THESOLVATION OF CHROMICM(III) ION
Oct. 5 , 1964
isotope effect in the autoprotolysis constant of water (KH,~,IKD,o= 6.5"). Conclusions T h e similarity of Pd(I1) to Pt(I1) which is seen in the discussion above implies t h a t the mechanism of Pd(I1) substitution reactions is the same as for P t ( I I ) , a t least in the gross features. Edwards and PearsonZ0 have discussed a model for nucleophilic reactivities in terms of the basicity and polarizability of the entering nucleophile. Analysis of the data for Pt(I1) has led to the observation t h a t the dominant feature is polarizability. For Pd(I1) the increasing rates of substitution H 2 0 < C1- < Br- < I- < SCN- suggest that polarizability is also the important factor in determining nucleophilic reactivity. For Pt(dien)Br+ the relative reactivities are given as 1 : 2 X lo3:1 X 104for H 2 0 , C1-, and Br-. For Pd(acac)2, the relative reactivities are 1 : l . sx 102:4 X 102. For both Pt(I1) and P d ( I I ) , hydroxide ion is a poor nucleophile. I t is interesting to compare the data for the relative trans effect of C1- and Br- in Pt(I1) to that estimated for Pd(I1) in this work. For P t ( I I ) , the relative trans effect of Br- vs. C1- shows a threefold increase in the rate of trans substitution.?' For Pd(acac)X2 the relative trans effect of Br- v s . C1- is estimated to be 10: 1. (19) R. W. Kingerley and V. K. La M e r , J . A m . Chem. Soc., 6 3 , 3256 (1941). (20) J . 0. Edwards and R. G. Pearson, i b i d . , 8 4 , 16 (1962). (21) 0. E. Zvyagintsev and E . F. Karandasheva, Dokl. A k a d . N a u k S S S R , 101, 93 (1955).
[CONTRIBUTIOK FROM
THE
3989
This larger ratio is somewhat surprising. Earlier, very fragmentary evidence? suggested that while a trans effect existed for palladium(II), it was of less importance than in the case of platinum(I1). The data of Table I and particularly Table 11, where lower concentrations of hydrogen ion could be used, show t h a t the rate of dissociation of Pd(acac)2 goes to zero as [Hf] goes t o zero. Table IV shows also that the rate goes to zero as [OH-] goes t o zero. Thus the dissociation of the intermediate I' Pd(acac)(acac')OHs
+ HzO +
+ acac-
(15)
Pd(acac)(OH2)2
has a negligible rate compared to the reclosing of the chelate ring governed by k-1. I t is precisely this ratio of the rate of closing the ring compared to dissociation which creates the extra stability of a chelate ligand compared to a unidentate ligand.** For other bidentate chelates such as ethylenediamine and glycine, this ratio is about 20-30.23 The correspoqding ratio for the anion of acetylacetone must be greater than 100. Consequently, a very large chelate effect exists. Acknowledgment.-This work was supported in part by the U. S. Atomic Energy Commission under Contract At(ll-l)-1087. The authors are indebted to Professor F. Basolo and Mr. John Moore for valuable aid. (22) See ref. 2a, p. 18, for a discussion of t h e chelate effect, (23) A. K. S. Ahmed and R. G. Wilkins, J . Chem. SOL., 2901 ( l 9 6 0 ) , G. G. H a m m e s and J. I. Steinfeld, J . A m . Chem. SOL.,8 4 , 4639 (1962).
DEPARTMENTS OF CHEMISTRY OF THE UNIVERSITY OF WISCONSIN, MADISON,WISCONSIN, AND UNIVERSITY O F COLORADO, BOULDER, COLORADO]
THE
The Solvation of Chromium(II1) Ion in Acidic Water-Methanol Mixed Solvents1j2 BY
JERROLD
c. J A Y N E
AND
EDWARD L. K I N G 3
RECEIVED APRIL20, 1964 T h e low, rate of exchange of solvent molecules between the first coordination shell of solvated chromium( 111) ion and the solvent allows evaluation of f i , the average number of methanol molecules bound per chromium(II1) ion, as a function of solvent composition in acidic water-methanol solutions. The data indicate t h a t with respect to first shell coordination chromium(II1) ion discriminates in favor of water over methanol, A t 60", fi ranges from 0.17 a t Z X ~ O= H 0.155 t o 3.60 at Z M ~ O=H 0.98. ( T h e mole fraction of methanol calculated of R a t 30" are only very slightly lower. An without account being taken of solute species is Z Y ~ O H .\-slues ) independent type of experiment allowed evaluation of the fraction of chromium( 111) present as hexaaquochromium( 111) ion. This quantity evaluated in solvents as rich i n methanol as Z x e o ~= 0.85 is consistent with the ii data. Equilibrium constants for the stepwise replacement of water by methanol in Cr(OH2)8-j ( O H l ~ l e ) ~ have 3 + been calculated from the R data.
This paper describes experiments on the inner-sphere solvation of chromium(II1) ion in the mixed solvent, water-methanol. The success of these experiments depends upon the low rate of exchange of solvent molecules between the first coordination shell of solvated chromium(II1) ion and the solvent, analogous to the low rate of exchange of water molecules between the first coordination shell of hydrated chromium(1II) ion and solvent water in aqueous solution.4 Two types of (1) Taken from t h e P h . D . thesis of Jerrold C. J a y n e , University of Wisconsin, 1963. Presented a t t h e Solvation Symposium sponsored by t h e Chemical Institute of Canada a t Calgary, Alberta, August 2 9 , 1968. (2) This work was supported in p a r t hy t h e Research Committee of t h e Graduate School, University o f Wisconsin t h e United States Atomic Energy Commission (Contract A T - f l l - 1 ) - I 1 6 8 ( U . of Wisconsin)), and t h e S a t i o n a l Science Foundation (Grant GP-680 iU of Colorado)). (3) Author t o whom inquiries should be addressed, Department of Chemist r y , University of Colorado.
experiments were performed. The average number of methanol molecules bound per chromium(II1) ion, f i , was evaluated after using an ion-exchange procedure to separate chromium(II1) ion with its methanolcontaining coordination shell from the parent solvent. An ion-exchange procedure was used also in the second type of experiment to separate hexaaquochromium(II1) ion from the mixture of aquomethanol-chromiutn(II1) species present at equilibriuni in solutions in the mixed solvents With an isotopic dilution procedure establishing the extent of recovery of hexaaquochromium(111) ion, the fraction of chromium(II1) present as hexaaquochroniiurn(II1) ion, ao, was accessible. The relationships of these two functions fz and a0 to the concentrations of species Cr(OH2)6--3 (OHhle)j3+ (4) J P H u n t and H Tauhe, J
Chem. P h y s . , 19, 602 (1951)
3990
JERROLD
c. JAYNE
AND
are
a0 =
[Cr(OHd& 1 B [Cr(OH2)6-j(OHMe)j3+]
+ MeOH
=
(2)
+
Cr(OH?)s-,(OHMe),3-7 H 2 0
withj
=
I,2 , . . . . Experimental
Reagents .-.Ill solutions were prepared using reagent grade methanol and doubly-distilled water, the second distillation being from alkaline permanganate solution using a Barnstead still. The water content of reagent grade methanol was determined from measurement of its density. Chromiuni(II1) perchlorate was prepared from reagent grade potassium dichromate by the reaction of hydrogen peroxide and chromiutnjl'l) in pefchloric acid solution. Chromium(II1) perchlorate (Cr(ClO,),~SH,O) was crystallized from the reaction solution and then recrystallized acid solution. In this procedure, three times from 1 &'perchloric potassium perchlorate was removed almost completely. From the light absorption in the region of 230 nip, the stock solutions of chromium( 111) perchlorate were judged t o be essentially free of dimeric species.j Chromium-51 was obtained in the form of chromiurn(II1) chloride in hydrochloric acid from the Oak Ridge Sational Laboratory. Ion-eschange procedures involved use of Dowex-SOW-IC-12 200-100 mesh cation-exchange resin ( 5 . T . Baker): which was treated before use by a sequence of reagents, hydrochloric acid, sodium citrate, hydrochloric acid, sodium hydroxide, hydrochloric acid, and perchloric acid.6 Analytical Procedures.--halytical procedures involved use of primary standard potassium dichromate, reagent grade sodium hydroside, cerium( I\?) solutions in sulfuric acid prepared from ammonium hesanitratocerate ( G . F. Smith), and iron(I1) sulfate solutions prepared from either reagent grade iron(I1) sulfate or iron( 11) aInmonium sulfate. .Inalyses for chromium, in both stock solutions and equilibrated solutions, were performed by treatment with hydrogen peroxide and escess base followed by measurement of light absorption a t 372 nip, where chromate ion has an absorbancy indes of 1.83 X lo3 1. mole-' c m - 1 . The concentration of hydrogen ion in chromium( 111) perchlorate-perchloric acid stock solutions was determined by titration with standard base after first complesing chroniiutn(II1) with excess osalate ion.' The total normality of the stock solutions was determined by titration of the acid in the combined effluent solution and rinses after an aliquot of solution had passed through a column of cation-exchange resin in the hydrogen ion form. The methanol content of aqueous solutions of aquomethanolchromium( I11 1 species was determined by oxidizing methanol to carbon dioxide with ceriuin(I\-), using chromiurn(V1) as a catalyst. 'The procedure, suggested by an analytical method for formic ncid,s required a fourfold excess of osidaut and -11 31 sulfuric acid, The heat of mixing which developed with addition ~
~
Vol. 86
of concentrated sulfuric acid t o give this acidity raised the temperature t o - l l O o , and this was sufficient t o cause reaction t o go t o completion during the time required for the solution to cool before titration. The radioactivity of eluent portions was determined with a scintillation counter coupled with a y-ray spectrometer.
Values of fi were obtained a t 60" for solutions to 98.2 mole yc methanol and a t 30" for solutions to 96.3 mole % methanol. Values of cyo were obtained a t 60" to 85.3 mole yc methanol. (Throughout this paper, the presence of solutes will not be taken into account in calculating the solvent composition.) The quantities fi and cy0 are of interest in themselves, but their interest is enhanced since, within the framework of simplifying assumptions, their dependence upon solvent coniposition allows calculation of the equilibrium quotients for the reactions Cr(OH2)7-,(0HMe)j-13+
EDWARD L. KING
~.
J . A 1,aswick and R. A . Plane, J . A m . Chenz. Sor., 81, 3564 (1959). IT. R i e m a n , 111, and A . E Brei-er, " C h r o m a t o g r a p h y . Columnar
Liquid-Solid I o n Exchange Processes.'' in "Treatise o n Analytical Chemis t r y , " P a r t I , T'ol. 111, I . M. K o l t h o f f . ef ai , E d . , Interscience Publishers, S e x V o i - k , S .>-., 1'361, p. 1556. ( i ) \V. J. Blaedel and J , J . Panos. A d . C h e w . , 22, 910 (1950). ,Yl S , S Sharrna and R . C. h l e h r o t r a , A ? i d Ckitn. A d a , 13, 420 (1955).
Results Experiments.-Solutions containing water, methanol, chromium(II1) perchlorate, and perchloric acid were prepared by combined use of volumetric ware and gravimetric measurements to give solute molarities and mole fraction composition of the solvent. These solutions were equilibrated in closed Pyrex vessels a t GOo for 7 hr. or more (in many cases for much longer periods of time) and a t 30" for 130 days. These equilibration times were proved to be more than adequate by measurements of fi as a function of time, by studies in which the equilibrium value of n was approached from too high a value, and by independently obtained kinetic data.g Following equilibration, 10 to 50 ml. of solution was chilled and poured through a jacketed column of cationexchange resin maintained close to 0" (in a few experiments, the temperature was as high as 8 " ) . Chromium(111) ion went into the resin phase under these conditions, and the column was rinsed with chilled aqueous 0.03 M sulfuric or perchloric acid. This rinsing, requiring 3-0 hr., removes solvent methanol but does not elute chromium(II1) species. The duration of rinsing was selected to minimize errors due both to incomplete removal of solvent methanol from the column and to aquation of aquomethanol-chromiuni(111) species during rinsing, l o Following the rinsing, !%-lOOTc of the chromium(II1) ion with its first coordination shell intact was eluted from the column with 2-3 If sulfuric acid. This eluent was analyzed for chromium and methanol by the methods already described. These data allow calculation of fi values which are given as a function of solvent composition in Tables I and 11. The solvent coniposition is expressed in two ways, as Z h l e o ~the , mole fraction of methanol, in the calculation of which the presence of solutes is not taken into account, and also as I , the ratio of moles of free methanol to moles of free water in the solvent, i n the calculation of which correction was made for the amount of water tied up by chrornium(II1) ion ((6 - ri) moles per mole of chromium(II1) ion) and hydrogen ion (1 mole per mole of hydrogen ion). In making this correction for binding of one water molecule per hydrogen ion, it is assumed first that water is more basic than methanol and second that hydronium ion does not discriminate between water and methanol in its next shell. The uncertainty in the value of Y arises largely from uncertainty in the water content of the methanol used in preparing the solutions. The values of iz are uncertain by 0.5-2.07c. At the highest methanol concentration, complications appeared in experiments of long duration a t GOo. In such experiments, the value of fi decreased a t long times, and part of the chroniium(II1) ion was eluted from the ion-exchange resin with greater difficulty. The value of reported for such an experiment is the maximum value. It seems reasonable to interpret this fi
(9) R . J . Baltisberger a n d E. 1, King, J . A m . Chem. Soc., 86, 795 (1964). (10) An uncertain extrapolation of t h e r a t e constants reported in sef. 9 indicates t h e half-time for aquation of methanolpentaaqnochromiumiIII) ion a t 1" t,> be 10' hr.
THESOLVATION OF CHROMIUM(III) ION
Oct. 5, 1964
ZMleOH
T A B L EI E Q U I L I B R I UVALUES M OF fi AT 60" 0 010 kfCr(ClO4)8, 0 10 .If Hc104a
It
Y
3991
ZMleOH
r
11
ZYeOH
r
-
n
2 72 2 649 23' 0 169 0 722 1 01 0 954' 0 1820 4 62h 25l 2 68 0 174 0 818 1 31 0 959* 0 155 0 185' 6 06h 31' 2 78 0 854 1 52 0 964 0 331 0 302 0 435' 6 lof 363 2 89 1 56 0 853 0 965' 0 393 0 355 0 552, 2 96 38' 0 162 0 882c 8 OBh 1 74 0 966' 0 412* 0 705' 451 3 14 0 529 0 892 8 6' 1 82 0 974e n 453 0 836' 48' 3 31 1 82 0 58 0 897* 9 Oh 0 975 0 499 1 00v 12 552 0 584 0 924e 2 10 0 980d 3 53 1 008' 0 498C 14 5' 641 0 70 0 931 2 18 0 981h 3 6 0 566 1 314* 65 3 60 0 77 0 943c 19 St 2 38 0 982' 0 627 1 70" 223 2 60 0 91 0 953 0 €185' 2 19' 0.002 -21 Cr(C104)3, 0.05 M HC104. E 0.003 Jf Cr(C104)3,0.116 0 0 -1fHC104. C 0.20 -14' HC104. a Unless otherwise noted Uncertainty in value of 7 is 1.0-2.0~ob. -1f HC104. 1 Uncertainty in value of r is
