NOTES
Nov., 1959 than those due to Wideqvist8and to F r e n ~ h .It ~ is however specifically designed thereafter for the study of product composition in the case where equal equivalents of A and B are present initially. Reaction equations 1 and 2 below A+B+C+D C+B+E+D
(1) (2)
in which C and E are the products of mono- and disubstitution, respectively, lead to the differential equation
edt
= kzCB
(3) (4)
Division of (3) by (4),(elimination of t ) , gives dE IclC (5) d(C
+E)
Making the substitutions AIAo = a; CIAO = x; EjAo = y; x
+ y = z; k&l
=k
where the subscript 0 refers to initial concentrations, (5) becomes
1979
be greater than that of the second by a t least a factor of 300, and if more than a third of the product is composed of disubstitution product then kz must be greater than kl. It follows from these results that where one, or less than one, equivalent of a substituting reagent leads to a mixture of unchanged substrate and disubstitution product in which no monosubstitution product can be detected, as in the case of the bromination of substituted 1-naphthylamines,lo that the specific rate constant for the second substitution must exceed that of the first. Thus in the present case, since the first introduced bromo-substituent will deactivate the nucleus toward electrophilic substitution, it must be concluded that the second stage, if not the first also, cannot be a normal electrophilic substitution. The mechanistic significance of this conclusion will be discussed in a later communication. (10) Cl. H. H. Hodgson and D. Hsthaway, J . Chsm. Boo., 21 (1944); E. H. Hodgson and R. Dean, ibid., 822 (1950); A. Hardy, E. R. Ward and L. A. Day, i b i d . , 1979 (1956); E. R. Ward and P. R.
Wells, unpublished work.
RHODIUM(II1) I N AQUEOUS SOLUTIONS Solution of equation 6 with the condition that y = z = 0 a t t = 0 yields k(l y=l+---(1
- a)
- k)
(1 (1
- z)k - k)
(7)
BY J. 5. FOR RESTER^ AND G. H. AYRES Contribution from the Analytical Research Laboratory of the University of Tezas Received April 4, 1969
Trivalent rhodium has strong complex-forming properties similar to chromium and cobalt. This fact explains the wealth of apparently uncorrelated facts reported for the behavior of rhodium salts in solution. Grube and Kesting2 titrated solutions By stoichiometry, at any time made by dissolving Rh(0H)a in perchloric acid; Bo - B = Ao - A + E (9) results indicated the formation of a complex, If A . = BO,as in the special case under discussion, Rh(OH)2+. Perchloric acid solutions of rhodium prepared from rhodium hydroxide also have been then at completion, i.e., B = 0 investigated by electrophoresis and ion-exchange A = E, Le., a y (10) chromatography. Schuklaa recently has reported Hence (8) becomes on these studies and postulated the existence of Rh(HzO)B+++. 9’ ~ ( l 2k) k - 1 = 0 (11) The preparation and X-ray powder data for solid Graphical solution of equation 11 gives the follow- rhodium perchlorate hexahydrate have previously ing values been published by Ayres and F ~ r r e s t e r . ~Using Y k ki/kr this salt as a starting material, aqueous solutions of 0.01 300 rhodium(II1) have now been studied under condi.02 .0067 150 tions relatively free from complexation. or
-
+
-
+
.03 ,0125 80 .05 .0250 40 .10 .0765 13 .25 .50 2 .320 1.0 1 .38 2.0 0.5 .45 5.5 0.2 .49 25 0.04 ,495 50 0.01 Solution of equation 6 for k = 1 under the above conditions yields log, 9 = 2 - l/y which can be solved numerically for y.
Thus in order that the reaction product shall contain less than 1% of disubstitution product, the specific rate constant of the first substitution must 8. Wideqvist, Acta Chsm. Scand., 4, 1216 (1960). (9) D. Frenah, J . A m . Chsm. Boc., 7 2 , 4806 (1950).
(8)
In order to assure solutions of maximum purity, large crystals of rhodium perchlorate were dissolved in triple distilled, deaerated water. As the quantity of stock solution repared in this manner was limited, it was decided to com{ine the data from three different experimental methods; potentiometric, conductimetric and spectophotometric measurements were made on each sample. A stock solution of rhodium(II1)perchlorate, 0.00728 M , was pre ared and the spectral curve recorded. This curve shows aisorption maxima at 300 mp (a,,, = 69 g. moles-’ cm.*) and 395 mp (a,,, = 62 g. moles-’ cm.*). A 5.0-ml. aliquot of this stock solution was diluted with 25.0 ml. of water and titrated potentiometrically with 0.0316 N sodium hydroxide. After the end-point was reached, a reverse titra(1) Esso Researah Laboratoriea, Esso Standard Oil Company, Baton Rouge, La. (2) G. Grube and E. Kesting, 2. Elshtrochem., 89, 965 (1933). (8) 8. K. Sohukla, J . Chromatography, 1, 457 (1958). (4) Q. H. Ayrea and J. 8. Forrester, J . Inorg. Nucl. Chsm., 8 , 365 (1957).
1980
NOTES
corded from the stock solution over a period of one week showed no noticeable change. Refluxing solutions for one hour and also for a 24-hour period caused pronounced changes in the spectral curves. Two solutions, refluxed for one hour and for 24 hours, respectively, also were titrated potentiometrically and conductime trically by the procedures described previously. The dashed line in Fig. 1 again illustrates the results. The first break observed in the titration curves of freshly prepared solutions has shifted; the second break is unchanged. The formation of hydrous rhodium (111) oxide was again indicated by a visible precipitate. A t first, i t appears that boiling resulted in further hydrolysis of the Rh(OH)++ ion according to the equation Rh(OH)++ 2H90 Rh(0H)s 2H+ However, the absence of a break a t [OH-]/[Rh+++] = 1, in the curve for the reverse titration with perchloric acid (after previous titration with sodium hydroxide), indicates that the species Rh(OH)++ is not re-formed. It may be that some dimerization or other bridging has occurred; one possibility might be 2Rh(OH)++ + Rh-O-Rh++++ HzO. However, the very marked decrease in pH after reflux of the solution is not compatible with this explanation. Photometric curves of the refluxed solutions show a loss of spectral details, suggesting the disappearance of a single species.
I
I
PL
10.0
9.0
+
8.0
@
Vol. 63
7.0
+
+
5.0
4.0
r
3.0 0
- 4 -
I
I
1.0 2.0 3.0 Mole ratio [OH-]/[Rh(III)].
Fig. 1.-Potentiometric
4.0
titrations of rhodium perchlorate.
tion was made with 0.0544 N perchloric acid. This last titration served to check the reversibility of the hydrolysis of the rhodium cation. A conductimetric titration then was made on an identical aliquot of the stock solution. Both titrations may be interpreted similarly. Figure 1 illustrates the data of the potentiometric titration. The first of two changes in slope in the curve strongly suggests the titration of a hydrogen ion resulting from hydrolysis. Reaction ( 1 ) may be postulated R h + + + H20 Rh(OH)++ H + (1) and from the initial pH of 3.29, the stability constant, K , for the Rh(OH)++ ion may be calculated as 3.7 X Increasing the pH after the first end-point resulted in a turbid system. The hydrous oxide of rhodium was precipitated quantitatively when the molar ratio of hydroxyl to rhodium, [OH-] /[Rh+++], reached three. This end-point was accompanied by a sharp change in the slope of the titration curve. For this reaction we may write Rh(OH)++ 2 0 H - +Rh(0H)a (2) and calculate the solubility product constant for Rh(OH)a (K.= ~ 4.8 x 10-23). The reversibility of the hydrolysis in the titration described previously is represented in Fig. l by the triangles. During these reverse titrations the hydrated rhodium showed a slight hysteresis effect as evidenced by slow attainment of equilibrium after the addition of increments of titrant. This effect appears graphically as a small displacement of the titration curves during the reverse titration. The hysteresis effect may also partially account for the displacement, along the absorbance axis, of the two spectrophotometric curves recorded before and after the titrations. In addition, this displacement is ascribed to the lower concentration of rhodium in solution and to the change in ionic strength; these effects result from addition of titrants used for the precipitation and redissolution. Some observations were made on the state of the rhodium (111) ion after aging at room temperature and an elevated temperature. An examination of the spectral curve^ re-
+
Discussion Extensive hydration and possible bridging phenomena prevent clearly defined interpretation of experimental results. Although there is good evidence for the formation of the Rh(OH)++species, the results are not conclusive. I n the titration of freshly prepared rhodium perchlorate solution with sodium hydroxide, the appearance of the first inflection point (Fig. 1) somewhat below a [OH-]/ [Rh+++]ratio of 1 suggests the possible formation of a dimer or even a trimer. Such a species could add more hydroxy groups for a final formation of the hydrous oxide. One might suggest the reactions
I
I1
+
+
r
0
1++
Similar species have been suggested recently for iron(II1) by Hedstrom5 and Mulay.6 B. 0 . A. Hedstrom, A r k . Kemi, 6 . l(1953). . (6) L. N. Mulay and P. W, Selwppd, J ; A n . Chen. Soc., 77, 2693 (1955). (5)
Nov., 1959
NOTES
1981
The existence of a Rh(OH)++ species is contra- Higher areas were in general obtained with larger samples. dictory to the findings of Grube and c o - ~ o r k e r s ~With ~ ~ the largest samples (10 g. or more) a fast exothermic reaction started at 350" and the temperature in the solid who postulated the formation of Rh(OH)2C104 mass rose quickly above 400' for a brief period. It appeared from titration of rhodium hydroxide with perchloric that this temperature runaway was related to the surface acid; no strong evidence for the Rh(OH)2+ ion area variations, probably because of effects on rate of reducIt seemed likely that the temperature in small samples was found in the present study. A very slight tion. g. or less) remained nearly the same as that of .the hyirregularity in the titration curves of Fig. 2 and 3 (0.1 drogen during heating and that the rate of reduction was may be observed at [OH-]/[Rh+++] ratios of 2; therefore slower. A number of experiments are described below in which the however, these can hardly be noticed above the of reduction of small samples was controlled and varied; experimental scattering of the data. If Rh(OH)2+ rate results are shown in Table I. The reduction was carried out was present in the solutions, its concentration was in a 5-ml. glass cell having a sintered glass plate to support negligible compared to the observed species. the sample. The same cell was employed as the adsorption Several strong indications for oxy or hydroxy cell for B.E.T. measurement of the surface area. bridges were evident during the study. I n the TAbLE 1 preparation of rhodium per~hlorate,~ extensive SURFACE AREAS OF MoSz PREPARED FROM MoSa boiling of the solutions ultimately led to a color Gas flow rate, 5 ml. per min., atmospherk pressure; outchange from light yellow to dark brown. Crys- gassing temp. for area measurements, 500 ; 30 mg. MoS tals of rhodium perchlorate hexahydrate could not ( < 20 mesh) be isolated from the darkened solution. If, Final Surface Rate of tpp., area, however, these solutions were refluxed with hydroGas heatinga C. m.Z/g. chloric acid and the rhodium was reconverted to .. Untreated tri..
