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Solvation of ions—enthalpies, entropies and free energies of transfer
SOLVATION AND
School
OF
IONS-ENTHALPIES,
FREE
ENERGIES
of Mathematical
OF
and PhysIcal
Murdoch.
ENTROPIES TRANSFER
Sciences. Murdoch
Wrsrern
University.
Australia
CF,CH,OH and CH,N02) or a strong solvator like thio DMF and acetonitrile. Values of E” Ag+/Ag (TATS assumption) are m Table 2. together with E K+/K (TATB). 1‘s n/w in water[3].
For the past five years, at the Australian National LJniversity, Drs. B. G. Cox, G. R. Hedwig, D. A. Owcnsby and I have been measuring heats of solution and heats of precipitation of electrolytes in nonaqueous solvents[l, 21. We have used an LKB ProducKter Model 8700-l precision calorimeter. The heats lead to enthalpies of transfer of single ions. The same group, ably assisted by the late Dr. John Diggle. sn outstanding electmchcmist. have measured rlectrode potentials and the kinetics of electrode processes for ions in non-aqueous solvents. using a PAR 170 electrochemical system, and Radiometer pH M26 equipment. When combined with solubihties. the data Iead to free energies of transfer of single ions[l. 3-51. Supporting measurements include molar volumes and nmr chemical shifts of solvents m solvatlon shells of electrolytes in non-aqueous solvents[6]. The measurements are routine for simple electrolytes in aqueous systems. the novelty is in the variety of solvents and electrolytes and in the calculation of the extratherrnodynamic quantities AC;,,. AH,, and AS,,.. for transfer of single ions between solvents[5]. Perhaps the data and some of our ideas about ions in solution may be of interest to electrochemists. 1 will deal only with the chemistry of dilute (
An interesting demonstration of wme of the differences in chemistry when one transfers from aqueous to non-aqueous systems. is the observation that NaCl is very soluble in water. but insoluble in thio DMF. whereas AgCl is insoluble in water and very soluble in thio DMF.
Scientists nowadays are under increasing pressure to consider the relevance of their research. and rightly so. Free energies of transfer to non-aqueous solvents determine large changes in rates of reaction[S], solubilities. rcdox potentials. stability constants, and dlstribution coefficients. All of these are important to everyday chemical technology, yet much of the chemical technologist’s thinking and applications are in terms of aqueous systems. Further, the environment in which many biological processes take place (ry clefts in proteins) may be much more “amide like” than “water like” so non-aqueous data in. for example DMF, may help us to understand biological processes
better. If we are to understand the highly complex chemistry of aqueous solutions and the unique character of water. we need first to understand the chemistry
of the much
simpler
noI1-aqueous
solutions.
One example of an application of non-aqueous chemistry is OUI- invention of a new method of ploceasing copper Co solutions of cuprous sulphatc in acidified acetonitrile-water mixtures[9P13]. Crude acetonitrile is a cheap solvent, and cuprous rulphate
Some very large effects of solvent transfer on the chemistry of ions in solution have been observed. The following examples. which are given in an electrochemical context. arc iilustratlvc. (a) The cw!f’of cell A. varies by up to 2.1 V according to the solvenls used (Table I). This is because trifluoroethanol is a poor solvent for all cations. dimethylformthioamide is a poor solvent for K+ but a good solvent for Agf and HMPT is an excellent solvent for all cations[X:]. (b) There are substantial anodic and cathodic changes in reduction potentials (TATB assumption. t.ic/e infrtr) on transfer of various redox couples from water to acetonitrile as solvent (Fig. 1)[7]. (c) The chemistry of Ag + is very susceptible lo wlvent transfer. Reduction potentials of silver dither by 1.S V. I’S nhc, in water, according to whether the solvent is a of silver poor solvator cation (tq
CF,CH,OH Thlo
DMF
HMPT CF,CII,OH HMPT
Thio
DMF
Thio DMF HMPT CF,CH20il CF-,CH,OH
* Dam from reL 3. t Theo DMF IS N.N-dimethylformthioemide. hcxarneth)l ~~ho~phor~~rl-iamide. 671
HMPT
15
672
A.
J. PARKER
Fe3fFe2+ Cd2+
Cd2* I -0.5
Ii’
AuCl;
CuZkuf
Hf
cu2*
cu+
AQ+
I 0.5
cl
Ag’
CUZ’
cuvcu
+
Fe?+/ F&
I 1.0
V
Fig.
I. Reduction
potentials
of redox
in water versus nhe(aqueous) nhr(acctonitrile).
systems
solutions are stable in water, with respect to the disproportionation of copper(I), in the presence of at least 4 mole of acetonitrile per mole of copper(I) ion. Thus the disproportionation constant for 2Cu+ ti Cu + CU’+, varies from 10+6M-’ in pure water to IO ” Mm ’ in 0.5 n-ml fraction acetonitrile water, to 10 “Mu- ’ in anhydrous acetonitrile[lO]. Chopper can he electrorefined, using soluble copper anodes, in a solution of copper(I) sulphate, sulphuric suitable non-volatile acid and water, containing water-soluble organic nitriles, like 2-hydroxycyanoethane to give good quality copper cathodcs[ll]. Since the electrolysis is a one electron process, there are savings in power and time over the conventional electrorefining using copper(U) sulphate. sulphuric acid, water as electrolyte. Capper can be electrowon, using insoluble anodes, from a solution of copper(I) sulphate, sulphuric acid, and water, containing suitable organic nitriles like acetonitrile and 2-hydroxycyaIloettlane. to give good quality copper calhodes[9]. The anodic process is not production of acid with evolution of oxygen. as in conventional electrowinning, but is oxidation of copper(1) to copper(H). Thus in the one electron nitrile
and
in
acetonitrile
US
process, the power consumed is only 107t of that in electrowinning from aqueous acidic cuprrc sulphate solutions[12, 131. Of course, it is ncccssary to reduce the cupric ion in the anolyte to cuprous ions, but this can be done in a variety of useful ways, including the use of particulate copper. Extremely pure copper powder can be obtained from solutions of cuprous sulphate, sulphuric acid and water, containing acetonitrile by a process known as thermal disproportionation, by distilling the BOO/, acetonitrile-water azeotrope, using waste steam as the heat source. Removal of the acetonitrile from the water, allows disproportionation of the copper(I) ion[9, 12, 131. This leads to an attractive method of refining particulate copper, eg scrap cement copper, high-grade copper-nickel mattes, or reduced particulate copper from sulphide and oxide concentrates. The principle is illustrated in Fig. 2. Measuring
free
energies
qf tran.sfcr of
single
ions
If one is to record and discuss the thermodynamics of single ions in solution, it is necessary to make an cxtrathermodynamic assumption. The assumption we have chosen to use is the TATS assumption, ir that ; AH,,Ph*As+ = AH,,Ph4 AG,,Pb,As + = AG,,Ph4BAS,,Ph,B: AS,Ph,As+ = B-: AS,,Ph,As+ =
Table 2. Standard electrode reduction potentials (US nhr. water) of potassium and silver cations in solvents at 25’. Assumption
AG,,Ph,As
’ =
E Ethanol Ck ,CH,OH HMPT NMe pyrrolidone McOH MeNO, DMF McCN DMA Sulpholane DM SO
SDMF
Prop. Carb. H,U Formam~de
AG,,Ph,B-
K+/K
E’
Ag+/Ag
-
2.709
~ ~ _
2.518 3.085 3.085 2.76
~ ~ -
2.661 3.028 2.826 3.047 2.996 3.050
0.405 0.496 0.x7x 1.060 0.622 0.574 0.557 0.761 0453
- 2.656
- 0.240
~ 2.918 - 2.924 - 2.948
v
co!xW rer,n,ng
solvent*
+ 0.882
v
I.301 I
0.965 0.800 0.639
m
x :+ Leo& C”% Cu.*&” 1&>15rn,” 25” Fig. 2. Parker proportionation
&“o, x, Dlrtll x===+ 2C” An; Flo*n
method of refining copper via thermal of solutions of cuprous sulphate acetonltrilc-water.
disin
of ions
Salvation
0.1 M NEt,Pictrate in acetonitrile and 0.01 M electrolyte solutions in other solvents[ 171. The liquid junction potential for the calomcl rcfcrcnce electrode is also shown[16]. These potentials, if subtracted from the end of cell I3 (or its equivalent), give the “true” UYJ based on the TATB assumption and thus lead to E- and AG,, values for single ions, based on the TATB assumption. The NEt,Picrate bridge is not suited for strongly acidic solutinns and NEt,ClO, is prcfcrrcd.
A.S,Ph,B; where the subscript fr denotes transfer of the ion from a reference solvent to another solvent and s denotes solution. ir transfer from any crystal containing the ion to a solution. Our justification for using this assumption has been presented elsewhere[l I. 14, IS]. In practice, the TATB assumption sometimes is awkward to apply to free energies of transfer although it is well suited to enthalpiesL2]. We find it convenient to measurr the EMF of clectmchemical cells like B. containing a silver reference electrode in acetonitrile, or a silver reference electrode in the solvent being studied[3]. Since AG,,Ag’ (TATB assumption) for transfer from water or acetonitrile is known (cf. Table 2) AC,, of other cations (TATB) from water. or E’~ M/M’ 1’s &c~ in water. is easily calculated from the I-.MF‘ of cell Rr31.
We have heen especially interested in dipolar aprotic solvents. of high dipole moment and high diclcctric constant. They are not donors of hydrogen bonds and the centre of positive charge density is usually at a crowded site in the moleculeLX]. On the other hand the centre of negative charge density is usually on a highly basic. 0, S or N atom, which is highly exposed for intermolecular interaction with positive or acidic centres. Typical structures are shown in Fig. 3. together with dipole moments. I note that the Iresonance structures shown could be a major contributor to the structure of the solvent molecules in the first salvation shell ahout a cation.
I can strongly recommend the Pleskov electrode. Ag/AgClO, 0.01 M in acetonitrile, as a reference electrode for clcctrochemical work (es polarography) in non-aq~leous solventy. It is a very stable electrode and the acetomtrrle, unhke water. is less active than most polar solvents towards most cations except Cu’, Ag+ and Au+ Thus minor contamination by acetonitrile can be tolerated. WC much prcfcr the Plcskov clcctrade to the SC<’ electrode which has higher liquid junction potentials because of transfer of Clacross a junction and which could contaminate the test solvent with water[ 163. Table 3 shows the liquid junction potentials (TATB assumption) to be expected between thi< electrode. with a salt hl-idge of
Table 3. Liquid jullctinrl reference electrode
potentials Ag
and the calomci-water
1
with These
Junction*
assumption)
AgCIO,
R”kcMN / Yzg
1 Lean;;
(
(
elcctrodr* in other solvents at electolyte concentrations values should bc subtracted from the obscrvcd en?f of the cell retl/NEt,Pic/tcst E,,(Pleskov)t ~ 0.065
HMF”I,‘An
~ 0.06
MeOH/An McNOqiAn DMFJAn TM S/An DMSO,‘An PC/An H$/An HCONHJAn
- 0.039 - 0.063 0.005 i 0.101 - 0.03 I f 0.049 -0.041 + 0.003
Junction V
these
arc
E,,(calomel)$
EtOH/H*U HMPT/H,O MeOII/H,O McNO,iH,O DMFjH,6 TMS/H,O DMSO/H,O PC/H,0 An/H;0 HCONHJHlO
I
are An. acctonitrile. that
for the silver-acetonitrile
ref. electrode
EtOH/An
* Ahbrrviations lcne carbonate. t Ref 17; notr in ref. 16. : Rcf 16
Although interrelated. it is profitable to distinguish at least seven types of clearly defined ion-solvent interaction[I, 81. The relative contribution of these tn the total salvation energy of a univalent anion or cation, (ie 300-500 kJ/g ion in solvents of dielectric
(TATR
ca?~~el when combined
673
TMS,
slightly
tetramethylene
different
from
-0.030 V -0. IS2 -0.025 - 0.059 -0.172 ~ 0.223 -0.174 -0.135 - 0.093 ~ 0.078 sulphone; values
PC, propy-
published
hy
us
674
A. Dsmlor
:&-
-
-;--r;r:
;N-y=O
-
>r;ZC_S
:N-C=S
s
:L-,
-0:
--C--N:
Fig.
aprottr. solvents
-
:S
J. Pna~rn
6:
DMSO 3.90
Bul k(region 4)
&D I
DMF 3.90 SDMF 4.4 D
3. Resonance structures of dipolar aprotic and their dipole moments.
In pnnclple: AS+,= N,‘?AS)’
+ N,*(AS)‘CN~~(ASI~
solvents
const 25.-100) is shown below in parenthesis. The intcractions are: “Born-type” solvation (2 itO>,;): anion-solvent H-bonding (5 IO”,:,); hard--soft (5 20-4,); back bonding of 6” cations (5 10%): donor-acceptor or acid- base (< IO::,): structure making (~5”;~) and structure breaking (<5?“). People often forget that “Bol-x-type” salvation. as represented by the electrostatics of a highly charged sphcrc in a uniform diclcctric. can account fonr-more than SO%, of the tolal sol\:ltion energy (vacua to solvent) of an ion in a solvcnL of dielectric constant > 25[8]. However, for II.UJI.\/(V* ~f’iorrs herwrer7 solvents. of dielectric constant 2545. the Born term is fairly constant and changes in the other six Ion- solvent lntcractions become of grcatcr importance in determining AG,, ion. T-o illustrate, the free energy of solvatlon of silver ion (vacua to solvent) is -432 kJ/g ion in trifluoroethanol (‘I‘PE) and - 5 18kJ/g ion in hexamethylphosphoramide (HMPT)[3]. The free energy of transfer of Ag’ from TFE to HMPT is -X6 k.Ijg ion. In both solvents. the cation is solvatcd through an oxygen atom. although of very ditferent hasicity and the two solvents have virtually the same dielectric constant. of 27 28. A change of X6 k.1 is one of the largest fr-ee energies of transfer that we have observed. for a simple ion. and yet AG,,Ag+ represents only about I5Y,, of the total salvation cncrgy. AG,Ag+. Having acknowledged the importance of Born-typr salvation. I now note that free energies of transfer of I(&50 k.l/g ion. values frequently encountered in our work. can cause enormous changes in the chemistry of ions in different solutions. Thus the non-Born interactions are worthy of consideration. Some examples of such considerations follow.
This was lirst cmphasircd III 1962[38]. and is of fundamental importance in explaining the chemistry of many anions in dipolar aprotic solvents. It is illustrated by the free energy of transfer of acetate ion. Cl-, I- and ClO; from acetonitrile to methanol[l]. The two solvents have much the same dielectric constunt. hut CH,CN is a very much weaker hydrogen
Fig. 4. (a) Regions of solvent ordering and disordering ahnlit a cation (see text): (b) Salvation of thr liral kind for cation in wata (see text). bond donor than CH,OH. The anionic potential and thus the ability of the anions to nccrpt hydrogen bonds. decreases in the series OAc> Cl- > I- 1 ClO, It is not sul-prising that transfer of these anions from acetonitrile to methanol is strongly exergonic (ic meth‘anol is a more efl&tive solvent) in the order: OAc(-4OkJ/gion) > Cl-(-29) > I-(-12) > Clo,(+ l)Cl]-
Pearson’s HSAB concept[ 197 of favourable interactions of hard acids with hard bases and of soft acids with soft bases is a useful working concept, despite concern about its obvious superficiality. Related conccpts are those of class a and class h character of elements[20], and covalency[Zl] and mutual polarizability[X] but. for cxamplc, none arc as satisfactory as the HSAB principle in helping us to superficially understand the frrc energies of tranafcr of calions between dimethylformamide (DMF) and its sulfur analogue. dimethylformthioamide, SDMF[4]. DMF solvatcs cattons through its hard basic oxygen whereas SDMF solvates cations through its soft basic sulfur atom (Fig. 3). Thus DMF is a hard solvent, SDMF is a soft solvent. Followers of the HSAB prin-
Salvation ciple would claim that the hardness of a series of cations decreases in the order Li’ > K’ > Tl+ > to very soft Ag’. The free Ag+, from very hard Lit energy of transfer of these cations from hard DMF to soft SDMF changes from endergonic to exergonicL4].ieLi+(+64kJ);K+(+37kJ);Tl’ (-4kJ); Agf (-SlkJ). The HSAB explanation is that lithium cation has fidvourable hard cation-hard solver11 interactions with DMF but unfavourable hard cation-soft solvent interactions with SDMF, so AG,,Li+ is endergonic. Thallous cation on the other hand has unfavourahle soft cation-hard solvent interactions with DMF but favourablc soft cation-soft solvent intcractions with SMDF. so AG,,Tl+ is exergonic.
Singly charged d’* cations, ry Ag+, Cu+, Au+, are capable of back bonding their d electrons into a Tl* orbital of, for example, a nitrile group. They do not back bond for example to water. The interaction can be represented as CH,CgN: -+Ag*, and allows singly charged d’O cations to be much more strongly solvated by nitriles than would be expected from the solvation of less gifted cations (Ed Kf) by nitrlles. Thus AG,,K+ from water to acetonitrile is f9.S kJ/gion. but AG,,Ag’ is exergonic -22 kJ and AG,,Cu+ is -50 kJ. because these latter two cations, unlike K+. are capable of back bonding to acetonitrile[3].
These have been effectively popularized by the work of Victor GutmannlZZ] and I illustrate by the free energy of transfer of Kt between ethanol (CH,CH,OH) and lrlfluoroethanol (CF,CH,OH)[3]. Trifluoroethanol has a much less basic oxygen than ethanol, hecause of the electron-withdrawing effect of the Ck-, group t’s clcctron donation by CH, of ethanol. The two solvents have virtually the same dielectric constant of LU. 26 and the structure about oxygen is rather similar. As expected. AG,,K+ from TFE to ethanol is exergonic at - 19 kJ/gion, ic, K+ has a stronger interaction with the more electron rich oxygen of the basic ethanol. Dipole moment is not a factor. TFE has a greater dipole moment (6.8 D) than ethanol (5.5 D)[X], yet ethanol is the stronger solvator of K’.
Water is effectively polymeric and has a unique well-developed hydrogen-bonded structure of low entropy[23, 241. However. water has the ability to form an even more ordered “surface”? of even lower entropy. when certain “hydrophobic solutes”. rg many organics. neon. argon, and even “hydrophobic” large ions. ‘(I NBu,’ are added to water. This is called salvation of the second kind[2S]. Solvent-solvent interactions and the concept of ions as structure makers or structure brcakcrs m water are old concepts, which are sometimes forgotten. They have important consequences to the thermodynamics of hydration, especially in so Tar ah entropy changes are concernedll. 51. Acetonitrile, unlike water, has weak solvent-solvent interactions, it is not extensively ordered and is a solvent of relatively high entropy[Zb]. All Ions in acetomtnle and indeed in all dipolar aprotic solvents, tend to be nctt structure
of ions
675
makers, although ions of low ionic potential, kike NBu,’ and Rb’ are only weak structure makers in dlpolar aproticsl I, 51. The following are best explained in terms of structurc making. structure breaking interaction. There is a very large loss of entropy (A&NBui = - 175 ‘) when large hydrophobic NBud is transJk- ’ g ion ferred from acctonitrile to water[ I]. NBuz has little effect on the structure of acetonitrile and hence the enlropy of its acetonitrile solution. However, NBu,’ in water undergoes salvation of the second kind. where the water is rejected by NBuz and forms an ordcrcd surface of very low entropy about the large hydrophobic cation. Thus NRuz is a nett structure maker- in water and the free energy of transfer from water is very acetonitrile to endergonic (AG,,NBui = +33 kJ)[l]. because of entropic: considerations. is a very There large gain of entropy ‘) when large hydro(AS,“Rb+ = + 100 kJ ’ g ion philic Rb’ is transferred from acetomtrile to water[l]. Rb+. although large, has a higher ionic and so more strongly orientates potential than NBuz acetonitrile about itself. In water. Rb+ also weakly orients water about itself. ie there is salvation of the first kind which is sufticient to partially break up the structure of hulk water in the vicinity of the Rb+. The net rrsull is that Rb+ is a structure breaker in water and there is a substantial gain in AS,,Rh’ from acetonitrile to water. This leads to an exergonlc AG,,Rb+of --7 kJ/g mn[l]. Linetr~ ,free erwryy
relufionships
Attempts have been made to record various properties of solvents which can be used in lineal- plvta tu predict behaviour in solution. For example, Gutmann’s donor numbers[22] have proved very useful in understanding cation salvation. The donor number is an cnthalplc property for solvents in an inert diluent. A more fundamental property, if seeking relationships to predict free energies of ion-solvent interactions. is the free energy of transfer of potassium cation, and we have observed an acceptable linear relationship of the type AG,,M”+ = mAG,,K+. which relate free energies of transfer of cations to the hehaviour of the model potassium cationC3.41. Deviations from linearity. of AG,,Ag+ in MeCN and SDMF, or in waterr4J. denote “abnormal” ry nonof G,,NBu,l Born) ion-solvent interactions. like back bonding. covalency and solvation of the second kind. The sensitivity, m, to solvent transfer of a cation M” _ in this relationship, relative to rn = 1 for K+ is of course grcatcst for cations of the greatest ionic Table 4. Sensitivity of AG,.M”+ to bolvenl transfer. Values of m in the expression ACi,,M”’ = mACi,,K+ * m” * Znz+ Cd* + Ba’ II’ Ll+
+
* Data
m
M”+
m
4.6 3.7 3.7 3.1 1.7
Na+ Ag+ K+ CS+ Ph,As+
1.3 1.3 1.0 0.7 0.3
from
refs. 4 and 17.
A. J. PARKER
676
potential, cg Zn’+, ionic potential, accorded in Table THERMODYNAMICS
and is least for eg Ph,As+[4]. 4. OF
TRANSFER
OF
cations of lowest Sensitivities are
IONS
TO
WATER
now examine AG,, ion in more d&ail by examining the enthalpy and entropy of transfer, as they contribute 10 AG,,ion = AH&n - TAS,,lon. Enthalpies and entropies of transfer to water from less complex solvents tells us a great deal about salvation in water. Some typical vaIues are in Table 5. Table 5 illustrates some frequently observed general points about transfer of ions from non-aqueous solvents to water. Thus: (1) Water is a very poor solvent enthalpywise for most of those cations whose solvation is of the first kindll, 2,5]. This is because a large number of waterwater hydrogen bonds arc broken (loss of enthalpy) when such cations are transferred to water. Transfer from dipolar aprotic solvent to water of monovalent cations is always, and of divalent cations is usually. an andother-mic process. (2) Water is an cxccllent solvent entropywise for all ions whose salvation is of the first kind[l. 51. Ions tend to break up the low-entropy ordered structure of water so there is always a large gain of entropy on transfer of all but hydrophobic ions from nonaqueous solvents to water. (3) Enthalples of transfer of ions to water vary considerably, accordmg to the type of ion and the solvent from which transfer was ma&. Thus chloride ion has an exnthermic transfer from DMF to water because of hydrogen bonding between water and chloride ion, but H-bonding is negligible when CIO, is transferred, so the “usual” endothermic transfer to water, common for cations, is observed. As noted, silver cation has a back bonding interaction with acetonitrile. this is reflected solely in the enthalpy, so All,,Ag+. for transfer from acetonitrile to water. is strongly endothermic. (4) Despite very large variations in AH,,ion, values of -TAS,,ion are remarkably constant through a series of ions[l, 51. Thus in Table 5, entropies vary enthalpics of transfer by only 25 kJ g ion- I, whereas vary by X0 kJ g ion- ’ In particular, - TAS,,K+ , and -TAS,,Ag+ from acctonitrile to water arc virtually the same, despite very different enthalpies of transfer. The near equality of -TAS,,Na’ and -TAS,,ClI
Table
5. Enthalpics
(DMF-+ H,O) despite very different values of AH,,ion 1s also striking. It seems likely that once the translational entropy of a certain number of solvent molecules is lost hy restncting them in the salvation sphere about the ion. then no matter how much stronger another interaclion, thcrc is no substantially greater loss of entropy, provided that the number of molecules so restricted by either interactlon is not increased. One can imagine that a similar number of molecules of acetonitrile (rg 6) are in the salvation shells of K ’ and Ag ‘, and it is these whose translation is restricted. Since translational entropy is the major factor, the entropy change need be no greater just because Ag+ binds acetonitrilc more strongly (in an enthalpic sense) than does K+. (5) The effect of transferring hydrophobic cations from non-aqueous solvents to water is illustrated by the final two examples in Table 5. In water. salvation of NBu; and of Ph,As+ is of the second kind[25]. As noted, the formation of a hydrogen bonded surface of water about hydrophobic ions Involves a Iarge loss of entropy, but this is in fact compensated for by the enthalpic advantage of forming strong hydrogen bonds in the “surface of water”. Thus enthalpies of transfer of hydrophobic ions to water arc often cxothermic or at worst only weakly endothermic. hllt -TAS,, ion is usually very positive, ie thcrc is a large loss of entropy.
It is helpful to our understanding of salvation if we construct models for the various regions of solvent in the vicinity of ions[l, 51. Such models for cations are shown diagrammatically in Fig. 4. For cations in water, we distinguish four regions, firstly the primary salvation shell[l] of ion-centred. ordered water: surrounded by a region 2 of ordered water, hydrogen bonded to the acidic water in region 1. and a region 3 of unstructured water between region 1 and the structured bulk water, the latter being rcglon 4. The number of molecules in each r-egion is N,, NZ, N, and N4 respectively. The population of these regions, N, etc.. should pay due regard to the principles and stereochemistry of ion-ligand coordination. the dimensions nf ion and solvent molecules, packing theory and the requirements for hydrogen bonding by water, eg linearity. Thus it is unreasonable on sleric considerations to
snd entropies of transfix assllmptlun)*
lo II (a) Acetonitrilc to water A&!+ K+ Zn” (b) DMF to water Na’ c’1r CIO, Zn2 + NBu; Ph * Data from refs I-5
or
ions
to
water
(TATR
- 298 AS,,ion
AII,,ion +53kJgiun-’ f23 -20
-31 -33 -49
+33kk.lgion-’ -21 f23 ~-63 -15 f2O
-22.5 -25 -23.5 ~33 f43.5 + 18
kJ L: io11-
’
kJ 6 ion-’
Salvation
expect that more than 6 water molecules (4 is more likely) could closely fit about a small lithium or zinc cation in a primary salvation sphere (region 1). If region 2 consists of water hydrogen-bonded to water in region 1. then if there are N, waters in region 1. there cannol be more than 2N1 waters in region 2. This. of course, IS because each water about a cation in region 1 has only two acidic hydrogen5 available as H-bond donors[l]. Construction of a model for hydrated K’ with N, = 6 and N1 : 12 water molecules assuming linear hydrogen bonds between water in region 1 and region 2. shows that there is much open space in region 2[27]. It is expected that the space would be filled. depending on the size of the cation, by between 10 and 20 disordered waters of region 3. which does not have a well defined boundary with region 2. Region 2 exists because water molecules in region 1 about cations of high ionic potential, are quite acidic and donate hydrogen bonds to water. It is Interesting to speculate[l] whether a [region 2 exists for cations in dipolar aprotic solvents, like DMSO. DMF and HMPT. where the primary salvation shell is unable to donate hydrogen bonds to other solvent molecules. In these solvents, the positive charge of the cation may bc shielded from the bulk solvent by methyl groups, as in II and III. We expect that.
0
o=s
,C”,
@
‘-.CH,
(I)
..
O=C_NICH,
A
(II)
----CH,
(III)
for any cation, region 2 is much less extensive in dipolar aprotic solvents than in water, so it follows that unstructured region 3, which depends in part on the size of region 2, is less extensive in dipolar aprotic than in water. As noted, the very high degree of structure in bulk water (region 4) is unique to water. and for solvents like acetonitrile. region 4 is only poorly dcvcloped structurally. These concepts of electrolyte solutions which have ion and solvent centred regions of solvent. as well as unstructured regions, are not new[23--251. I note them because they are beautifully illustrated by entropies of transfer of single ions[l. 51. Thus in water regions 1, 2 and 4 are of much lower entropy than region 3. but in dipolar aprotics, regions I and 2 are of much lower entropy than region 4. which is ot slightly lower entropy than region 3. In rather loose terms. solvent acctonitrile is a “higher entropy liquid” than is solvent water.
In order to understand entropies better, we have developed[lS] the idea of entropy of transfer of an ion from an ideal unimolar solution to the corresponding ummolar real solution (AS,,1 + R). The idea is based in part on the TATS assumption and details of the procedure are given elsewhere[15]. This entropy of transfer is given by: A&,.( I where
S,
is
R) =
AS,
Lhc cntrupy
-
12.6 of
-
ir, from
crystal
677
to solution, (TATB assumption), p is the density of the solvent of molecular weight MW. The ideal soIutlon is one in which one mole of single ions in a crystal has melted and been dispersed through one litre of the relevant real solvent, without interfering with solvent-solvent interactions and without introducing ion-ion or ion-solvent interactions. The entropy change for this process (12.6 + RIn 1000p/MW) is compared with the entropy change for the real process of dissolving one mole of ions in real solvent (AS,) to give A&,(1 R) which is thus the sum of entropy changes prodnced by- the ion in gcncrating regions 1. 2 and 3 liom region 4. AS,..(I+
R) = N,AS(4-
1) + N>AS(4-2) +
N,AS(4+
3).
(1)
Some values of AS,,{1 R) for single ions are in Table 6[5]. In Table 6. the solvents are listed as increasing in solvent structure (ir> in region 4) from HMPT. with weakly developed structure. to water. with highly developed structure. There is an enormous loss of entropy on transferrmg catlons from idcal HMPT to real HMPTLS]. The loss is much greater for Cd’+ than for K+. no doubt bccau~t. of the much greater ionic potential UT Cd’+. The loss of entropy is in forming a structured primary salvation shell (region 1) from region 4 of the weakly structurrd solvent, HMPT. In olher words. N,AS(4+ I) in equation (1) is strongly negative, and is the only significant term on the right of equation (1 ). The number N, of HMPT molecules in region 2 is expected to be small because of shieIding of the positive charge by the bulky solvent in region 1. so N,AS(4+ 2) is small. Since region 4 is only weakly structured. the term (N,AS(4+ 3) is also of little co,,sequence in determining the entropy of transfer of cations from ideal to real HMPT. The loss of entropy on transferring cations from idcal DMSO to real DMSO solution (Table 6) is also large. but is considerably less than the loss for HMPT[S]. This is explained by the likelihood that DMSU solvent has a more dcvclopcd structure m region 4 than has HMPT, ic DMSO is a “lower entropy solvent” than HMPT. Thus the term contributing a gain of entropy, ie N,AS(4+ 3) to equation (I), is more positive for DMSO than for HMPT, and if N, + NZ for DMSO is similar to HMPT. the terms N,AS(41) + N,AS(42). are less negative for DMSO than fol- HMPT. The loss of entropy shown in Table 6 on transferring cations from ideal water to real water solution is very much less than the loss for the corresponding transfer in all the dipolar aprotlc solvents. Indeed for K’. there is very little loss of entropy, ideal to real water. This is because bulk water in region 4 is in a highly structured state of polymeric clusters and Table 6. Entropies of transfer of ions from corresponding real snlvents AS,,(IR) JK
Ion g’
Rln(1000$>,‘MW)
solullon.
of ions
HMPT /
* Data
to
DMF
DMSO
H,O
- 100 _ 284
-87 -266
-65 -224
-I -178
rrll 5.
the
’ g inn ‘*
CH ,CN
- 124 - 40x from
l&al
A. J. PARKER
67X
thus has low entropy. Thus AS(4 I ) + AS(4 - 2) is only moderately negative and AS(4-+ 3). the entropy gain for creation of unstructured water in region 3. is strongly positive. That there is a significant loss of entropy for Cd’+ in water. ie A&,(1 - R) Cd’+ very negative, suggests that the hydrogen-bonded secondary hydration shell (region 2) is extensive (N2 large) about this divalent cation in water. The entropies of transfer of cations from ideal to real solutions become more and more negative as the Ionic potential of the cation increases. and thus the population (N, + N,) of regions 1 and 2 increases. This is shown in Table 7 for cations of increasing Ionic potential in both DMF and water. As in Table 6, the loss of entropy is much grcatcr for ions in the less structured solvent. DMF. than in the highly structured water. Large rubidium cation is seen to be a net structure breaker of water, ie AS,,(lR) Rb’ is positive[l, 51. Cations are always net structure makers in dlpolar aprotic solvents, but cithcr a net breaking or a making is possible in water, because of the fine balance between regions 1 + 2 and 3.
The least number of solvent molecules which have lost their translational entropy in the primary plus secondary salvation shells (regions 1 + 2) about cations can be estimated from h&,(1R) and the entropy of free&lg of the pure solvent. AS,. ,e
A&,(1-R) ~___ AS,
N,+NL> zzz
N,AS(4-+ ~ ~~~
1) + N,A%4+2)
+ N,AS(4+
3)
AS,
The assumption is made that AS., 2 AS(4+ I) = AS(4--*2), ie that entropy lost when pure solvent is fro7en. is more or as much as could be lost in “freeLing” solvent in the primary and secondary salvation shells about a cation. This recognizes loss of translational entropy as a major factor in both processes. Further. the effect on entropy of forming I-egion 3. N,AS(4+ 3). which tends to make A&,(1+ R) less negative and 1s related to deviationa from Trouton’s constant[l], is not allowed for in this calcularion of nlininmm N, + N,. N,. for example. can bc up to 20 if region 2 is fully developed in water. Thus the solvaticrn number. N, + N,. is a minimum on two counts. As noted, N,AS(43) is a quite substantial term for many cations in water. so that the estimated rnininru,?l salvation numbers, for cations in water, arc probably much less than the real salvation numbers. Table 7. Entropies of transfer of ions from ideal to real solvents. Effect of mcrcaslng 10nlc potential of cations. AS,,(I-HI JK~‘~:I~II~‘* Rh+ K’ Increasing
* Data
from
[.i Na Ap’ Ionic potential
I-cf.
I
and 5.
’
RaL’
Cd”
Zn”’
Table 8. Muknal salvation numbers of cations in water (AS,- = -22 JK ’ mole I) and DMF (ASI -37)* N, + NZ > [AS,,(lR)]/AS, Hz0 C-s+ K’ Li‘ &I’+ CdL ’ ZlI*+ * Data
>O >o >3 >5
z-8 >9.5
from
DMF -,2 2 2.5 2 3.5 ,8 Z-7 2X.5
increaslng ionic potential I
ref. 5.
Minimum salvation numbers for cations in water and DMF are shown in Table 8. As expected, as the ionic potential of the cation increases, so the minimal salvation number increases in both solvents. An important observation from Table 8 is that there is a secondary salvation shell (region 2) about divnlcnt cations like Cd’+ and Zn’+. This is as true for DMF as for water and follows from the calculated minimal salvation numbers of >6 for these small ions in both solvents. Since It is not possible to fit more than six (and possibly only 4) solvent molecules in the primary salvation shell about these small ions of high ionic potential, the extra structured solvent must be in region 2. This result[5] was surprising for cations in DMF. We had expected[l] that there would be effective insulation of the charge on Cd’+ and Zn2+ by bulky DMF, as in III. and thus little tendency for a second layer of structured DMF to form about the solvated cation. For reasons already given, the minimal salvation number of >9..5 water molecules structured around Zn*+ is expected to be much less than the true solvation number, because models show that N, is between 10 and 20 when N2 is &12. However, Ihe minimal values of z 8.5 DMF molecules about Znzf in less structured DMF is probably only a little less than the true salvation number. Thus we expect that there are significantly more water than DMF molecules in the respective structured salvation shells about Cd’+ and Zn2 + than is indicated by Table 8. The entropy losses on freezing solvents, ie change region 4 to solld, arc related through Ioss of translational entropy to AS(4 -+ 1) and Aq4-+ 2) and are: -22 JK-’ mol-’ for Il,O: -36 for acetonitrile: -37 for DMF; - 48 for DMSO and -60 for HMPT[5]. Much more entropy is lost when poorly structured HMPT. rather than highly structured water. is frozen This correlates with the enormous losses of entropy when cations are transferred from ideal HMPT lo real HMPT solution (Table 6). Minimal salvation numbers for solvents translationally bound to zinc(l1) cation are b-9.5 in water: =_ 10 in acetonitrile: >8.5 in DMF: >5 in DMSO: z=-5.5 in HMPT[S]. The development of models for the salvation shells about ions is at an early stage but Professor Watts is continuing our work in this area[27]. To summarize, it seems likely that many cations in water have a primary solvalion shell of ar Irrrsr 4-6 water molecules. divalent cations have ~lt Ic~?.st a secondary solvation shell. of nor store rhan 12 waters. which are hydrogen-bonded to the primary shell. There are a
Solvatian
number (up to 20) of unstructured non-polymeric water molecules (region 3) filling space in the secondary salvation shell (region 2), the whole blending into region 4. the highly structured polymeric bulk water. The picture is simpler for cations in dipolar aprotic solvents. Thcrc is a well developed primary salvation shell for most cations and a few cations have a sparsely populated secondary solvaliun shelf. However, the distinction between bulk solvent in region 4 and unstructured solvent in region 3 is less well defined than in water. because the bulk solvent is at best of-ten only weakly structured. Perhaps the most interesting conclusion from our work on entropies of transfer is confirmation that the unique position of water as a good solvent for electrolytes[23] is due to water-s highly developed structure, ic, to the vel-y favout-able entropy changes (relative to other solvents) accompanying salvation of the first kind. when ions are introduced into water. Conversely. the reluctance of water to dissolve significant amounts of uncharged non-polar solutes 1s due to solvation of the second kind. it, to a very unfavourable loss of entropy, accompanymg the formation of a highly structured water surface about hydrophobic solutes
of ions
D. A. Owensby and A. J. Parker. J. 5. G. R. Hedwig. .4m. chra,. so<. 97, 388 (1975). J. p/r>,.\. 6. B. G. Cox. A. J. Parker and W. E. Waghor-nc. C‘hrm. 78. 1731 (1974). Calculated room free energies of transfer 7. A. J. Parker. in ref. I nt- unpublished work. 8. A. J. Parher. Chrm. RPL.. 69, 1 (1969). 9. A. J. Parker. W. E. Waghorne. D. E. Giles. J. H. Sharp. R. Alexander and U. M. MUX. U. S. t’atent 3.X65.744 (1975):
10 11. 12. 13. 14.
I 5. 16. 17. 18. 19. 20. 21
REFKRKNC‘ES 1. B. G.
Cox.
G.
Watts.
Amt.
3.
2. G. R. Hedwig 6589 (1974). 3. D. A. Owcnsby. c/ten,. Sot 96, 4 R Alrxander. E. Waghorne.
R. Hedwig. A. J. Parker and D. W. Chrm. 27. 477 (1974). and A. J. Parker, J. Am. churn. Sot. 96. A. J. Parker and J. W. Diggle. J. Am. 2682 (1974). D A Owennhy. A. _I. Parker and W. Arrt. .J. Chrrn. 27, 933 (1974).
679
27. 37
77.
Brltiah
Patent
1381666
(1975).
W. F. Waghorne. Ph.D. Thesis. Australian National Ilniversity, Canberra. 1973. D. M. Muir. A. J. Parker. J. H. Sharp and W. E. Waghornc. H\lir-n,nutall~r~~,’ I, 61 (1975). A. J. Parker. Scurc/~ 4, 426 (1973). A. J. Parker. f’roc. K ,4x$(. c/~i,m. Invr. 163, (1972). B. G. Cux and A. .I. Parker. J. .4/u dwim Sot. 95. 402 (1973). R. G. C-ox and A. J. Parker. ./. .¶f,z. L./IPIII. Sot. 95, 687Y (1973). J. W. Dig& and A. J. Parker. .4usr. .1. Chrvi. 27. 1617 (lY74). D A. Owznsby. Cnmpnrntive Sol\ntion in Various Media. Ph.D. Thesis. Australian Nat~nnnl Llnlversity. Canberra. 1975. A. J. Parhcr. Q. Rrr. 163, (1962). R. G. Pearson. J. .4,tr. clte,?~. Svc. 85, 3533 (1963). S. Ahrland. J. Chatt and N. Davies. Q, &I-. 12, 265 (lY58). R. S Drago and B B. Waylund, .J 4191. clrunl. SOL.. X7, 3571 (1965). LJ Mayer and V. Ciutmann. St~.~,~tidl.<,un,l Brr~xiirig Vol. 12. Springer-Verlag. Berlin. lY72.
D. W. Watts.
Personal
communication.
School
OF
IONS-ENTHALPIES,
FREE
ENERGIES
of Mathematical
OF
and PhysIcal
Murdoch.
ENTROPIES TRANSFER
Sciences. Murdoch
Wrsrern
University.
Australia
CF,CH,OH and CH,N02) or a strong solvator like thio DMF and acetonitrile. Values of E” Ag+/Ag (TATS assumption) are m Table 2. together with E K+/K (TATB). 1‘s n/w in water[3].
For the past five years, at the Australian National LJniversity, Drs. B. G. Cox, G. R. Hedwig, D. A. Owcnsby and I have been measuring heats of solution and heats of precipitation of electrolytes in nonaqueous solvents[l, 21. We have used an LKB ProducKter Model 8700-l precision calorimeter. The heats lead to enthalpies of transfer of single ions. The same group, ably assisted by the late Dr. John Diggle. sn outstanding electmchcmist. have measured rlectrode potentials and the kinetics of electrode processes for ions in non-aqueous solvents. using a PAR 170 electrochemical system, and Radiometer pH M26 equipment. When combined with solubihties. the data Iead to free energies of transfer of single ions[l. 3-51. Supporting measurements include molar volumes and nmr chemical shifts of solvents m solvatlon shells of electrolytes in non-aqueous solvents[6]. The measurements are routine for simple electrolytes in aqueous systems. the novelty is in the variety of solvents and electrolytes and in the calculation of the extratherrnodynamic quantities AC;,,. AH,, and AS,,.. for transfer of single ions between solvents[5]. Perhaps the data and some of our ideas about ions in solution may be of interest to electrochemists. 1 will deal only with the chemistry of dilute (
An interesting demonstration of wme of the differences in chemistry when one transfers from aqueous to non-aqueous systems. is the observation that NaCl is very soluble in water. but insoluble in thio DMF. whereas AgCl is insoluble in water and very soluble in thio DMF.
Scientists nowadays are under increasing pressure to consider the relevance of their research. and rightly so. Free energies of transfer to non-aqueous solvents determine large changes in rates of reaction[S], solubilities. rcdox potentials. stability constants, and dlstribution coefficients. All of these are important to everyday chemical technology, yet much of the chemical technologist’s thinking and applications are in terms of aqueous systems. Further, the environment in which many biological processes take place (ry clefts in proteins) may be much more “amide like” than “water like” so non-aqueous data in. for example DMF, may help us to understand biological processes
better. If we are to understand the highly complex chemistry of aqueous solutions and the unique character of water. we need first to understand the chemistry
of the much
simpler
noI1-aqueous
solutions.
One example of an application of non-aqueous chemistry is OUI- invention of a new method of ploceasing copper Co solutions of cuprous sulphatc in acidified acetonitrile-water mixtures[9P13]. Crude acetonitrile is a cheap solvent, and cuprous rulphate
Some very large effects of solvent transfer on the chemistry of ions in solution have been observed. The following examples. which are given in an electrochemical context. arc iilustratlvc. (a) The cw!f’of cell A. varies by up to 2.1 V according to the solvenls used (Table I). This is because trifluoroethanol is a poor solvent for all cations. dimethylformthioamide is a poor solvent for K+ but a good solvent for Agf and HMPT is an excellent solvent for all cations[X:]. (b) There are substantial anodic and cathodic changes in reduction potentials (TATB assumption. t.ic/e infrtr) on transfer of various redox couples from water to acetonitrile as solvent (Fig. 1)[7]. (c) The chemistry of Ag + is very susceptible lo wlvent transfer. Reduction potentials of silver dither by 1.S V. I’S nhc, in water, according to whether the solvent is a of silver poor solvator cation (tq
CF,CH,OH Thlo
DMF
HMPT CF,CII,OH HMPT
Thio
DMF
Thio DMF HMPT CF,CH20il CF-,CH,OH
* Dam from reL 3. t Theo DMF IS N.N-dimethylformthioemide. hcxarneth)l ~~ho~phor~~rl-iamide. 671
HMPT
15
672
A.
J. PARKER
Fe3fFe2+ Cd2+
Cd2* I -0.5
Ii’
AuCl;
CuZkuf
Hf
cu2*
cu+
AQ+
I 0.5
cl
Ag’
CUZ’
cuvcu
+
Fe?+/ F&
I 1.0
V
Fig.
I. Reduction
potentials
of redox
in water versus nhe(aqueous) nhr(acctonitrile).
systems
solutions are stable in water, with respect to the disproportionation of copper(I), in the presence of at least 4 mole of acetonitrile per mole of copper(I) ion. Thus the disproportionation constant for 2Cu+ ti Cu + CU’+, varies from 10+6M-’ in pure water to IO ” Mm ’ in 0.5 n-ml fraction acetonitrile water, to 10 “Mu- ’ in anhydrous acetonitrile[lO]. Chopper can he electrorefined, using soluble copper anodes, in a solution of copper(I) sulphate, sulphuric suitable non-volatile acid and water, containing water-soluble organic nitriles, like 2-hydroxycyanoethane to give good quality copper cathodcs[ll]. Since the electrolysis is a one electron process, there are savings in power and time over the conventional electrorefining using copper(U) sulphate. sulphuric acid, water as electrolyte. Capper can be electrowon, using insoluble anodes, from a solution of copper(I) sulphate, sulphuric acid, and water, containing suitable organic nitriles like acetonitrile and 2-hydroxycyaIloettlane. to give good quality copper calhodes[9]. The anodic process is not production of acid with evolution of oxygen. as in conventional electrowinning, but is oxidation of copper(1) to copper(H). Thus in the one electron nitrile
and
in
acetonitrile
US
process, the power consumed is only 107t of that in electrowinning from aqueous acidic cuprrc sulphate solutions[12, 131. Of course, it is ncccssary to reduce the cupric ion in the anolyte to cuprous ions, but this can be done in a variety of useful ways, including the use of particulate copper. Extremely pure copper powder can be obtained from solutions of cuprous sulphate, sulphuric acid and water, containing acetonitrile by a process known as thermal disproportionation, by distilling the BOO/, acetonitrile-water azeotrope, using waste steam as the heat source. Removal of the acetonitrile from the water, allows disproportionation of the copper(I) ion[9, 12, 131. This leads to an attractive method of refining particulate copper, eg scrap cement copper, high-grade copper-nickel mattes, or reduced particulate copper from sulphide and oxide concentrates. The principle is illustrated in Fig. 2. Measuring
free
energies
qf tran.sfcr of
single
ions
If one is to record and discuss the thermodynamics of single ions in solution, it is necessary to make an cxtrathermodynamic assumption. The assumption we have chosen to use is the TATS assumption, ir that ; AH,,Ph*As+ = AH,,Ph4 AG,,Pb,As + = AG,,Ph4BAS,,Ph,B: AS,Ph,As+ = B-: AS,,Ph,As+ =
Table 2. Standard electrode reduction potentials (US nhr. water) of potassium and silver cations in solvents at 25’. Assumption
AG,,Ph,As
’ =
E Ethanol Ck ,CH,OH HMPT NMe pyrrolidone McOH MeNO, DMF McCN DMA Sulpholane DM SO
SDMF
Prop. Carb. H,U Formam~de
AG,,Ph,B-
K+/K
E’
Ag+/Ag
-
2.709
~ ~ _
2.518 3.085 3.085 2.76
~ ~ -
2.661 3.028 2.826 3.047 2.996 3.050
0.405 0.496 0.x7x 1.060 0.622 0.574 0.557 0.761 0453
- 2.656
- 0.240
~ 2.918 - 2.924 - 2.948
v
co!xW rer,n,ng
solvent*
+ 0.882
v
I.301 I
0.965 0.800 0.639
m
x :+ Leo& C”% Cu.*&” 1&>15rn,” 25” Fig. 2. Parker proportionation
&“o, x, Dlrtll x===+ 2C” An; Flo*n
method of refining copper via thermal of solutions of cuprous sulphate acetonltrilc-water.
disin
of ions
Salvation
0.1 M NEt,Pictrate in acetonitrile and 0.01 M electrolyte solutions in other solvents[ 171. The liquid junction potential for the calomcl rcfcrcnce electrode is also shown[16]. These potentials, if subtracted from the end of cell I3 (or its equivalent), give the “true” UYJ based on the TATB assumption and thus lead to E- and AG,, values for single ions, based on the TATB assumption. The NEt,Picrate bridge is not suited for strongly acidic solutinns and NEt,ClO, is prcfcrrcd.
A.S,Ph,B; where the subscript fr denotes transfer of the ion from a reference solvent to another solvent and s denotes solution. ir transfer from any crystal containing the ion to a solution. Our justification for using this assumption has been presented elsewhere[l I. 14, IS]. In practice, the TATB assumption sometimes is awkward to apply to free energies of transfer although it is well suited to enthalpiesL2]. We find it convenient to measurr the EMF of clectmchemical cells like B. containing a silver reference electrode in acetonitrile, or a silver reference electrode in the solvent being studied[3]. Since AG,,Ag’ (TATB assumption) for transfer from water or acetonitrile is known (cf. Table 2) AC,, of other cations (TATB) from water. or E’~ M/M’ 1’s &c~ in water. is easily calculated from the I-.MF‘ of cell Rr31.
We have heen especially interested in dipolar aprotic solvents. of high dipole moment and high diclcctric constant. They are not donors of hydrogen bonds and the centre of positive charge density is usually at a crowded site in the moleculeLX]. On the other hand the centre of negative charge density is usually on a highly basic. 0, S or N atom, which is highly exposed for intermolecular interaction with positive or acidic centres. Typical structures are shown in Fig. 3. together with dipole moments. I note that the Iresonance structures shown could be a major contributor to the structure of the solvent molecules in the first salvation shell ahout a cation.
I can strongly recommend the Pleskov electrode. Ag/AgClO, 0.01 M in acetonitrile, as a reference electrode for clcctrochemical work (es polarography) in non-aq~leous solventy. It is a very stable electrode and the acetomtrrle, unhke water. is less active than most polar solvents towards most cations except Cu’, Ag+ and Au+ Thus minor contamination by acetonitrile can be tolerated. WC much prcfcr the Plcskov clcctrade to the SC<’ electrode which has higher liquid junction potentials because of transfer of Clacross a junction and which could contaminate the test solvent with water[ 163. Table 3 shows the liquid junction potentials (TATB assumption) to be expected between thi< electrode. with a salt hl-idge of
Table 3. Liquid jullctinrl reference electrode
potentials Ag
and the calomci-water
1
with These
Junction*
assumption)
AgCIO,
R”kcMN / Yzg
1 Lean;;
(
(
elcctrodr* in other solvents at electolyte concentrations values should bc subtracted from the obscrvcd en?f of the cell retl/NEt,Pic/tcst E,,(Pleskov)t ~ 0.065
HMF”I,‘An
~ 0.06
MeOH/An McNOqiAn DMFJAn TM S/An DMSO,‘An PC/An H$/An HCONHJAn
- 0.039 - 0.063 0.005 i 0.101 - 0.03 I f 0.049 -0.041 + 0.003
Junction V
these
arc
E,,(calomel)$
EtOH/H*U HMPT/H,O MeOII/H,O McNO,iH,O DMFjH,6 TMS/H,O DMSO/H,O PC/H,0 An/H;0 HCONHJHlO
I
are An. acctonitrile. that
for the silver-acetonitrile
ref. electrode
EtOH/An
* Ahbrrviations lcne carbonate. t Ref 17; notr in ref. 16. : Rcf 16
Although interrelated. it is profitable to distinguish at least seven types of clearly defined ion-solvent interaction[I, 81. The relative contribution of these tn the total salvation energy of a univalent anion or cation, (ie 300-500 kJ/g ion in solvents of dielectric
(TATR
ca?~~el when combined
673
TMS,
slightly
tetramethylene
different
from
-0.030 V -0. IS2 -0.025 - 0.059 -0.172 ~ 0.223 -0.174 -0.135 - 0.093 ~ 0.078 sulphone; values
PC, propy-
published
hy
us
674
A. Dsmlor
:&-
-
-;--r;r:
;N-y=O
-
>r;ZC_S
:N-C=S
s
:L-,
-0:
--C--N:
Fig.
aprottr. solvents
-
:S
J. Pna~rn
6:
DMSO 3.90
Bul k(region 4)
&D I
DMF 3.90 SDMF 4.4 D
3. Resonance structures of dipolar aprotic and their dipole moments.
In pnnclple: AS+,= N,‘?AS)’
+ N,*(AS)‘CN~~(ASI~
solvents
const 25.-100) is shown below in parenthesis. The intcractions are: “Born-type” solvation (2 itO>,;): anion-solvent H-bonding (5 IO”,:,); hard--soft (5 20-4,); back bonding of 6” cations (5 10%): donor-acceptor or acid- base (< IO::,): structure making (~5”;~) and structure breaking (<5?“). People often forget that “Bol-x-type” salvation. as represented by the electrostatics of a highly charged sphcrc in a uniform diclcctric. can account fonr-more than SO%, of the tolal sol\:ltion energy (vacua to solvent) of an ion in a solvcnL of dielectric constant > 25[8]. However, for II.UJI.\/(V* ~f’iorrs herwrer7 solvents. of dielectric constant 2545. the Born term is fairly constant and changes in the other six Ion- solvent lntcractions become of grcatcr importance in determining AG,, ion. T-o illustrate, the free energy of solvatlon of silver ion (vacua to solvent) is -432 kJ/g ion in trifluoroethanol (‘I‘PE) and - 5 18kJ/g ion in hexamethylphosphoramide (HMPT)[3]. The free energy of transfer of Ag’ from TFE to HMPT is -X6 k.Ijg ion. In both solvents. the cation is solvatcd through an oxygen atom. although of very ditferent hasicity and the two solvents have virtually the same dielectric constant. of 27 28. A change of X6 k.1 is one of the largest fr-ee energies of transfer that we have observed. for a simple ion. and yet AG,,Ag+ represents only about I5Y,, of the total salvation cncrgy. AG,Ag+. Having acknowledged the importance of Born-typr salvation. I now note that free energies of transfer of I(&50 k.l/g ion. values frequently encountered in our work. can cause enormous changes in the chemistry of ions in different solutions. Thus the non-Born interactions are worthy of consideration. Some examples of such considerations follow.
This was lirst cmphasircd III 1962[38]. and is of fundamental importance in explaining the chemistry of many anions in dipolar aprotic solvents. It is illustrated by the free energy of transfer of acetate ion. Cl-, I- and ClO; from acetonitrile to methanol[l]. The two solvents have much the same dielectric constunt. hut CH,CN is a very much weaker hydrogen
Fig. 4. (a) Regions of solvent ordering and disordering ahnlit a cation (see text): (b) Salvation of thr liral kind for cation in wata (see text). bond donor than CH,OH. The anionic potential and thus the ability of the anions to nccrpt hydrogen bonds. decreases in the series OAc> Cl- > I- 1 ClO, It is not sul-prising that transfer of these anions from acetonitrile to methanol is strongly exergonic (ic meth‘anol is a more efl&tive solvent) in the order: OAc(-4OkJ/gion) > Cl-(-29) > I-(-12) > Clo,(+ l)Cl]-
Pearson’s HSAB concept[ 197 of favourable interactions of hard acids with hard bases and of soft acids with soft bases is a useful working concept, despite concern about its obvious superficiality. Related conccpts are those of class a and class h character of elements[20], and covalency[Zl] and mutual polarizability[X] but. for cxamplc, none arc as satisfactory as the HSAB principle in helping us to superficially understand the frrc energies of tranafcr of calions between dimethylformamide (DMF) and its sulfur analogue. dimethylformthioamide, SDMF[4]. DMF solvatcs cattons through its hard basic oxygen whereas SDMF solvates cations through its soft basic sulfur atom (Fig. 3). Thus DMF is a hard solvent, SDMF is a soft solvent. Followers of the HSAB prin-
Salvation ciple would claim that the hardness of a series of cations decreases in the order Li’ > K’ > Tl+ > to very soft Ag’. The free Ag+, from very hard Lit energy of transfer of these cations from hard DMF to soft SDMF changes from endergonic to exergonicL4].ieLi+(+64kJ);K+(+37kJ);Tl’ (-4kJ); Agf (-SlkJ). The HSAB explanation is that lithium cation has fidvourable hard cation-hard solver11 interactions with DMF but unfavourable hard cation-soft solvent interactions with SDMF, so AG,,Li+ is endergonic. Thallous cation on the other hand has unfavourahle soft cation-hard solvent interactions with DMF but favourablc soft cation-soft solvent intcractions with SMDF. so AG,,Tl+ is exergonic.
Singly charged d’* cations, ry Ag+, Cu+, Au+, are capable of back bonding their d electrons into a Tl* orbital of, for example, a nitrile group. They do not back bond for example to water. The interaction can be represented as CH,CgN: -+Ag*, and allows singly charged d’O cations to be much more strongly solvated by nitriles than would be expected from the solvation of less gifted cations (Ed Kf) by nitrlles. Thus AG,,K+ from water to acetonitrile is f9.S kJ/gion. but AG,,Ag’ is exergonic -22 kJ and AG,,Cu+ is -50 kJ. because these latter two cations, unlike K+. are capable of back bonding to acetonitrile[3].
These have been effectively popularized by the work of Victor GutmannlZZ] and I illustrate by the free energy of transfer of Kt between ethanol (CH,CH,OH) and lrlfluoroethanol (CF,CH,OH)[3]. Trifluoroethanol has a much less basic oxygen than ethanol, hecause of the electron-withdrawing effect of the Ck-, group t’s clcctron donation by CH, of ethanol. The two solvents have virtually the same dielectric constant of LU. 26 and the structure about oxygen is rather similar. As expected. AG,,K+ from TFE to ethanol is exergonic at - 19 kJ/gion, ic, K+ has a stronger interaction with the more electron rich oxygen of the basic ethanol. Dipole moment is not a factor. TFE has a greater dipole moment (6.8 D) than ethanol (5.5 D)[X], yet ethanol is the stronger solvator of K’.
Water is effectively polymeric and has a unique well-developed hydrogen-bonded structure of low entropy[23, 241. However. water has the ability to form an even more ordered “surface”? of even lower entropy. when certain “hydrophobic solutes”. rg many organics. neon. argon, and even “hydrophobic” large ions. ‘(I NBu,’ are added to water. This is called salvation of the second kind[2S]. Solvent-solvent interactions and the concept of ions as structure makers or structure brcakcrs m water are old concepts, which are sometimes forgotten. They have important consequences to the thermodynamics of hydration, especially in so Tar ah entropy changes are concernedll. 51. Acetonitrile, unlike water, has weak solvent-solvent interactions, it is not extensively ordered and is a solvent of relatively high entropy[Zb]. All Ions in acetomtnle and indeed in all dipolar aprotic solvents, tend to be nctt structure
of ions
675
makers, although ions of low ionic potential, kike NBu,’ and Rb’ are only weak structure makers in dlpolar aproticsl I, 51. The following are best explained in terms of structurc making. structure breaking interaction. There is a very large loss of entropy (A&NBui = - 175 ‘) when large hydrophobic NBud is transJk- ’ g ion ferred from acctonitrile to water[ I]. NBuz has little effect on the structure of acetonitrile and hence the enlropy of its acetonitrile solution. However, NBu,’ in water undergoes salvation of the second kind. where the water is rejected by NBuz and forms an ordcrcd surface of very low entropy about the large hydrophobic cation. Thus NRuz is a nett structure maker- in water and the free energy of transfer from water is very acetonitrile to endergonic (AG,,NBui = +33 kJ)[l]. because of entropic: considerations. is a very There large gain of entropy ‘) when large hydro(AS,“Rb+ = + 100 kJ ’ g ion philic Rb’ is transferred from acetomtrile to water[l]. Rb+. although large, has a higher ionic and so more strongly orientates potential than NBuz acetonitrile about itself. In water. Rb+ also weakly orients water about itself. ie there is salvation of the first kind which is sufticient to partially break up the structure of hulk water in the vicinity of the Rb+. The net rrsull is that Rb+ is a structure breaker in water and there is a substantial gain in AS,,Rh’ from acetonitrile to water. This leads to an exergonlc AG,,Rb+of --7 kJ/g mn[l]. Linetr~ ,free erwryy
relufionships
Attempts have been made to record various properties of solvents which can be used in lineal- plvta tu predict behaviour in solution. For example, Gutmann’s donor numbers[22] have proved very useful in understanding cation salvation. The donor number is an cnthalplc property for solvents in an inert diluent. A more fundamental property, if seeking relationships to predict free energies of ion-solvent interactions. is the free energy of transfer of potassium cation, and we have observed an acceptable linear relationship of the type AG,,M”+ = mAG,,K+. which relate free energies of transfer of cations to the hehaviour of the model potassium cationC3.41. Deviations from linearity. of AG,,Ag+ in MeCN and SDMF, or in waterr4J. denote “abnormal” ry nonof G,,NBu,l Born) ion-solvent interactions. like back bonding. covalency and solvation of the second kind. The sensitivity, m, to solvent transfer of a cation M” _ in this relationship, relative to rn = 1 for K+ is of course grcatcst for cations of the greatest ionic Table 4. Sensitivity of AG,.M”+ to bolvenl transfer. Values of m in the expression ACi,,M”’ = mACi,,K+ * m” * Znz+ Cd* + Ba’ II’ Ll+
+
* Data
m
M”+
m
4.6 3.7 3.7 3.1 1.7
Na+ Ag+ K+ CS+ Ph,As+
1.3 1.3 1.0 0.7 0.3
from
refs. 4 and 17.
A. J. PARKER
676
potential, cg Zn’+, ionic potential, accorded in Table THERMODYNAMICS
and is least for eg Ph,As+[4]. 4. OF
TRANSFER
OF
cations of lowest Sensitivities are
IONS
TO
WATER
now examine AG,, ion in more d&ail by examining the enthalpy and entropy of transfer, as they contribute 10 AG,,ion = AH&n - TAS,,lon. Enthalpies and entropies of transfer to water from less complex solvents tells us a great deal about salvation in water. Some typical vaIues are in Table 5. Table 5 illustrates some frequently observed general points about transfer of ions from non-aqueous solvents to water. Thus: (1) Water is a very poor solvent enthalpywise for most of those cations whose solvation is of the first kindll, 2,5]. This is because a large number of waterwater hydrogen bonds arc broken (loss of enthalpy) when such cations are transferred to water. Transfer from dipolar aprotic solvent to water of monovalent cations is always, and of divalent cations is usually. an andother-mic process. (2) Water is an cxccllent solvent entropywise for all ions whose salvation is of the first kind[l. 51. Ions tend to break up the low-entropy ordered structure of water so there is always a large gain of entropy on transfer of all but hydrophobic ions from nonaqueous solvents to water. (3) Enthalples of transfer of ions to water vary considerably, accordmg to the type of ion and the solvent from which transfer was ma&. Thus chloride ion has an exnthermic transfer from DMF to water because of hydrogen bonding between water and chloride ion, but H-bonding is negligible when CIO, is transferred, so the “usual” endothermic transfer to water, common for cations, is observed. As noted, silver cation has a back bonding interaction with acetonitrile. this is reflected solely in the enthalpy, so All,,Ag+. for transfer from acetonitrile to water. is strongly endothermic. (4) Despite very large variations in AH,,ion, values of -TAS,,ion are remarkably constant through a series of ions[l, 51. Thus in Table 5, entropies vary enthalpics of transfer by only 25 kJ g ion- I, whereas vary by X0 kJ g ion- ’ In particular, - TAS,,K+ , and -TAS,,Ag+ from acctonitrile to water arc virtually the same, despite very different enthalpies of transfer. The near equality of -TAS,,Na’ and -TAS,,ClI
Table
5. Enthalpics
(DMF-+ H,O) despite very different values of AH,,ion 1s also striking. It seems likely that once the translational entropy of a certain number of solvent molecules is lost hy restncting them in the salvation sphere about the ion. then no matter how much stronger another interaclion, thcrc is no substantially greater loss of entropy, provided that the number of molecules so restricted by either interactlon is not increased. One can imagine that a similar number of molecules of acetonitrile (rg 6) are in the salvation shells of K ’ and Ag ‘, and it is these whose translation is restricted. Since translational entropy is the major factor, the entropy change need be no greater just because Ag+ binds acetonitrilc more strongly (in an enthalpic sense) than does K+. (5) The effect of transferring hydrophobic cations from non-aqueous solvents to water is illustrated by the final two examples in Table 5. In water. salvation of NBu; and of Ph,As+ is of the second kind[25]. As noted, the formation of a hydrogen bonded surface of water about hydrophobic ions Involves a Iarge loss of entropy, but this is in fact compensated for by the enthalpic advantage of forming strong hydrogen bonds in the “surface of water”. Thus enthalpies of transfer of hydrophobic ions to water arc often cxothermic or at worst only weakly endothermic. hllt -TAS,, ion is usually very positive, ie thcrc is a large loss of entropy.
It is helpful to our understanding of salvation if we construct models for the various regions of solvent in the vicinity of ions[l, 51. Such models for cations are shown diagrammatically in Fig. 4. For cations in water, we distinguish four regions, firstly the primary salvation shell[l] of ion-centred. ordered water: surrounded by a region 2 of ordered water, hydrogen bonded to the acidic water in region 1. and a region 3 of unstructured water between region 1 and the structured bulk water, the latter being rcglon 4. The number of molecules in each r-egion is N,, NZ, N, and N4 respectively. The population of these regions, N, etc.. should pay due regard to the principles and stereochemistry of ion-ligand coordination. the dimensions nf ion and solvent molecules, packing theory and the requirements for hydrogen bonding by water, eg linearity. Thus it is unreasonable on sleric considerations to
snd entropies of transfix assllmptlun)*
lo II (a) Acetonitrilc to water A&!+ K+ Zn” (b) DMF to water Na’ c’1r CIO, Zn2 + NBu; Ph * Data from refs I-5
or
ions
to
water
(TATR
- 298 AS,,ion
AII,,ion +53kJgiun-’ f23 -20
-31 -33 -49
+33kk.lgion-’ -21 f23 ~-63 -15 f2O
-22.5 -25 -23.5 ~33 f43.5 + 18
kJ L: io11-
’
kJ 6 ion-’
Salvation
expect that more than 6 water molecules (4 is more likely) could closely fit about a small lithium or zinc cation in a primary salvation sphere (region 1). If region 2 consists of water hydrogen-bonded to water in region 1. then if there are N, waters in region 1. there cannol be more than 2N1 waters in region 2. This. of course, IS because each water about a cation in region 1 has only two acidic hydrogen5 available as H-bond donors[l]. Construction of a model for hydrated K’ with N, = 6 and N1 : 12 water molecules assuming linear hydrogen bonds between water in region 1 and region 2. shows that there is much open space in region 2[27]. It is expected that the space would be filled. depending on the size of the cation, by between 10 and 20 disordered waters of region 3. which does not have a well defined boundary with region 2. Region 2 exists because water molecules in region 1 about cations of high ionic potential, are quite acidic and donate hydrogen bonds to water. It is Interesting to speculate[l] whether a [region 2 exists for cations in dipolar aprotic solvents, like DMSO. DMF and HMPT. where the primary salvation shell is unable to donate hydrogen bonds to other solvent molecules. In these solvents, the positive charge of the cation may bc shielded from the bulk solvent by methyl groups, as in II and III. We expect that.
0
o=s
,C”,
@
‘-.CH,
(I)
..
O=C_NICH,
A
(II)
----CH,
(III)
for any cation, region 2 is much less extensive in dipolar aprotic solvents than in water, so it follows that unstructured region 3, which depends in part on the size of region 2, is less extensive in dipolar aprotic than in water. As noted, the very high degree of structure in bulk water (region 4) is unique to water. and for solvents like acetonitrile. region 4 is only poorly dcvcloped structurally. These concepts of electrolyte solutions which have ion and solvent centred regions of solvent. as well as unstructured regions, are not new[23--251. I note them because they are beautifully illustrated by entropies of transfer of single ions[l. 51. Thus in water regions 1, 2 and 4 are of much lower entropy than region 3. but in dipolar aprotics, regions I and 2 are of much lower entropy than region 4. which is ot slightly lower entropy than region 3. In rather loose terms. solvent acctonitrile is a “higher entropy liquid” than is solvent water.
In order to understand entropies better, we have developed[lS] the idea of entropy of transfer of an ion from an ideal unimolar solution to the corresponding ummolar real solution (AS,,1 + R). The idea is based in part on the TATS assumption and details of the procedure are given elsewhere[15]. This entropy of transfer is given by: A&,.( I where
S,
is
R) =
AS,
Lhc cntrupy
-
12.6 of
-
ir, from
crystal
677
to solution, (TATB assumption), p is the density of the solvent of molecular weight MW. The ideal soIutlon is one in which one mole of single ions in a crystal has melted and been dispersed through one litre of the relevant real solvent, without interfering with solvent-solvent interactions and without introducing ion-ion or ion-solvent interactions. The entropy change for this process (12.6 + RIn 1000p/MW) is compared with the entropy change for the real process of dissolving one mole of ions in real solvent (AS,) to give A&,(1 R) which is thus the sum of entropy changes prodnced by- the ion in gcncrating regions 1. 2 and 3 liom region 4. AS,..(I+
R) = N,AS(4-
1) + N>AS(4-2) +
N,AS(4+
3).
(1)
Some values of AS,,{1 R) for single ions are in Table 6[5]. In Table 6. the solvents are listed as increasing in solvent structure (ir> in region 4) from HMPT. with weakly developed structure. to water. with highly developed structure. There is an enormous loss of entropy on transferrmg catlons from idcal HMPT to real HMPTLS]. The loss is much greater for Cd’+ than for K+. no doubt bccau~t. of the much greater ionic potential UT Cd’+. The loss of entropy is in forming a structured primary salvation shell (region 1) from region 4 of the weakly structurrd solvent, HMPT. In olher words. N,AS(4+ I) in equation (1) is strongly negative, and is the only significant term on the right of equation (1 ). The number N, of HMPT molecules in region 2 is expected to be small because of shieIding of the positive charge by the bulky solvent in region 1. so N,AS(4+ 2) is small. Since region 4 is only weakly structured. the term (N,AS(4+ 3) is also of little co,,sequence in determining the entropy of transfer of cations from ideal to real HMPT. The loss of entropy on transferring cations from idcal DMSO to real DMSO solution (Table 6) is also large. but is considerably less than the loss for HMPT[S]. This is explained by the likelihood that DMSU solvent has a more dcvclopcd structure m region 4 than has HMPT, ic DMSO is a “lower entropy solvent” than HMPT. Thus the term contributing a gain of entropy, ie N,AS(4+ 3) to equation (I), is more positive for DMSO than for HMPT, and if N, + NZ for DMSO is similar to HMPT. the terms N,AS(41) + N,AS(42). are less negative for DMSO than fol- HMPT. The loss of entropy shown in Table 6 on transferring cations from ideal water to real water solution is very much less than the loss for the corresponding transfer in all the dipolar aprotlc solvents. Indeed for K’. there is very little loss of entropy, ideal to real water. This is because bulk water in region 4 is in a highly structured state of polymeric clusters and Table 6. Entropies of transfer of ions from corresponding real snlvents AS,,(IR) JK
Ion g’
Rln(1000$>,‘MW)
solullon.
of ions
HMPT /
* Data
to
DMF
DMSO
H,O
- 100 _ 284
-87 -266
-65 -224
-I -178
rrll 5.
the
’ g inn ‘*
CH ,CN
- 124 - 40x from
l&al
A. J. PARKER
67X
thus has low entropy. Thus AS(4 I ) + AS(4 - 2) is only moderately negative and AS(4-+ 3). the entropy gain for creation of unstructured water in region 3. is strongly positive. That there is a significant loss of entropy for Cd’+ in water. ie A&,(1 - R) Cd’+ very negative, suggests that the hydrogen-bonded secondary hydration shell (region 2) is extensive (N2 large) about this divalent cation in water. The entropies of transfer of cations from ideal to real solutions become more and more negative as the Ionic potential of the cation increases. and thus the population (N, + N,) of regions 1 and 2 increases. This is shown in Table 7 for cations of increasing Ionic potential in both DMF and water. As in Table 6, the loss of entropy is much grcatcr for ions in the less structured solvent. DMF. than in the highly structured water. Large rubidium cation is seen to be a net structure breaker of water, ie AS,,(lR) Rb’ is positive[l, 51. Cations are always net structure makers in dlpolar aprotic solvents, but cithcr a net breaking or a making is possible in water, because of the fine balance between regions 1 + 2 and 3.
The least number of solvent molecules which have lost their translational entropy in the primary plus secondary salvation shells (regions 1 + 2) about cations can be estimated from h&,(1R) and the entropy of free&lg of the pure solvent. AS,. ,e
A&,(1-R) ~___ AS,
N,+NL> zzz
N,AS(4-+ ~ ~~~
1) + N,A%4+2)
+ N,AS(4+
3)
AS,
The assumption is made that AS., 2 AS(4+ I) = AS(4--*2), ie that entropy lost when pure solvent is fro7en. is more or as much as could be lost in “freeLing” solvent in the primary and secondary salvation shells about a cation. This recognizes loss of translational entropy as a major factor in both processes. Further. the effect on entropy of forming I-egion 3. N,AS(4+ 3). which tends to make A&,(1+ R) less negative and 1s related to deviationa from Trouton’s constant[l], is not allowed for in this calcularion of nlininmm N, + N,. N,. for example. can bc up to 20 if region 2 is fully developed in water. Thus the solvaticrn number. N, + N,. is a minimum on two counts. As noted, N,AS(43) is a quite substantial term for many cations in water. so that the estimated rnininru,?l salvation numbers, for cations in water, arc probably much less than the real salvation numbers. Table 7. Entropies of transfer of ions from ideal to real solvents. Effect of mcrcaslng 10nlc potential of cations. AS,,(I-HI JK~‘~:I~II~‘* Rh+ K’ Increasing
* Data
from
[.i Na Ap’ Ionic potential
I-cf.
I
and 5.
’
RaL’
Cd”
Zn”’
Table 8. Muknal salvation numbers of cations in water (AS,- = -22 JK ’ mole I) and DMF (ASI -37)* N, + NZ > [AS,,(lR)]/AS, Hz0 C-s+ K’ Li‘ &I’+ CdL ’ ZlI*+ * Data
>O >o >3 >5
z-8 >9.5
from
DMF -,2 2 2.5 2 3.5 ,8 Z-7 2X.5
increaslng ionic potential I
ref. 5.
Minimum salvation numbers for cations in water and DMF are shown in Table 8. As expected, as the ionic potential of the cation increases, so the minimal salvation number increases in both solvents. An important observation from Table 8 is that there is a secondary salvation shell (region 2) about divnlcnt cations like Cd’+ and Zn’+. This is as true for DMF as for water and follows from the calculated minimal salvation numbers of >6 for these small ions in both solvents. Since It is not possible to fit more than six (and possibly only 4) solvent molecules in the primary salvation shell about these small ions of high ionic potential, the extra structured solvent must be in region 2. This result[5] was surprising for cations in DMF. We had expected[l] that there would be effective insulation of the charge on Cd’+ and Zn2+ by bulky DMF, as in III. and thus little tendency for a second layer of structured DMF to form about the solvated cation. For reasons already given, the minimal salvation number of >9..5 water molecules structured around Zn*+ is expected to be much less than the true solvation number, because models show that N, is between 10 and 20 when N2 is &12. However, Ihe minimal values of z 8.5 DMF molecules about Znzf in less structured DMF is probably only a little less than the true salvation number. Thus we expect that there are significantly more water than DMF molecules in the respective structured salvation shells about Cd’+ and Zn2 + than is indicated by Table 8. The entropy losses on freezing solvents, ie change region 4 to solld, arc related through Ioss of translational entropy to AS(4 -+ 1) and Aq4-+ 2) and are: -22 JK-’ mol-’ for Il,O: -36 for acetonitrile: -37 for DMF; - 48 for DMSO and -60 for HMPT[5]. Much more entropy is lost when poorly structured HMPT. rather than highly structured water. is frozen This correlates with the enormous losses of entropy when cations are transferred from ideal HMPT lo real HMPT solution (Table 6). Minimal salvation numbers for solvents translationally bound to zinc(l1) cation are b-9.5 in water: =_ 10 in acetonitrile: >8.5 in DMF: >5 in DMSO: z=-5.5 in HMPT[S]. The development of models for the salvation shells about ions is at an early stage but Professor Watts is continuing our work in this area[27]. To summarize, it seems likely that many cations in water have a primary solvalion shell of ar Irrrsr 4-6 water molecules. divalent cations have ~lt Ic~?.st a secondary solvation shell. of nor store rhan 12 waters. which are hydrogen-bonded to the primary shell. There are a
Solvatian
number (up to 20) of unstructured non-polymeric water molecules (region 3) filling space in the secondary salvation shell (region 2), the whole blending into region 4. the highly structured polymeric bulk water. The picture is simpler for cations in dipolar aprotic solvents. Thcrc is a well developed primary salvation shell for most cations and a few cations have a sparsely populated secondary solvaliun shelf. However, the distinction between bulk solvent in region 4 and unstructured solvent in region 3 is less well defined than in water. because the bulk solvent is at best of-ten only weakly structured. Perhaps the most interesting conclusion from our work on entropies of transfer is confirmation that the unique position of water as a good solvent for electrolytes[23] is due to water-s highly developed structure, ic, to the vel-y favout-able entropy changes (relative to other solvents) accompanying salvation of the first kind. when ions are introduced into water. Conversely. the reluctance of water to dissolve significant amounts of uncharged non-polar solutes 1s due to solvation of the second kind. it, to a very unfavourable loss of entropy, accompanymg the formation of a highly structured water surface about hydrophobic solutes
of ions
D. A. Owensby and A. J. Parker. J. 5. G. R. Hedwig. .4m. chra,. so<. 97, 388 (1975). J. p/r>,.\. 6. B. G. Cox. A. J. Parker and W. E. Waghor-nc. C‘hrm. 78. 1731 (1974). Calculated room free energies of transfer 7. A. J. Parker. in ref. I nt- unpublished work. 8. A. J. Parher. Chrm. RPL.. 69, 1 (1969). 9. A. J. Parker. W. E. Waghorne. D. E. Giles. J. H. Sharp. R. Alexander and U. M. MUX. U. S. t’atent 3.X65.744 (1975):
10 11. 12. 13. 14.
I 5. 16. 17. 18. 19. 20. 21
REFKRKNC‘ES 1. B. G.
Cox.
G.
Watts.
Amt.
3.
2. G. R. Hedwig 6589 (1974). 3. D. A. Owcnsby. c/ten,. Sot 96, 4 R Alrxander. E. Waghorne.
R. Hedwig. A. J. Parker and D. W. Chrm. 27. 477 (1974). and A. J. Parker, J. Am. churn. Sot. 96. A. J. Parker and J. W. Diggle. J. Am. 2682 (1974). D A Owennhy. A. _I. Parker and W. Arrt. .J. Chrrn. 27, 933 (1974).
679
27. 37
77.
Brltiah
Patent
1381666
(1975).
W. F. Waghorne. Ph.D. Thesis. Australian National Ilniversity, Canberra. 1973. D. M. Muir. A. J. Parker. J. H. Sharp and W. E. Waghornc. H\lir-n,nutall~r~~,’ I, 61 (1975). A. J. Parker. Scurc/~ 4, 426 (1973). A. J. Parker. f’roc. K ,4x$(. c/~i,m. Invr. 163, (1972). B. G. Cux and A. .I. Parker. J. .4/u dwim Sot. 95. 402 (1973). R. G. C-ox and A. J. Parker. ./. .¶f,z. L./IPIII. Sot. 95, 687Y (1973). J. W. Dig& and A. J. Parker. .4usr. .1. Chrvi. 27. 1617 (lY74). D A. Owznsby. Cnmpnrntive Sol\ntion in Various Media. Ph.D. Thesis. Australian Nat~nnnl Llnlversity. Canberra. 1975. A. J. Parhcr. Q. Rrr. 163, (1962). R. G. Pearson. J. .4,tr. clte,?~. Svc. 85, 3533 (1963). S. Ahrland. J. Chatt and N. Davies. Q, &I-. 12, 265 (lY58). R. S Drago and B B. Waylund, .J 4191. clrunl. SOL.. X7, 3571 (1965). LJ Mayer and V. Ciutmann. St~.~,~tidl.<,un,l Brr~xiirig Vol. 12. Springer-Verlag. Berlin. lY72.
D. W. Watts.
Personal
communication.