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1812 Inorganic Chemistry, Vol. 18 , No. 7, 1979 Paul Hemmes and J. J . McGarveyContribution from th e Departments of Chemistry, Rutgers University, Newark, New Jersey 07 102,and Queen's University of Belfast, Belfast BT9 SAG, Northern Ireland

Determination of the Ratio of Contact to Solvent-Separated Ion Pairs in Z nS 04 inMethanol via High-Field Conductometric MeasurementsPAUL HEMMES* and J. J . McGARVEYReceived October 25, 1978

High-field conductometric measurements of the ratio of contact to solvent-separated ion pairs have been made on the systemZnS04 n methanol ( K = 5.8 X lo4) . The method used has quite general applicability for such determination and is oneof the few such generally useful methods. The method is based on the dynamic response of th e system to a short high-fieldpulse. Under most conditions th e ion-pair interconversion cannot take place during the pulse and then the electrolyte behavesas if it contained only a free ion outer-sphere complex equilibrium.Th e general Eigen mechanism' for metal ion substitutionreactions has been very successful in treating kinetic datainvolving numer ous ions and diverse types of ligands. In thismechanism we have (for a symmetrical electrolyte)

kl k2 k3k i k-2 k-3

M?I++ Xn--- M,,X __ M ,Xe Xwhere M ,,X is a doubly solvent-separated ion pair (anion andcation each retaining a solvation shell), M,X is a solvent-separated ion pair, and M X is the contact pair. In the usualcase, the final process refers to the desolvation of the cation .Th e ra te constant k 3 s on the order of magn itude of the rat eof solvent exchange which for m any systems leads to a re-laxation time for the system on the order of s or more.In t he analysis of the da ta, th e second step is often omittedand the f irs t s tep is t rea ted as a fast preequilibrium. Th eequilibrium constant for this step is then evaluated by meansof the Fuoss equation.* For a two-step mechanism th e slowerrelaxation time is given by

T,-' = k @ + k,@ = O / ( O + K- ' )6 = M n + + x n -with a superscript bar indicating an equilibrium concentration.k f an d k, are the forw ard and reverse rate constants for ion-pairinterconversion. Clearly the value of k f obtained will beaffected by errors in th e calculations of K-'. In addition, thevalidity of the neglect of the anion desolvation process issuspect sin ce discrete anion desolvation processes have beenf o u n d i n n o n a q u e ~ u s ~ , ~nd aqueous solution^.^ I t wastherefore of considerable interest to obtain an experimentalmethod to check the validity of this procedure by directmeasurement of the outer-sphere complex formation consta nt.The method employed is based on the application of highelectric field pulses to the electrolyte and observation of theconductometric change observed due to the second Wien

effect.6 This effect is the enhan ced dissociation of weakelectrolytes in high fields.Theorythe Eigen scheme asIf we again neglect anion desolvation momentarily an d write

t h e fast relaxation time will be given by the expression71-l = klO + k-1 + k2 + k-2

If we limit discussion only to those ions whose rate of solventexchange (o r more objectively, the rat e of ligand substitution)*To whom correspondence should be addressed a t Rutgers University.

is relatively ~ lo w -l o -~ s or longer-then we can neglect k zand k- 2 compared to the first terms. This is due to the factthat k l is almost always diffusion controlled or nearly so an dthus k l = 10'O M-' SKI.or a w eak electrolyte with a totalassociation constant, KT, very large we haveKT = Ki(1 + K2)

where K 1 ( 2 )s th e association constant for t he first (second)step and 6' = ~ ( C T / K T ) ' / 'it h cThe total concentration ofelectrolyte. Then

71-l = ~ ~ , ( C T / K T ) ' / ~k-1or

71-1= ~ , [ ~ ( C T / K T ) ' / 'K 1- ' ] (1)Suppose KT and K 1 are each on the order of lo4 M-' whileCTis about M. Then 71 is about 2.5 X lO-'s. Supposewe apply a pulse of high voltage to this solution. Acco rdingto the theory of the second Wien effect there will be a relativechange in conductance

with E the app lied field in kV an d a the degree of dissociationat zero field. If the field is applied as a step function, th econductance will lag behind the field and will reach itsequilibrium value after roughly five relaxation times. For thesystem we have described the re are two relaxation tim es, onea t 2.5 X s and the other 711 > lo 4 s. If the field is appliedas a pulse with a pulse width 7p chosen such that 57 ' < 7p

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Contact to Solvent-Separated Ion Pairs in ZnS0 4the ratio of solvent-separated to contact ion pairs.In principle we have an int ernal consistency check on th eresults. If T can be measured as a function of CT,hen a plot7-l vs. 0 gives k l as slope and Kl/kl as intercept. If the lattercan be evaluated accurately, we have an independent checkon the value of Kl . Experimentally this was not possible inour case due to severe electrical ringing which preventedmeasurement of 7.As for th e influence of an anion desolvation step, we mustconsider the fact t hat all such processes to da te have shownrelaxation time in the ultras onic region, th at is with T < 10 01118 Thus anion desolvation will probably be fast comparedto ion-pair formation and the relaxation time observed in themicrosecond region will be given by the expression

7-l = k10+ (k - 1) / (1 + KAD)where KAD is the ratio of desolvated anion pairs to solvatedones. Th e ratio of slope to intercept will be

K* = KI(1 + KAD)Since both anion desolvation an d ion pairing will equilibratein the field pulse, the value of K obtained from the relativechang e in conductance will correspond to K*. It is importantto note that if K A D >> 1 the use of the Fuoss equation toevaluate stopped-flow or Joule heating 7"-jump kinetic resultswill lead to anomalously large rate constants for ligandsubstitution since K* >> KFuoss.Hen ce the use of the pulsedfield technique to directly measure K* will be very useful inany case of anomalously fast substitution kinetics.Experimental Section

The system studied was ZnSOd in methanol. The instrument usedwas a conductometric detection E-jump which has been previouslydescrib ed in detail.* Briefly it consisted of two cells, samp le andreference, which have adjus table electrode spacing. Th e referencecell contains a strong electrolyte to cancel first Wien effects. Th ereferences used were N aBP hp in methanol or in water-ethylene glycolmixtu res. Th e latter is especially convenient for matching the lowsample conductivities with a reasonable concentration of electrolyteso that adsorption is not a problem as occu rs with IO-' M concentration.The reference cell electrode spacing is adjusted to give an exactlymatch ed resistance a t zero field. It is not possible to match bothzero-field conductance and capacitance. Th e mismatch of the lattergave rise to serious ringing during the first microsecond of the pulsewhich precluded measurements of the relaxation time. However, sincethe pulse (obtained by a cab le discharge) was 9 gs long, the limitingvalue of the conductance change was easily determined. The valueof K was independent of reference solution used. Th e range of fieldsused were from 8 to 25 kV/cm. No variation of K with field wasobserved outside experimen tal errors. Th e value of KTwas determinedby using conventional conduc tance methods. Hyd rated zinc sulfate

Inorganic Chemistry, Vol. 18 , No. 7, 1979 1813Table I

(1 - 4 1ANA, E , kV/cm (2 -a) aC = 1.6 x12.0 28 0.164 0.808.14 24 0.130 0.855.7 20 0.109 0.86

16.0 25 0.24 0.69

M ZnSO, in M e O H , E = 32.63

c = 5.0 x 10-4was dissolved in anhydrous methanol for all measureme nts. Th econcentrations used were from 0.5 to 1.0X M . Added waterin small amounts had no noticeable effects.Results and DiscussionData ar e shown in Table I. The mean value of K 1obtainedfrom high-field methods was (1.3 f .2) X l o 3 M-l. T heconventional low-field cond uctan ce value gave 7.5 X lo 6 M-l.Th e ratio of solvent-separated to contact pairs was therefore5.8 X lo3. This result should be com pared to the value of KFUwfor a 2:2 electrolyt e obtain ed by Lovas et al.9 which is 980 M-Iusing a size'parameter of 1.35 nm estimated from hydro-dyna mic radii. Th e precision of the results is not very highsince changes in conductance were obtained by measurementsof voltage changes from oscilloscope photograph s. Th e ac-curacy of the results suffers from the fact that ZnS04. nmethanol contains some triple ions (Le., Zn(S04)22-)whichcontribute to the observed conductance leading th erefore toerrors in A A l h . However, the population of such triple ionsis very small and the concentration independence of K showsthat the effect of these species is negligible.

Acknowledgment. The authors would like to thank theScientific Affairs Office of the North Atlantic Treaty Or-ganization for a travel gran t which mad e this work possible.P.H. wishes to thank the U S . Department of Energy forsupport under Grant N o. ER-78-S-02-494 5 during the finalstages of this project.References and Notes

Registry No . ZnSO,,, 7733-02-0.

(1) M. Eigen and K. T amm, Z . Elektrochem., 66, 93 (1962).(2) R. M. Fuoss, J . Am. Chem. SOC.,0, 5059 (1958).(3) H. C. Wang and P. Hemmes, J . Am. Chem. SOC., 5, 5115 (1973).(4 ) S. Petrucci and M . Battistini, J . Phys. Chem., 71, 1181 (1967).( 5 ) P. Hemmes, K. Sherr, D. Saar, S.Nishikawa, and F. Jordan, manuscriptin oreoaration(6) M.=