1216
CLARENCE POSTMUS AND
(111) reaction, which finds no simple explanation if the iron(II1) reaction were exactly analogous to reaction 7, may be explained in the same terms as employed in the last section; a decrease in coordination number upon acid dissociation Fe( OH& + ++ = Fe( OH2)30H++
+ H + 2H20 +
rationalizes both the more positive value of AH aiid the more positive value of A S for the iron(II1) reaction. The Stability of Outer-sphere Complexes.-It appears that " outer-sphere" complexes of hexaaquochromium(II1) ion and a particular anion are considerably less stable than are corresponding "outer-sphere" complexes of hexaammine-cobalt(111)ion. Extrapolating various measured association quotients to zero electrolyte concentration by 35' in solutions of r = 1.00 determined by R. E. Connick, el ai. The value of AH obtained from these measurements ia +8 8 kcal, a value decidedly lower than earlier values.*'~4' The value of A S obtained frem this value of AH and the equilibrium quotient value a t 25' is 17 e.u. This value corresponds more nearly to the value of AS7 and thus there may be little necessity for finding an explanation of the difference between the iron(II1) and chromium(II1) reactions.
EDWARD L. KING
VOl. 59
equation 3 using the same a value as was valid for KI, one finds KOI'values a t 25": Cr(OH2)68CN++, 7 ; Cr(OH.2)6 4 3 1 + +, 13lQb; C O ( N H ~ ) ~ . N ~5Vb; ++, and Co(NH3)&1++, 210Pb The greater acidity of water compared to ammonia might lead one to expect the peripheral hydrogens in the aquocatjon to be more positive than in the amine complex and thus attract anions more strongly. Such is not the case. The probable explanation for this is to be found in a consideration of the structures of these species in more detail than simply consideration of the positive nature of the individual hydrogen atoms. While the periphery of the amine complex consists of eighteen hydrogen atoms, all positive in nature, the periphery of the hexaaquocation consists of 12 hydrogen atoms, all positive, and six regions of high electron density, the six unshared electron pairs. An anion is, therefore, much less strongly attracted by the aquocation since it cannot be in close proximity to the positive hydrogen atoms without at the same time being close to a localization of negative charge.
THE RATE LAW FOR THE FORWARD AND REVERSE OF THE REACTION Cr(OHJs+++ SCN- = Cr(OHz)sNCS++ H201-3 BY CLARENCE POSTMUS4 A N D EDWARD L. KING
+
+
Contdmlion from Ihe Department of Chemistry, University of Wisconsin, Madison, Wisconsin Received M a y 18, 1066
+
+
Although the reaction Cr(OH2),+++ SCNc r ( o H ~ ) ~ N C s + + .H 2 0 proceeds very slowly a t room temperature, it is ppssible to evaluate the rates of both the forward and reverse reactions during the few tenths of a per cent..of reaction. Such IS possible using spectrophotometric measurements because CrNCS++ is very opaque compared to Cr+++in the ultraviolet and FeNCS++, which rapidly forms with free SCN-, is very opaque compared to C r + + +and CrNCS++ in the visible re ion of the spectrum. Measurements upon the forward reaction demonstrate that the rate law is d(CrNCS++)/dt = +++)(SCN-){kl kz(H+)-l k3(H+)-2). The combination of this with the equation for the net reaction leads t o the rate law for the reverse reaction +d(SCN-)/dt = (CrNCS++)(k-l kda(H+)-l L s ( H + ) - * which was confirmed by the direct measurements to the extent of a demonstration of first-order dependence upon CrNCd++ and the evaluation of IC-,. The rate law terms kz(Cr+++)(SCN-)(H+)-l and k3(Cr+++)(SCN-)(H+)-2 correspond to reaction paths with activated complexes containing one and two hydroxide ions. The activated complexes which involve one and two hydroxide ions are more important than are the chromium(II1) species containing one and two hydroxide ions despite the less favorable electrostatic attraction between the reactants in these paths. The first-order dependence of the reaction ratmeupon the thiocyanate ion concentration does not rule out reaction mechanisms with activated complexes with coordination number SIX. Measurements of the rate of the forward and reverse reactions at 14.0, 25.1 and 30.0' allow the evaluation of the equilibrium quotient for the reaction a t these temperatures.
ccg.
+
+
In the preceding paper,l the equilibrium quotient for the reaction
+
+
(a) establish the rate law which yields the composition of the activated complex(es), and (b) calculate the value of the equilibrium constant for Cr(OH&+++ + SCN- = Cr(OH&NCS++ + H20 (Reaction 1) reaction 1 from the rate constants for the forward has been determined as a function of the electrolyte and reverse reactions. This provides a mutual concentration a t six temperatures in the range 30.0- check of the rate and direct equilibrium studies at 94.6". In the present paper, the results of kinetic 30°, where both types of data were obtained and, studies upon this reaction at three temperatures in in addition, extends the temperature range over the range 14.0-30.0' will be presented. Both the which values of K I o , the equilibrium constant for forward and reverse reactions have been studied. reaction 1, are known to temperatures at which The studies had two purposes; it was desired to: the direct equilibration requires extraordinary amounts of time. (1) Taken in part from the Ph.D. Thesis of Clarence Postmus, University of Wisconsin, 1954. The system has proved an ideal one to study in (2) Supported in part by grants from the U. 6. Atomic Energy spite of the very low rate of reaction because an Commission and the Researah Committee of the Graduate School, accurate evaluation of the rates of both the fofward University of Wisconsin. (8) Presented before the 127th National Meeting of the American and reverse reactions can be obtained while the Chemical Society at Cincinnati, Ohio, April 4, 1955. respective reactions are proceeding less than 1% (4) U. S. Rubber Company Fellow, 1953-1954; present addrcss, toward equilibrium. This makes it possible to Argonne National Laboratory, Lemont, Illinois. 89, 1208 (1955). perform the experiments in a reasoilable time while (5) C.Postmua and E. L. King, THIBJOURNAL,
Dec., 1955
THERATELAWFOR
THE CHROMIUM(III)-THIOCYANATE
realizing experimental conditions which make the rate of the opposing reaction negligible. Measurements upon solutions in which the forward reaction is occurring demonstrate that the rate law ise d(CrNCS++) dt (Cr+++)(SCN-)(kI
+ kz(H+)-I + lr3(H+)-2}
(I)
The combination of this with the equation for the net reaction leads to the rate law for the reverse reaction d(SCN -) +-= dt (CrNCS++)llc-l
+ k-z(H+)-l + /c-~(H+)-Z] (2)
which was confirmed experimentally to the extent of showing a first-order dependence of the rate upon CrNCS ++, The measurements of the reverse rate were carried out a t acidities which allowed the evaluation of but did not allow the evaluation of k- and k- 3. Experimental Equipment and Reagents.-In general, the equipment and reagents were the same as used in the equilibrium measurements.6 There were, however, some changes which will be described. Since the rate of the forward reaction was, in some cases, followed by using a particular portion of solution in the spectrophotometer cell which was kept in the cell housing t,hroughout the run, more precise temperature control of the cell housing was needed than in the equilibrium studies. Installation of a more efficient pump with which to circulate the thermostat water through the cell holder resulted in temperature control to d~0.01'which is comparable to the control in the thermostat. In the study of the reverse reaction, solutions containing CrNCS++ at a concentration greater than corresponds to equilibrium were required. One of the simplest ways of realizing such a solution was the dilution of a concentrated solution in which the equilibrium in reaction 1 had been established. It was found, however, that the rate of appearance of thiocyanate ion in such a solution was too high (see discussion below) and it was concluded that the side reactions which are responsible for the disappearance of thiocyanates in the equilibration produces a substance which catalyzes the reaction. Ion-exchange techniques which have been used to produce relatively small amounts of the separated complexes6J have proved effective in the preparation of relatively large batches of perchloric acid solutions of CrNCS++. Use of the light colored cation exchange resin Dowex 50-W has proved advantageous; one can readily see what is occurring since the chromium( 111) species are purple in color. The complex Cr(NCS)Z+ was removed by washing of the column with 0.15 M perchloric acid prior to the elution of CrNCS++ with 1.0 M perchloric acid. This washing also removed the interfering decomposition products since the rate coefficient k-1 of the rate law for the reverse reaction of CrNCS++ which was prepared in this manner had a lower value; this lower value of k - I , when coupled with the rate coefficient kl of the rate law for the forward reaction, yielded a value of the equilibrium quotient which was in agreement with the directly determined value.6 (This seems a reasonable criterion for the validity of the rate measurements. ) Details of Experimental Procedure.-In the study of the forward reaction, solutions containing chromium(II1) per(6) As was true in the preceding paper, the water molecules in the first coordination sphere of chromium(II1) species will generally not be shown. A formula in parentheses stands for the molar concentration of the indicated species. The k's of the rate equations, which are valid for a particular medium under consideration, will be called rote coefiients; the term rats conatant, which will be designated by a zero superscript (Le., ,769, will be reserved for the values extrapolated to infinite dilution. (7) E. L. Iiiiiy & i d E. B. Uisiiiukus, J . A ~ LC'korc. . Soc., 1 4 , 1674
(llJ52).
REACTIOK
1217
chlorate, sodium thiocyanate and perchloric acid were prepared from the appropriate stock solutions. A solution was placed in 2, 5 or 10 cm. cylindrical type cell and the absorbancy was measured as a function of time in the Beckman Model DU Spectrophotometer. An extremely small change in the concentration of CrNCS++ can be measured by evaluating the absorbancy of the solution a t 292 mM where CrNCS++ has a molar absorbancy index of 2.90 X loa. At this wave length, hexaaquochromum(111) ion and thiocyanate ion are essentially transparent. Thus, in a solution with a concentration of hexaaquochromium(II1) ion of 0.01 111,0.1% conversion of this to CrNCS++ results in a change in absorbancy of 0.29 (per ten cm. of light path), making such measurements with a ten cm. cell yield rather precise data during a small extent of reaction. Because the extent of reaction is so low (
