Brian G. Cox

Print publication date: 2013

Print ISBN-13: 9780199670512

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199670512.001.0001

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Solvation and Acid–Base Strength

Chapter:
(p.21) 3 Solvation and Acid–Base Strength
Source:
Acids and Bases
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670512.003.0003

Abstract and Keywords

The change in dissociation constant of an acid with solvent is directly and quantitatively related to the change in solvation energies of the species involved. The solvation of electrolytes and non-electrolytes across a wide range of solvents is reviewed. The transfer of simple anions from water to non-aqueous solvents is almost universally unfavourable because of the loss of important hydrogen-bond interactions with water. Cation solvation is strongly dependent upon the basicity of the solvent. It is highly favourable in solvents such as dimethylsulphoxide, which are strong Lewis bases, but much weaker than water in low-polarity and low-basicity solvents such as acetonitrile and tetrahydrofuran. Non-electrolytes, such as carboxylic acids and amines, are more stable in non-aqueous media, but the effects are generally much smaller than for ions. In mixed solvents, preferential solvation by the most favourable solvent component determines the dependence of solvation and dissociation constants upon solvent composition.

Neutral acids, HA, such as carboxylic acids and phenols, eq. (3.1), are often very much weaker in non-aqueous solvents than in water or, equivalently, their anionic conjugate bases are very much stronger. On the other hand, the acidity of protonated amines and related nitrogen bases, eq. (3.2), is much less dependent on solvent.

$Display mathematics$
(3.1)

$Display mathematics$
(3.2)

A brief inspection of eqs. (3.1) and (3.2) suggests a possible underlying reason for their different sensitivities to solvent; namely, that the dissociation of PhOH results in the generation of two charged species, whereas there is no change in charge on dissociation of R3NH+.

In general, we expect charged species to be much more sensitive to solvent changes than neutral species, and indeed we will see that the dominant influence of a solvent lies in its ability to stabilize charge.

In this chapter we consider the influence of solvent on the (free) energy of electrolytes and non-electrolytes and the relationship between these changes in free energy and the dissociation constants in the solvents; e.g., in eq. (3.1) the effect of solvent on the free energies of PhOH, H+ and PhO. The solvation energies provide a basis for the understanding of the solvent-dependence of dissociation constants and they can also be used to enable reliable estimates of pKa in the absence of directly measured values. For convenience, we use water as the reference solvent from which the species are transferred, but the change in free energy between any other pair of solvents can be readily obtained by difference.

3.1 Solvation and acid dissociation constants: free energies of transfer

The difference in free energy of a species in two solvents is termed the free energy of transfer, ∆G tr. The relationship between ∆G tr for the various acid–base species and the change in pKa with solvent—for example, between water and solvent S—is best illustrated using a Born–Harber cycle, as in Scheme 3.1. (p.22)

Scheme 3.1. Born–Haber cycle for the dissociation of acid HA

In Scheme 3.1, ∆G tr(HA) represents the change in free energy of the undissociated acid on transfer from water to solvent S, and similarly for ∆G tr(H+ + A) = ∆G tr(H+) + ∆G tr(A). $Δ G S 0$ and $Δ G aq 0$ are the free energies of dissociation of HA in solvent S and water, respectively. It follows from the standard relationship between equilibrium constant, K, and the corresponding free energy change, ∆G, i.e., ∆G = −RTlnK, that the pKa and the free energy of dissociation, ∆G o, of HA are related by eq. (3.3).

$Display mathematics$
(3.3)

The Born–Haber cycle in Scheme 3.1 shows furthermore that

$Display mathematics$

Thus, by combining the expression for ∆GS o with eq. (3.3), it follows that the change in pKa of acid HA on transfer between water and solvent S, ∆pKa, is given by eq. (3.4), and similarly eq. (3.5) for acid BH+.

$Display mathematics$
(3.4)

$Display mathematics$
(3.5)

Eqs (3.4) and (3.5) show, therefore, that we should be able to understand and, in principle, predict changes in pKa-values with solvent from the influence of solvent on the free energies of the various participants in the acid–base equilibria. We may note that the changes in solvation energies of ions on solvent transfer are normally considerably higher than those of neutral species, especially when differences between two non-aqueous solvents are considered (see Section 3.4), and hence are expected to dominate the corresponding changes in pKa-values.

In numerical terms, it follows from the relationship between pKa and ∆G, eq. (3.3) that at 25°C:

$Display mathematics$
(3.6)

Thus, a free energy change of 5.7kJ mol−1 equates to a change of one unit in pKa. (p.23)

3.1.1 Solvent-transfer activity coefficients

An equally valid and widely used alternative means of reporting the changes in free energy occurring when a species Y is transferred from a reference solvent O (in our case water) to solvent S, is via solvent-transfer activity coefficients (OγS), also called medium effects or degenerate activity coefficients [1, 2]. They are related to the corresponding free energies of transfer by eq. (3.7), for transfer between water and solvent S.

$Display mathematics$
(3.7)

In the case of electrolyte MX, the analogous equation is eq. (3.8).

$Display mathematics$
(3.8)

Free energies of transfer and transfer activity coefficients may, therefore, be used interchangeably to represent changes in solvation energy.

The change in Ka of acid HA with solvent can also be readily expressed in terms of solvent-transfer activity coefficients, as in eqs. (3.9) and (3.10).

$Display mathematics$
(3.9)

$Display mathematics$
(3.10)

There is, therefore, a direct and obvious relationship between solvent-transfer activity coefficients (log aqγS) and changes in pKa-values.

The main advantage of using log aqγS values, as in eq. (3.10), is the numerically simple relationship between changes in pKa and log aqγS: a change of 1 unit in log aqγS for any of the species involved in the equilibria corresponds directly to a change of 1 unit in pKa.

Most chemists, however, are more comfortable with the notion of free energies than with activity coefficients, and we will, therefore, normally use free energies of transfer in preference to solvent-transfer activity coefficients to express changes in solvation energies and hence equilibrium constants. Occasionally, it will be convenient also to include log aqγS values because of their direct equivalence to changes in pKa.

3.2 Determination of free energies of transfer

3.2.1 Non-electrolytes

(i) Solubility measurements. The most widely used method for determining the change in free energy of a species Y between solvents is based on measurement of the solubility of Y in the different solvents.

The free energy of solution of substrate Y in a given solvent, ∆Gs (Y), is related to its solubility, So, in that solvent by eq. (3.11).

$Display mathematics$
(3.11)

(p.24) Thus, the difference in the solubility of Y in two different solvents can be usedto determine the change in energy, ∆G tr(Y), on transfer between the solvents.

The method is illustrated for benzoic acid, via the simple Born–Haber cycle shown in Scheme 3.2, in which $Δ G s aq$ and $Δ G s S$ represent the free energies of solution of benzoic acid in water and solvent S, respectively.

Scheme 3.2. Born–Haber cycle for the solubility of benzoic acid

It is apparent from Scheme 3.2 that changes in solubility are a direct conseProvided the acid does not form a solquence of the difference in the free energy of benzoic acid in the two solvents. Thus, the free energy change of benzoic acid on transfer between water and solvent S, ∆G tr (benzoic acid), and its solubility in the two solvents are related by eq. (3.12).

$Display mathematics$
(3.12)

Table 3.1 lists the measured solubility of benzoic acid in water and some common solvents [3], together with the derived free energies of solution and transfer and the equivalent solvent-transfer activity coefficients.

The free energy of benzoic acid in the non-aqueous solvents is thus ~ 10kJ mol−1 lower than in water, reflecting the more effective solvation of benzoic acid. This decrease in free energy, which reduces its tendency to dissociate, contributes an increase of ~ 2 units to the pKa of benzoic acid on transfer from water (eqs. (3.4), (3.10)).

(ii) Vapour pressure measurements. A second commonly used method for the determination of free energies of transfer of non-electrolytes is based on the solvent-dependence of vapour pressure. The variation in vapour pressure of a volatile substrate with solvent is controlled directly by the difference in solvation in an analogous manner to that of its solubility. For a given solvent, the vapour pressure of substrate Y, PY, is proportional to its concentration, as expressed by Henry’s Law, eq. (3.13).

$Display mathematics$
(3.13)

Table 3.1 Solubility and free energies of transfer of benzoic acid at 25°Ca

Benzoic acid

H2O

MeO Hb

DMFb

MeCNb

So/M

0.0278

3.16

5.3

0.85

∆Gs/kJ mol−1

8.87

−2.85

−4.13

0.40

∆Gtr/kJ mol−1c

0

−11.7

−13.0

−8.5

log aqγSd

0

−2.0

−2.3

−1.5

(a) Ref [3];

(b) Abbreviations as in Table 1.1;

(c) Free energy of transfer from water to solvent;

(d) aqγS = So S/So aq is the solventtransfer activity coefficient (Section 3.1.1)

(p.25)

In eq. (3.13) the proportionality constant between pressure and concentration, H Y, is known as the Henry’s Law constant. It is determined experimentally by measuring the vapour pressure of Y over solutions of known concentration of Y.

The free energy of transfer of Y between water and solvent, S, is related to the change in Henry’s Law constant by eq. (3.14).

$Display mathematics$
(3.14)

Thus, measurement of Henry’s Law constant, or, equivalently, the vapour pressure of Y at constant concentration in different solvents, can be used to determine ∆G tr-values.

(iii) Distribution coefficients. Finally, ∆G tr-values for non-electrolytes may also be determined from measurement of distribution coefficients. The distribution coefficient for substrate Y between water and any non-miscible solvent, S, D = [Y]S/[Y]aq is linked to the corresponding free energy of transfer of Y by eq. (3.15).

$Display mathematics$
(3.15)

The method is of limited use as it is restricted to pairs of immiscible solvents— typically water and non-polar organic solvents. It can be used indirectly for water-miscible solvents, such as methanol, dimethylformamide, acetonitrile, etc., by comparing the separate partitioning of Y between the two solvents and a third, immiscible solvent, such as decalin or cyclohexane.

In each of the above methods, the free energy of transfer is based on equilibration of the solute between the solvent in question and a common (invariant) reference phase: the solid state (solubility measurements); the vapour phase (Henry’s Law); or an immiscible solvent (partition coefficients).

3.2.2 Electrolytes

(i) Solubility measurements. For a typical salt, such as sodium chloride, the solubility in different solvents, So = [NaCl]sat = [Na+]sat = [Cl]sat, is related to the corresponding free energy of transfer of the constituent ions in an analogous manner to that described above for non-electrolytes. The solubility product, Ksp = [Na+][Cl] = So 2, is related to the free energy of solution, ∆G s(NaCl), by eq. (3.16).

$Display mathematics$
(3.16)

The change in free energy of NaCl with solvent is illustrated in Scheme 3.3, which shows a Born–Haber cycle for the solution of NaCl in water and solvent.§

Scheme 3.3. Born–Haber cycle for the solubility of sodium chloride

(p.26)

Table 3.2 Solubility and free energies of transfer of NaCl at 25°Ca

NaCl

H2O

MeOHb

DMFb

MeCNb

So/M

7.0

6.3 × 10−2

3.2 × 10−3

7.2 × 10−5

Ksp/M2

49

3.9 × 10−3

1.0 × 10−5

5.2 × 10−9

∆Gs/kJ mol−1

−9.00c

13.72

28.49

47.28

∆Gtr/kJ mol−1d

0

22.7

37.5

56.3

log aqγSe

0

3.9

6.6

9.9

(a) Ref [2];

(b) Abbreviations as in Table 1.1;

(c) Free energy of solution at infinite dilution: Rossini, F.D., et al., U.S. Nat. Bureau of Standards, Circular 500 and supp. Notes 270–1 to 270–3;

(d) Free energy of transfer from water to solvent;

(e) Solvent-transfer activity coefficient

It follows from Scheme 3.3 and eq. (3.16) that the change in free energy is given by, eq. (3.17).

$Display mathematics$
(3.17)

Table 3.2 lists the measured solubility of sodium chloride in several solvents, together with the derived free energies of solution and transfer.

These effects are normally very large compared with those for non-electrolytes: the transfer of NaCl from water to acetonitrile, for example, is accompanied by a decrease in solubility product of some 10 orders of magnitude. We can anticipate similar, if not larger, effects when we come to examine acid–base dissociation and equilibria in different solvents.

(ii) EMF measurements. The solvent dependence of the EMF of appropriate electrochemical cells provides another important source of free energy data for electrolytes. Consider, for example, the following cell and its corresponding half-cell reactions, eq. (3.18):

$Display mathematics$

$Display mathematics$
(3.18)

The overall cell reaction is given by eq. (3.19).

$Display mathematics$
(3.19)

The free energy change, ∆G aq, for the cell reaction is related to the EMF of the cell, E aq, by eq. (3.20), in which F is the Faraday constant.

$Display mathematics$
(3.20)

The essential feature of cell (3.18) is that changes in EMF arising from a change in solvent are due entirely to changes in the free energies of the ions, H + and Cl . This is because the free energies of the (gaseous) products of the cell reaction, H2(g) and Cl2(g) (eq. (3.19)), are independent of solvent. Thus, if the corresponding EMF in solvent S, ES, is subtracted from that of the aqueous cell, eq. (3.20), the net process equates to the transfer of H+ + Cl from water to solvent S, eq. (3.21), and free energy change is given by eq. (3.22). (p.27)

Table 3.3 Electrochemical cells for determining free energies of transfer

Cella

Cell reaction

Ag, AgCl(c) |HCl(S)|H2(g), Ptb

H+ (S) + Cl (S) + Ag → 1/2H2(g) + AgCl(c)

Ag, AgBzO(c) |BzO (S) ∥H+ (S) |H2(g), Ptc

H+ (S) + BzO (S) + Ag → 1/2H2(g) + AgBzO(c)

Pt, Na(Hg) |Na+ (S) ∥Ag+ (S) |Ag

Ag+ (S) + Na(Hg) → Na+ (S) + Ag

(a) BzO = benzoateion.

(b) Cell saturated with respect to AgCl.

(c) Left hand half-cell saturated with respect to silver benzoate

$Display mathematics$
(3.21)

$Display mathematics$
(3.22)

Table 3.3 lists other examples of electrochemical cells that can be used to determine free energies of transfer of electrolytes, together with the overall cell reactions.

In each case, the only components whose free energies change with solvent are the ions; the remaining cell components are either solids or gases and hence their free energies are solvent-independent. Thus, the cells listed in Table 3.3, can be used to determine ∆G tr values for (H+ + Cl), (H+ + BzO), and (Ag+ − Na+), respectively.

(iii) Distribution coefficients. Finally, in a small number of cases in which the non-aqueous solvent is immiscible with water, e.g., nitrobenzene, free energies of transfer may be determined directly from the partitioning of salts between the two solvents, analogous to the partition method noted above for non-electrolytes (eq. (3.15)).

It is very important to note that all measurements on electrolyte solutions involve electrically neutral combinations of ions and hence can only give data pertaining to such combinations. These are either whole electrolytes, as in the case of the solubility of NaCl, or differences between ions of like charge, as in the final cell in Table 3.3, which measures the difference between Na+ and Ag+ on solvent transfer.

3.3 Free energies of ion solvation

3.3.1 Hydration of ions

In the first instance, we consider briefly the absolute free energies of solvation of ions, i.e., the transfer of ions from the gas-phase to solution, eq. (3.23) for cations and similarly for anions.

$Display mathematics$
(3.23)

The energies involved are enormous, comparable to the lattice energies of ionic crystals, as illustrated by the hydration energies of ions (eq. (3.23), S = H2O) listed in Table 3.4 [4]; values range from hundreds to thousands of kJ mol−1.

The absolute values are dominated by the very large electrostatic energies of the ions in the gas relative to the solution phase. Nevertheless, even in the (p.28)

Table 3.4 Free energies of hydration of ions at 25°Ca

Ion

rb

−∆G o h/kJ mol−1

Ion

rb

−∆G o h/kJ mol−1

H+

1089

Al3+

0.52

4615

Li+

0.60

511

Sc3+

0.75

3885

Na+

0.95

411

Y3+

0.93

3541

K+

1.33

337

Rb+

1.48

316

F

1.36

436

Cs+

1.69

284

Cl

1.81

311

Ag+

1.26

473

Br

1.95

285

Be2+

0.31

2442

I

2.16

247

Mg2+

0.65

1906

OH

1.40

403

Ca2+

0.99

1593

CN

1.90

310

Sr2+

1.13

1447

$NO 3 −$

1.89

270

Ba2+

1.35

1318

$NO 3 −$

2.36

178

(a) Ref [4];

(b) Pauling crystal radii for monatomic ions; thermochemical radii for polyatomic ions

gas phase the most significant interactions between ions and solvent molecules are those occurring within the first solvation sphere. This is shown by mass-spectrometric measurements on the association of ions with solvent molecules in the gas phase [5]. Thus, the equilibrium constants for the successive addition of water molecules to ions, eq. (3.24), show that beyond the first 5–6 water molecules, i.e., the first solvation shell, the decrease in free energy per additional water molecule is almost independent of the cation.

$Display mathematics$
(3.24)

Furthermore, the energy gain from addition of water molecules to the second-shell is very close to the free energy of condensing a water molecule from the gas phase to liquid water (∆G ~ −9kJ mol−1). Similar results were obtained for other common solvent molecules, such as methanol and acetonitrile.

3.3.2 Solvation in pure solvents

Changes in ion-solvent interactions on transfer of electrolytes between solvents are much smaller than the absolute solvation energies and differences in electrostatic energies play a much reduced role. They are nevertheless sufficiently large to cause dramatic changes in chemical reactions and equilibria involving ions. As expected, the changes result primarily from differences in specific interactions of the ions with the immediate-neighbour solvent molecules; for example, ion-dipole, Lewis acid–base and H-bonding interactions (Section 1.2.1).

Solubility data for simple electrolytes in polar solvents have been summarized by Johnsson and Persson [6], and from these and complementary measurements on appropriate electrochemical cells it is possible to derive the free energies of transfer of a wide range of electrolytes from water to a variety of solvents [2, 7–11]. Although experimental measurements of the free energies refer to whole electrolytes (or differences between ions of like charge), it is convenient to report them in terms of individual ions. The use of anionic and cationic values facilitates a comparison within groups of anions (p.29) or cations, and the individual values can also be recombined as appropriate to give values for a much wider set of electrolytes.

The division into ionic values could be achieved by arbitrarily assigning a value for, say, the proton and then reporting all other values relative to this. More satisfying, however, is the most widely used convention used for the reporting of individual values, whereby the free energies of transfer of Ph4As+ and Ph4B are equated, eq. (3.25) [2].

$Display mathematics$
(3.25)

This is because, to the extent that eq. (3.25) represents a chemically sensible division of the free energies of transfer of the salt [Ph4As+B $PH 4 −$], we may expect the resulting ionic values to be indicative of the actual changes in solvation energy of the individual ions.,

The build-up of a set of individual free energies of transfer of ions based on eq. (3.25) is straightforward. Thus, ∆G tr( $BPh 4 −$) follows from the application of eq. (3.25) to the change in solubility of Ph4AsBPh4. Then, for example, from the solubility of KBPh4 in solvents we obtain ∆G tr(K+) + ∆G tr( $BPh 4 −$), and hence G tr(K+). In a similar manner ∆G tr values for any number of ions follows: e.g., G tr(KCl) combined with ∆G tr(K+) gives ∆G tr(Cl) from which we may derive ∆G tr(H+) using cell 2.17, and ∆G tr(Na+) from the solubility of NaCl, etc.

Tables 3.53.7 list ∆G tr-values for the transfer of ions from water to alcohols, formamide, and aprotic solvents, respectively. ∆G tr-values for ions in formamide are reported separately; it is formally a protic solvent because of its relatively acidic NH-protons, but the presence of the carbonyl group makes it is significantly more effective than the alcohols at solvating cations.

Considering first the anions, the most obvious conclusion from the results in Tables 3.53.7 is that the transfer of anions from water is almost universally unfavourable. The effects are particularly striking for high-charge-density

Table 3.5 Free energies of transfer of ionsa from water to alcohols at 25°Cb

G tr/kJ mol−1

Ion

MeOH

EtOH

n-PrOH

n-BuOH

Ion

MeOH

EtOH

n-PrOH

n-BuOH

H+

10.4

9.1

F

17.0

27.0

Li+

5.0

11.0

11.3

Cl

13.0

20.0

25.5c

29.2c

Na+

8.0

14.0

16.8

19.8

Br

11.0

18.0

21.9c

28.7c

K+

10.0

16.0

17.7b

19.8

I

7.0

13.0

19.2

22.1

Rb+

10.0

16.0

19.3

22.6

OAc

16.0

36.9

Cs+

9.0

15.0

17.4

18.5

BzO

7.0

Ag+

7.2

$N 3 −$

9.0

17.0

Me4N+

6.0

11.0

10.6

12.1

CN

9.0

20.0

Et4N+

1.0

6.0

4.8

7.3

CNS

6.0

13.0

Pr4N+

−5.0

−6.0

−6.4

−6.7

$CIO 4 −$

6.0

10.0

17.3

21.5

Bu4N+

−21.0

8.0

−16.8

−11.7

Pic

−6.0

−1.0

Ph4As+

−24.0

−21.0

−25.2

−20.1

$BPh 4 −$

−24.0

−21.0

−25.2

−20.1

(a) Convention, ∆G tr(Ph4As+) = ∆G tr( $BPh 4 −$);

(b) Ref [2, 6–8, 10];

(c) ∆G tr/kJ mol−1 in iPrOH: H+ = 11.0, K+ = 22.5, OAc = 31.0, Cl = 22.0, Br− = 19.8; ∆G tr/kJ mol−1 in t-BuOH: H+ = 18.8, OAc = 38.9, Cl = 36.3, Br = 31.2, Ref [9, 10]

(p.30)

Table 3.6 Free energies of transfer of ionsa from water to formamide at 25°Cb

G tr/kJ mol−1

Cation

G tr/kJ mol−1

Anion

G tr/kJ mol−1

Li+

−9.6

F

24.7

Na+

8.0

Cl

13.8

K+

6.3

Br

11.3

Rb+

5.4

I

7.5

Cs+

7.5

CN

13.3

Ag+

22.6

OAc

20

Ph4As+

23.9

$BPh 4 −$

23.9

(a) Convention, ∆G tr(Ph4As+) = ∆G tr( $BPh 4 −$);

(b) Ref [9–11]

Table 3.7 Free energies of transfer of ionsa from water to aprotic solventsb at 25°Cc

G tr/kJ mol−1

Ion

DMF

DMAC

NMP

DMSO

Me2CO

MeCN

PC

MeNO2

PhNO2d

H+

−14.8

−18.9

−19.4

14.5

44.8

50

Li+

−15.1

−10.0

5.0

25.0

25.8

48

Na+

−10.0

−12.1

−13.7

9.0

15.0

15.2

31.6

K+

−10.0

−11.7

−11

−12.0

3.9

8.0

6.2

15.4

21.0

Rb+

−10.0

−8.0

−8

−10.8

4.0

7.5

4.9

11.1

19.3

Cs+

−11.0

−10

−12.5

4.0

6.0

2.3

5.7

17.8

Ag+

−17.7

−29.0

−19.8

−33.3

−22.8

16.7

24.7

Me4N+

−7.4

−5.0

−2.0

10.6

3.0

−4.6

4.0

Et4N+

−8.0

−9.0

−11.0

−7.0

−10.3

−4.8

Et3NH+

−5.4

Pr4N+

−17.0

−19.0

−20.0

−13.0

−20.0

−16.4

Bu4N+

−29.0

−36.9

−32.9

−30.9

Ph4As+

−38.4

−38.7

−39.0

−36.9

−32.9

−32.9

−35.4

−32.6

−36.0

OH

109e

F

85

61

60

70

58

Cl

47.9

54.9

55.2

40.0

56.4

41.9

39.4

37.7

43.9

Br

31.7

44.0

40.6

27.0

41.9

30.9

30.3

29.0

36.0

I

20.0

21

24.3

10.0

25.0

17.0

16.8

18.8

21.9

OAc

64.9

70

67.1

61.1

64.6

60.9

56.1

BzO

48.0

40.5

PhO

61.1 e

PhS

35.2e

$N 3 −$

36.0

31.7

26.0

43.0

34.3

28.3

25.1

CN

40.0

34.9

47.9

36.9

CNS

18.0

9.0

10.0

30.0

14.0

8.8

$CIO 4 −$

4.0

−6.0

10.0

2.0

−3.0

4.7

9.8

Pic

−7.0

14.0

14.0

4.0

−0.2

−3.4

$BPh 4 −$

−38.4

−38.7

−39.0

−36.9

−32.9

−32.9

−35.4

−32.6

−36.0

(a) Convention, ∆G tr(Ph4As+) = ∆G tr( $BPh 4 −$);

(b) Abbreviations as in Table 1.1;

(c) Ref [2, 6–8, 10, 11];

(d) Danil de Namor, A.F., Hill, T. J. Chem. Soc., Faraday Trans. 1, 1983, 79, 2713;

(e) Pliego, J.R., Riveros, J.M. Phys. Chem. Chem. Phys., 2002, 4, 1622

(p.31) anions, such as OH, F, Cl, $N 3 −$, CN, OAc, and PhO, on transfer to the various aprotic solvents, such as DMF, DMSO, and MeCN. The acetate ion, for example, shows an increase in free energy of some 60kJ mol−1 (equivalent to 10.5 units in pKa, log aqγS) in a range of aprotic solvents relative to water. The increases are considerably lower in the protic solvents methanol and formamide, but become systematically larger in progressing from methanol to butanol. This is not surprising, as the ‘solvating’ group, –OH, becomes increasingly ‘diluted’ as the alkyl chain increases.

Highly polarizable anions with significant charge dispersion, such as CNS, $CIO 4 −$, picrate, and $BPh 4 −$, show, as might be expected, much smaller increases (and in some cases a decrease) in free energy on transfer from water. For these ions, strong dispersion-force interactions in the non-aqueous solvents largely compensates for any loss of hydrogen-bond stabilization.

The behaviour of cations cannot be classified in such a simple manner, but it is qualitatively in line with expectations based on the structures and charge distributions of the different solvents. Water no longer holds a unique position: interactions of cations with non-aqueous solvents may be stronger or weaker than those with water, depending on the polarity and basicity of the solvent. Thus, ‘basic’ solvents (Chapter 1, Section 1.2), such as DMSO, DMF, NMP, formamide, and particularly hexamethylphosphoric triamide (HMPT), stabilize simple cations, and especially the proton, relative to water, generally in the order H+ 〉 Li+ 〉 Na+ 〉 K+ 〉 Rb+ ≈ Cs+. The order is reversed for solvents that are less basic than water (PC, MeCN, MeNO2, and acetone); smaller cations, and again especially the proton, may be considerably destabilized. Within the series of alcohols there is a general progressive destabilization of simple cations from methanol to butanol.

‘Organic’ cations, including the larger R4N+, Ph4As+, and $BPh 4 −$, are less stable in water and methanol than in polar aprotic solvents, but show little variation among polar aprotic solvents. The preference of the ‘organic’ cations for non-aqueous solvents increases with cation polarisability, as illustrated, for example, by the trend among R4N+ ions as the alkyl chain length increases.

3.3.3 Solvation in mixed solvents

Mixed aqueous–organic solvents and, in particular, alcohol–water mixtures are often convenient for synthetic and purification processes. They are, for example, frequently used for the purification and isolation of pharmaceutical actives, and for the separation of acid- or base-sensitive substrates by HPLC. There are clearly a vast number of such combinations and it is not possible to review the results in any detail. A useful principle, however, is that the properties of the solutes in the solvent mixture will be most strongly influenced by the component with which they interact most strongly in the pure solvents— a phenomenon normally referred to as selective or preferential solvation.

One obvious consequence of preferential solvation is that in mixed aqueous-organic solvents the major increases in free energy normally occur only when most of the water is removed from the system. This illustrated in Fig. 3.1, which shows the properties of NaCl and HCl in water–acetonitrile and water– methanol mixtures, respectively [12]. (p.32)

Fig. 3.1. Free energies of transfer of NaCl and HCl from water to MeCN–water and MeOH–water mixtures, respectively

In both cases there is a steep rise in free energy beyond 80 wt% of the organic component.

For the same reason, the presence of small amounts of water in weakly solvating media, such as acetonitrile, can have a strong influence on the properties of electrolytes and the ionization of acids (Chapter 7). In some solvents, such as propylene carbonate, the association of ions with water is sufficiently strong to allow the determination of equilibrium constants for the selective solvation of ions by water in the solvent [13].

A related phenomenon is the solubility in mixed solvents of organic molecules which contain both hydrophobic and hydrophilic components; these may be more soluble in mixed aqueous solvents—for example, THF–water mixtures—than in either of the component solvents separately.

3.4 Solvation of non-electrolytes

The free energies of transfer of various non-electrolytes from water to organic solvents are given in Table 3.8. As noted above, they are derived from measurements of solubility, vapour pressure (Henry’s Law coefficients), and partition coefficients between water and other solvents.

Two obvious conclusions may be drawn from the data. First, non-electrolytes are almost universally more stable in non-aqueous media than in water; larger and more polarisable solutes show greater decreases in free energy on transfer from water because of stronger dispersion-force interactions with the non-aqueous solvents [1]. Secondly, changes amongst the various non-aqueous solvents are normally small.

Importantly, though, the solubility of carboxylic acids is enhanced by H-bond formation with suitable solvents, such as DMSO and DMF, compared with solvents, such as MeCN, which are poor H-bond acceptors. Thus an extensive study of the solubility aromatic carboxylic acids and their esters, has shown that while their esters, in common with the majority of non-electrolytes, show little variation amongst a range of non-aqueous solvents, the carboxylic acids are more weakly solvated in solvents such as acetonitrile [3, 14]; compare, for example methyl, 4-bromobenzoate and 4-bromobenzoic acid. On (p.33)

Table 3.8 Free energies of transfer of non−electrolytes from watera to non−aqueous solventsb at 25°C

G tr/kJ mol−1c,d

Substrate

MeOH

DMF

NMP

DMSO

MeCN

Dioxane

ethane

−9.7

−6.3

ethylene

−7.4

−7.4

−5.2

CH3Br

−6.8

−8.5

CH3I

−8.0

−10.8

−12.0

−10.8

−10.3

t-BuCl

−17.1

−18.2

−16.5

t-butyl acetate

−12.6

acetic acid

0.0

1.1

−2.3

−4.6

2.3

ethyl acetate

−8.4

−9.2

−11.3

benzoic acid

−11.7

−13.0

−12.7

−8.5

4-bromobenzoic

−15.9

−20.9

−19.4

−11.4

Me,4-bromobenzoate

−16.7

−21.0

−19.4

−19.1

4-nitrobenzoic

−13.5

−19.9

−19.3

−9.5

Me,4-nitrobenzoate

−12.9

−18.5

−17.4

−17.7

3,4-dichlorobenzoic

−18.8

−24.1

−13.3

Me,3,4-dichlorobenzoate

−18.3

−20.8

−20.4

3,4-dimethylbenzoic

−16.7

−20.6

−12.0

fumaric acid

−5.7

−10.6

5.6

methyl fumarate

−5.7

−8.4

−2.0

−5.1

−6.5

−8.1

3.2

−8.2

−8.1

−8.2

(a) Free energy of solution in water, ∆G s/kJ mol−1: ethylene, 13.1; benzoic acid, 8.87; 4-bromobenzoic acid, 21.12 ; methyl 4-bromobenzoate, 19.65; 4-nitrobenzoic acid, 18.44; methyl 4-nitrobenzoate, 17.11; 3,4-dichlorobenzoic acid, 22.1; methyl,3,4-dichlorobenzoate, 18.4; fumaric acid, 7.32; methyl fumarate, 4.17; adipic acid, 4.87; methyl adipate, 4.11;

(b) Abbreviations as in Table 1.1;

(c) Molar concentration scale;

(d) Ref. [1, 3, 14]

average, the aromatic esters show a decrease in free energy of 19.1kJ mol−1 on transfer from water to both DMSO and MeCN, whereas the corresponding decreases in free energies of the carboxylic acids are 21.3 and 11.9kJ mol−1, respectively.

The free energy changes for non-electrolytes, although usually much smaller than those of electrolytes, can contribute up to three orders of magnitude to the observed changes in dissociation constants on transfer from water; for carboxylic acids and phenols, this tends to increase their pKa-values on transfer from water, whereas the opposite effect occurs for protonated amines and anilines (eqs. (3.4), (3.5)).

3.5 Solvation energies and solvent properties

The solvation energies of cations and anions are expected to be enhanced in solvents which are able to donate or accept electrons, respectively. Indeed, free energies of transfer of cations, such as Na+, correlate well with the solvent Donor Number, DN, which provides a measure of the ability to donate electrons, and those of anions with the solvent Acceptor Number, AN (Chapter 1, Section 1.2.1). This is shown in Fig. 3.2 for the transfer of Na+ and Cl among solvents. (p.34)

Fig. 3.2. Influence of solvent Donor Number (a) and Acceptor Number (b) on the free energies of transfer of Na+ and Cl, respectively, from water to non-aqueous solvents (data from Tables 1.1, 3.53.7)

The data in Fig. 3.2 provide good confirmation of the importance of electron donor-acceptor interactions in determining the free energies of transfer of simple ions among solvents. Thus, Na+ becomes progressively more strongly solvated as the Donor Numbers of the solvents increase, whereas Cl interacts more strongly with solvents having high Acceptor Numbers. The contrast between protic and aprotic solvents in the solvation of the chloride ion is also apparent in Fig. 3.2(b).

3.6 Solvation and acid strength

In anticipation of a more detailed discussion of dissociation constants in subsequent Chapters, it is instructive at this stage to illustrate the application of the thermodynamic solvation data to the analysis of pKa changes in different solvents, using the pKa of acetic acid as an example.

Table 3.9 provides an analysis of the change in pKa of acetic acid in acetonitrile, dimethylformamide, and methanol relative to water in terms of the free energy changes of the components of the equilibrium. The free energy changes of HOAc, H+ and OAc are expressed in terms of their solvent transfer activity coefficients, log aqγS, eq. (3.7), in order, illustrate more clearly their contribution to the change in pKa. The overall change in pKa to be expected then follows from eq. (3.10), i.e., (p.35)

Table 3.9 Influence of solvent on the dissociation constant of acetic acid

HOAc  ⇌  H+ + OAc

MeCN

DMF

MeOH

log aqγS(HOAc)a

0.4

0.2

0.0

log aqγS(H+)a

7.9

−2.6

1.8

logaqγS(OAc)a

10.7

11.4

2.8

∆pKab

18.2

8.6

4.6

pKa(H2O)

4.76

4.76

4.76

pKa(S calc)c

23.0

13.4

9.4

pKa(S obs)d

23.1

13.5

9.7

(a) log aqγS(Y) = ∆G tr(Y)/2.303RT, ∆G tr(Y) from Tables 3.5, 3.7–8;

(b) Eq. (3.10);

(c) pKa(H2O) + ∆pK;

(d) Measured values, Chapters 57

$Display mathematics$

Values calculated in this way from the solvation data can be seen to be in good agreement with directly measured pKa-values.

The greatest increase in pKa (18.2 units) when compared with aqueous values occurs on transfer to MeCN, where both H+ and OAc show large increases in free energy. In DMF, the acetate ion is similarly unstable compared with water, but the proton is more strongly solvated. The result is a much smaller increase in pKa (8.6 units) on transfer from water. Methanol shows a modest increase in pKa values; both H+ and OAc are solvated more poorly than in water, but the increase in free energy of OAc in particular is much lower than in either of the aprotic solvents.

3.7 Summary

The discussion may be summarized as follows:

• The absolute solvation energies of ions are very large (several hundred to several thousand kJ mol−1) and dominated by electrostatic effects, but changes among solvents are governed mostly by specific interactions within the first coordination sphere.

• Small, high-charge-density anions, such as hydroxide, carboxylate and halide ions, are strongly stabilized by hydrogen-bond formation in protic solvents. They show large increases in free energy on transfer to aprotic solvents, which may reach 100kJ mol−1, equivalent to 18 pK-units.

• Cations, such as the proton and alkali metal ions, are stabilized relative to water in ‘basic’ solvents, such as DMF, DMSO, and NMP, but (p.36) have considerably higher free energies in less basic solvents, such as acetonitrile.

• In mixed-aqueous solvents, the phenomenon of preferential solvation means that the major changes in free energy occur only as the better solvent (usually water) is significantly depleted.

• Semi-empirical measures of electron donor/electron acceptor properties, such as Donor Numbers, Hydrogen-bond Basicity, and Acceptor Numbers, provide a means of correlating and qualitatively predicting changes in free energies amongst solvents.

• Non-electrolytes are almost universally more stable in non-aqueous media, but the effects are generally much smaller than those for ions. Larger, ‘organic’ electrolytes, such as those involving alkylamonium ions, behave more like non-electrolytes in terms of their solvation behaviour.

• Analysis of the changes in acid dissociation constants and acid–base equilibria among solvents in terms of the changes in free energy of the individual species involved can provide an enhanced understanding of solvent effects on acid–base equilibria.

Free energies of transfer of electrolytes and dissociation constants of acids (Chapter 5, 8) in mixed solvents, most commonly in practice mixed-aqueous solvents, frequently show strong evidence of preferential solvation as, for example in the data for NaCl in acetonitrile–water and methanol–water mixtures, Section 3.3.3, Fig. 3.1.

There are three ways of expressing the composition of liquid mixtures, the choice of which can influence the interpretation of preferential solvation: mole fractions, weight fractions and volume fractions. The latter two are very similar, the differences depending only upon the relative densities of the component solvents, but differ strongly from the mole fraction scale when the two solvent components have very different molecular weights; this is typically the case when water is one of the components. Table A3.1 and Fig. A3.1 show the free energy of transfer of NaCl between water and water-MeCN mixtures according to the different composition scales.

All three curves exhibit evidence of preferential solvation by water in the mixtures, in that the increase in free energy is more marked at low water levels, but the effect appears to be more pronounced when composition scales are expressed in terms of vol% or wt%, rather than mol%.

An exactly analogous situation obtains for the dependence of acid dissociation constants upon solvent composition, discussed in subsequent chapters (Chapters 5 and Chapter 8). (p.37)

Table A3.1 Free energy of transfer of NaCl from water to wateracetonitrile mixtures at 25°Ca

Vol% MeCN

Wt% MeCN

Mol% MeCN

∆Gtr/kJ mol−1

0

0

0

0

10

7.9

3.6

1.13

20

16.4

7.9

2.13

40

34.3

18.6

5.19

60

54.1

34.1

9.33

80

75.8

57.9

16.5

90

87.6

75.5

29.4

95

93.8

86.9

40.6

100

100

100

56.1

(a) Ref [12]

Fig. A3.1. Free energy of transfer of NaCl from water to acetonitrile-water mixtures at 25°C

The most satisfactory choice for the composition scale as a basis for interpreting solvation changes is that of the volume fraction scale (or, almost equivalently, the weight fraction scale), which is the analogue of the molar concentration scale. It reflects more accurately the changes in chemical/physical interactions between the solvent components and the solutes that accompany changes in solvent composition. The mole fraction scale, by contrast, additionally includes a strong contribution arising purely from differences in the size of the solvent molecules, irrespective of the nature of the interactions. Thus, for example, in 60 vol% acetonitrile, the volume concentration of water molecules is reduced by 60%, compared with pure water, whereas there is a decrease of only 38% in the mole fraction of water molecules. It is the former which governs the free energy of interaction between the ions and water molecules and hence the free energies and dissociation constants of the acid– base species.

In practice we have chosen throughout this text to express solvent composition in terms of wt%. As an indicator of preferential solvation, it is essentially equivalent to the vol% scale (Fig. A3.1), but the preparation of mixtures by weight is more convenient than by volume, especially on a large scale; use of the wt% scale also avoids the minor issue of non-zero volumes of mixing of the solvent components.

(p.38) References

Bibliography references:

[1] Parker, A. J. Chem. Rev., 1969, 69, 1

[2] Kolthoff, I. M., Chantooni, M. K. J. Phys. Chem., 1972, 76, 2024

[3] Chantooni, M. K., Kolthoff, I. M. J. Phys. Chem., 1974, 78, 839

[4] Burgess, J. ‘Metal Ions in Solution’, 1978, Ellis Horwood, Ch 7

[5] Kebarle, P. Annu. Rev. Phys. Chem., 1977, 28, 445

[6] Johnsson, M, Persson, I. Inorg. Chim. Acta, 1987, 127, 15

[7] Abraham, M. H., Zhao, Y. H. J. Org. Chem., 2004, 69, 4677

[8] Marcus, Y. Pure & Appl. Chem., 1983, 55, 977

[9] Kolthoff, I. M., Chantooni, M. K. J. Phys. Chem., 1979, 83, 468

[10] Abraham, M. H., Acree, W. E. J. Org. Chem., 2010, 75, 1006

[11] Cox, B. G., Hedwig, G. R., Parker, A. J., Watts, D. W. Aust. J. Chem., 1974, 27, 477

[12] Cox, B. G., Waghorne, W. E. Chem. Soc. Rev., 1980, 9, 381

[13] Butler, J. N., Cogley, D. B., Grunwald, E. J. Phys. Chem., 1971, 75, 1477

[14] Chantooni, M. K., Kolthoff, I. M. J. Phys. Chem., 1973, 77, 527

Notes:

() Note that the factor of 2.303 in Scheme 3.1, eq. (3.3) and subsequent equations arises from the change from natural logarithms (lnKa = −∆G o/RT) to logarithms to the base 10: pKa = − log Ka = −Ka/2.303

() 2.303 RT = 5710 J mol−1 at 25°C

() Solvent-transfer activity coefficients reflect changes in solute–solvent interactions in different solvents, and hence may be very large. More familiar is the use of activity coefficients to quantify the much smaller, concentration-dependent solute–solute interactions in a given solvent, such as electrostatic attractions between ions of opposite charge (Chapter 4)

() Provided the acid does not form a solvate in the solid state, i.e., the solid state is unaffected by the change in solvent

() The equivalent expression for the solvent transfer activity coefficient is $log ⁡ aq γ S = − log ⁡ ( S o s / S o aq )$

() The most familiar example of the use of distribution coefficients is that of log P values, where P is the partition coefficient of a substrate between water and the immiscible solvent 1-octanol. They are widely used to provide a measure of the bioavailability of agrochemical and pharmaceutical products

(§) An assumption inherent in Scheme 3.3 is that the salt does not form a solvate with any of the solvents involved; this can be tested by analysis of the solid in equilibrium with solvent

() Equivalently, log aqγS = −log(So S/So aq)

() An exception is Volta-potential measurements (equivalent to electron work functions) which measure the total energy change in removing an ion from solution to the gas-phase: Farrell, J.R., McTigue, P.T. J. Electroanal. Chem., 1982, 139, 37

() The logic inherent in eq. (3.25) is that charges on these large and strongly shielded ions are sufficiently buried and dispersed so as to exclude any significant, charge-specific contributions to the total solvation energy of the ions

() For a discussion of the absolute free energy of the proton in different solvents relative to the gas-phase, see Himmel, D.; Sascha, K.G., Leito, I., Krossing, I. Angew. Chem. Int. Ed., 2010, 49, 6885

() The detailed shape of such curves (and similar curves for the dependence of acid strength upon solvent composition) depends upon the units used to define the solvent mixtures: wt%, vol%, or mol%. The issue and choice of scale is discussed in Appendix 3.1

() Note that because the dissociation equilibrium involves the neutral combination of H+ and OAc, the results are, therefore, independent of the convention used to derive the single-ion values of aqγS(H+) and aqγS(OAc)

() A similar argument applies to the properties of solvent mixtures in general. Thus, mixtures are normally defined as ideal when they obey Raoult’s law, i.e., the vapour pressure of each component is proportional to its mol fraction in the mixture. If we are interested primarily in the influence of the interaction energies between the components on their properties, however, the mol fraction scale is less than satisfactory. Thus, even in cases where the interaction energies between the components are identical, mixtures of molecules of different size exhibit non-ideal behaviour when expressed as mole fractions. An extreme example of this occurs in the thermodynamics of polymer-solvent mixtures, where volume fraction statistics are used in order to avoid this problem.