NO2, and in mixed solvents (2).

Equilibrium constants for lHAcTBP formation in one- and two-component

solvents are presented in Table S1. Note that the magnitude of Kadd decreases with

increasing permittivity. In this way, changing the permittivity of the universal solvent

allows us to change the output of thereaction. The percent output of complexes is listedin table below for initial concentration of 0.1 mol/l:0Mc

HAcTBP 2HAcTBP 3HAcTBP 4HAcTBP

% Complex in hexane

% Complex in nitrobenzene

84

43

46

13

32

4.5

22

2

The larger the electrostatic component of the process Gibbs energy ( ), the larger

the relative concentration change. Just as with our consideration of conformer

equilibrium, the solvent used here is an effective means of process adjustment. To reduce

the output of adduct HAcTBP in nitrobenzene to that in hexane, the nitrobenzene

solution would have to be cooled to 78

elG 0=

0C (taking into account that the enthalpy of

adduct formation is 15 kJ/mol) (3). Clearly, this process is not possible because the

melting point of nitrobenzene is +5.80C.

Table S1. Equilibrium constants (Kadd) of adduct (nHAcTBP) formation

in n-hexane (H), nitrobenzene (NB) and the mixed solvent (H + NB)at 298.15 K, and coefficients of equation (S6)

KaddSolvent

HAcTBP 2HAcTBP 3HAcTBP 4HAcTBPHexane (= 2.23)

H + NB (= 9.0)

H + NB (= 20.4)

Nitrobenzene (= 34.8)

327

28.1

19.617.4

8002

87.5

45.036.2

6.19105

27588.1

60.8

1.46107

1935518

337

Coefficients of equation (S6)

a

b

2.69

5.82

3.28

10.73

3.58

18.34

5.21

21.22

To demonstrate the effect of specific solvation on the equilibrium constant for

heteromolecular association, we begin by setting m= n= 1 in (S5):

A + B AB (S9)

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Generally bothAandBare subject to specific solvation:

A + S AS; B + S BS, (S10)

where ASand BS are solvated solute molecules. Note that the exact number of solvent

molecules interacting with the solutes is not important for the following.

Assuming that the specific solvation of the adduct ABis negligible in comparison

to the specific solvation of initial components, A-B interaction in the solvent S can be

represented by the scheme:

AS+BSAB+ 2S. (S11)

A and B are initially solvated by S, but when AB is formed, the specific interactions

between A and B replace those formerly between A and S, B and S. In this way,

heteromolecular association in a specific medium is a resolvation process, since each

initial component changes its solvation structure. Clearly, equilibrium constants of

heteromolecular association that are calculated without consideration of this circumstance

will not accurately represent process (S9), since there is a contribution to the equilibrium

from process (S11).

However, we can still determine the correct equilibrium constant for (S9)

KAB= [AB]/[A][B] (S12)

by removing the contribution of the resolvating process (S11)

KRP= [AB]/[AS][BS]. (S13)In dilute solutions, the concentration of the specific solvent S or the specific component

of a solvent mixture is much higher than the initial concentration of the equilibrium

species [A]0 and [B]0. In this case it is possible to use the approximation that the

activities of the equilibrium participants are equal to their concentrations, and then the

equations of mass balance for componentsAandBmay be obtained (4).

The equilibrium constant for adduct AB formation in a dilute solution was

obtained in terms of the solvating (S10) and resolvating (S11) processes (4):

KAB= KRP(1 + KAS)(1 + KBS). (S14)

A similar form for equation (S14) has been proposed elsewhere (5).

If the specific solvent concentration is not much larger than the concentration of

A andB, equation (S14) changes to

KAB= KRP(1 + KAS[S])(1 + KBS[S]). (S15)

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Let A be an acidic (electron-pair acceptor) reagent in reaction (S9), and B a basic

(electron-pair donor) reagent. Then, if S is an acidic solvent, one can neglect specific

solvation of reagent A, and the equations for the equilibrium constants of process (S9)

can be written in the form

KAB= KRP(1 + KBS); KAB= KRP(1 + KBS[S]). (S16)

If, on the other hand,Ais the basic component, equation (S16) can be re-written as

KAB= KRP(1 + KAS); KAB= KRP(1 + KAS[S]). (S17)

This analysis in the case of basic S will lead to a similar set of equations. Equations

(S16) and (S17) for specific solvation.were developed in Ref.s (6-8).

The constant KAB is identified in the literature as calculated by taking into

account the specific solvation (9), but to account for specific solvation one must obtain

the equilibrium constants for several processes. Process (S11) delivers KRP, (S10) gives

KASand KBS.

Fig. S1 provides a practical illustration of the approach described above by

presenting the equilibrium constants for the heteromolecular association of DMSO and o-

creosol

(CH3)2SO + o-CH3C6H4OH (CH3)2SOHOC6H4CH3 (S18)

in various binary solvent mixtures at 298.15 K: CCl4heptylchloride (10), two universal

solvent components (open circles); CCl4nitromethane (11), universal component (CCl4)and specific acceptor component (nitromethane) (closed circles); and CCl4ethyl acetate

(12), universal component (CCl4) and specific donor component (ester) (crosses). Note

that the linear dependence of ln Kon 1/is supported by fig. S1.

Lines 1-2 represent the initial solvation processes (cf. (S10)) for o-creosol in ethyl

acetate (KAS), and DMSO in nitromethane (KBS), respectively; lines 3-4 represent

resolvation (KRP) of the o-creosol DMSO complex (cf. (S11)). Line 5 gives the

heteromolecular-association equilibrium constants (KAB) calculated from lines 1 and 3, 2

and 4, as per equations (S16) and (S17). These derived KABare free of specific solvation

effects, and compare well with KAB for process (S18) occurring in the mixture of CCl4

and heptylchloride universal solvents.

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Fig. S1 indicates that specific solvation of one equilibrium participant decreases

the equilibrium constant compared to processes taking place in an isodielectric universal

solvent.

Figure S1. Equilibrium constant (lnK) vs. solution permittivity () for the heteromolecularassociation of DMSO with o-cresol (process 45). A range of solution permittivities were

obtained by varying the amount of heptylchloride (), ethyl acetate (), and nitromethane(). Lines 1 and 2 correspond to the initial specific solvation of a component, cf. process(S10). Lines 3 and 4 correspond to resolvation of the component, cf. process (S11). Line 5

presents a comparison of KABvalues: in the universal solvent mixture CCl4-heptylchloride

(); in the mixed universal/specific solvent mixtures CCl4-ethyl acetate () and CCl4-nitromethane (), calculated as per equation (S16).

1. KBSfor solvation of o-cresol in ethyl acetate;2. KBSfor solvation of DMSO in nitromethane;

3. KRPfor resolvation of o-cresol in DMSO. (DMSO in a CCl4 ethyl acetate mixture is

added to the o-cresol ethyl acetate mixture.)4. KRPfor resolvation of DMSO in o-cresol. (o-cresol in a CCl4 nitromethane mixture is

added to DMSO nitromethane mixture.);

5. Comparison of KABvalues for process (S18).

One method of studying the effect of specific solvation on the process of

heteromolecular association was described in Ref. (11), which focused on the equilibrium

process

C6H3(NO2)3+ C6H5N(CH3)2C6H3(NO2)3C6H5N(CH3)2 (S19)

in binary mixtures of universal solvent heptane with a specific component:

trifluoromethylbenzene, acetophenone or p-chlorotoluene. Trinitrobenzene is initially

solvated in these binary mixtures, so its interaction with the electron-donor component of

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the mixture represents the resolvation process. A charge transfer complex is formed as a

result:

C6H3(NO2)3S + C6H5N(CH3)2C6H3(NO2)3C6H5N(CH3)2+ S (S19a)

We can determine Kusing equation (14) written for heteromolecular association:

( ) .1ln )( B)( A)( AB

++=

solvspecsolv

spec

solv

spec

solv

v GGGGRT

K (S20)

For equilibrium (S19a) in mixed solvents we can assume 0 and 0.

Therefore, in the case of conditionally universal media, equation (14) can be converted

to:

)(

B

spec

solvG)(

AB

spec

solvG

.1

ln )( A

+=

solvspecsolv

v

RP GGRT

K (S20a)

It follows from equation (S20a) that lnKRP vs. 1/ will give a rectilinear plot.

Experimentally determined equilibrium constants for process (S19a) support this

conclusion (11).

The possibility for adjustment of the product yield for homomolecular

association is more dramatic in the case of the interaction between o-nitrobenzene and

triethylamine. The equilibrium constants for this process in several solvents are

determined in Ref. (12). The data indicate a 93% product yield in n-hexane, compared to

6% in 1,2-dichloroethane (DCE). To increase product yield in DCE to 93% it would be

necessary to cool the solution approximately by 1200C, which is below the melting point

of DCE. On the other hand, the temperature would have to be increased to nearly 3200C

to observe a product yield of 6% in n-hexane. This would require the use of high external

pressure or an autoclave.

Keto-enol tautomerism (2,13,14), ionization processes (4,15-23), acid-base

equilibia (4,23,24), transport and non-equilibrium processes (4), complex formation (23-

26), and solubility (4,27-31)provide further examples of the solvent control influence on

chemical processes; these are unfortunately beyond the scope of this paper. One article

cannot address every situation in which solvent may be employed to adjust chemical

equilibria, but the framework we have presented above provides a useful starting point

for investigating the role of solvent in various chemical processes.

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Literature cited.

1. Modell, M; Reid, R. Thermodynamics and its Applications. Prentice-Hall,Englewood Cliff: New Jersey, 1974.

2. Fialkov, Yu. Solvent as an Agent of Chemical Process Control, Khimiya:Leningrad, 1990 (Rus.).3. Chrisian, S; Lane, E., in Solutions and Solubilities, V.1, John Wiley&Sons: NewYork, 1975.

4. Fialkov, Y.Y.; Chumak, V.L. Mixed Solvents: in Handbook of Solvents, Ed. G.Wypych, ChemTec Publ., William Andrew Publ.: Toronto-N.Y., 2001, p. 505-

564.

5. Bishop, B; Sutton, L.J. Chem. Soc.1964, 6100.6. Bhownik, B; Srimani, P. Spectrochim. Acta 1973,A29, 935.7. Ewal, R; Sonnesa, A.J. Am. Chem. Soc. 1970, 92, 3845.8. Drago, R; Bolles, T.; Niedzielski, R.J. Am. Chem. Soc. 1966, 88, 2717.9. Fialkov, Yu.; Barabash, V. Theor. Exp. Chem. (Rus.)1986, 22, 248.10.

Barabash, V; Golubev, N; Fialkov, Yu.Doklady AN USSR, 1984, 278, 390.11.Borovikov, A.; Fialkov, Yu.Russian J. Gen. Chem. 1978, 48, 250.

12.Pawelka, Z; Sobczyk, L.Roczn. Chem. 1975, 49, 1383.13.Reichardt, Ch. Solvents and Solvent Effects in Organic Chemistry, VCH:

Wainheim, 1988.

14.Prezhdo, V.V.; Khimenko, N.L.; Surov; Yu.N. Ukr. Khim. Zh. 1986, 52, 58.15.Person, R.G.; Vogelgong, D.J. Am. Chem. Soc. 1963, 85, 3533.16.Falkenhagen, H.; Ebeling, W. in:Ionic Interaction. V.1. S. Petrucci, ed. Academic

Press: New York, 1971.17.Barthel, J.; Kreinke, H.; Kuntz, W. Physical Chemistry of Electrolyte Solutions.

Modern Aspects, Steinkopff, Dermstadt and Springer: New York, 1998.18.Cox, B.J.Ann. Rept. Progr. Chem. 1974, 70A, 249.19.Boyer, F.L.; Bircher, L.J.J. Phys. Chem. 1960, 64, 1330.20.Sakamote, N.; Masuda, R.Electrochim. Acta, 1981, 26, 197.21.Schmelzer, N.; Einfeld, J.; Grigo, M. J. Chem. Soc. Faraday Trans. I, 1988, 84,

931.

22.Fialkov, Yu.Ya.; Gorbachev, V.Yu; Kamenskaya, T.A.J. Mol. Liq. 2000, 89, 159.23.Gutmann, V. Coordination Chemistry in Non-Aqueous Solvents, Springer-Verlag:

Wien-N.Y., 1968.

24.Complexing in Non-Aqueous Solution. Ed. G. Krestov, Nauka: Moscow, 1989 (inRus).

25.Bak, M. Chemistry of Complex Equilibria, Akademiai Kiado:Budapest 1970.26.Burger, K. Solvation, Ionic, and Complex Formation in Non-Aqueous Solvent:

Experimental Methods for the Investigation. Elsevier Scientific Pub. Co.:Amsterdam-New York, 1983.

27.Hildebrand, J.H.; Scott, R.L. The Solubility of Non-Electrolytes, Reinold Publ.Corp.: N.Y. 1950.

28.Hildebrand, J.H; Pransnitz, J.M.; Scott, R.L. Regular and Related Solutions, VanNostrand: N.Y. 1970.

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29.Senichev V.Yu., Tereshatov V.V. General Principles Govering Dissolution ofMaterials in Solvents, in:Handbook of Solvents, Ed. G. Wypych, ChemTec Publ.,William Andrew Publ.: Toronto-N.Y., 2001, p. 101-132.

30.Gordon, J. The Organic Chemistry of Electrolyte Solutions. Wiley: New York,1975.

31.Marcus, Y.Ion Solvation, Wiley Limited: Chichester-New York, 1985.

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