NOTES
1978
Fig. 1.
the tensions of fluid interfaces. Methods for the direct determination of relative values already have been presented.2J Figure 1 demonstrates the case where varying masses of methylene iodide were brought into contact with the same column of air projecting into the aqueous phase. Each half of the photographic plate was exposed with a different mass of methylene iodide suspended on the same column of air. All the phases were mutually saturated. The methylene iodide had been distilled under reduced pressure and the water distilled from a block tin system. The temperature was 25’. By directly superimposing the photographed images on another plate (Le., plate 1, Fig. 2),*it was determined with good precision that the angle through the aqueous phase at the edge of common contact was the same in each case. From Fig. 1 it is apparent that the magnitude of the force that can act to hold the methylene iodide on the gas phase, after equilibrium with respect to the interfaces has been established, must be at least equal to the gravitational force due to the mass of methylene iodide suspended under the conditions depicted in the right half of Fig. 1. It can therefore be concluded that the gravitational force due to the mass of methylene iodide suspended under the conditions depicted in the left half of Fig. 1must be less than the total force that can hold it on the gas phase. It is evident from Fig. 1 that the difference between the gravitational forces due to the different masses of methylene iodide suspended in each case cannot be accounted for by the difference between the lengths of the circumferences of mutual contact. From these experiments we may conclude that equilibrium between the gravitational force and the force that can act to hold one fluid phase on another in the presence of a third fluid phase, after equilibrium with respect to the interfaces has been established, i s not a necessary condition for equilibrium with respect to the interfaces. Since the gravitational force due to the mass of methylene iodide suspended in the left half of Fig. 1 (2) W . Fox, J . Chem. Phys., 10, 623 (1942). (8) W . Fox, J . A m . Chem. Soc., 67, 700 (1945).
Vol. 63
must be less than the force that can hold it on the gas phase we can also conclude that the “excess” final edge force is balanced all around the circumference of contact. It is significant t o note that even under the influence of the “excess” edge force the smaller drop of methylene iodide does not become extended over the gas phase but remains in a position that gives the constant, reliable, reproducible angle characteristic of the system under investigation. These experiments also lead to an understanding of the necessary requirements for the determination of the linear force intensity, dF/dL, along the massless circumference of mutual contact, after equilibrium with respect to the interfaces has been established. The mass of fluid phase suspended must be increased until the maximum mass that can be suspended along the circumference of mutual contact is determined. The determination of this mass and the length of the circumference of common contact will give the linear force constant operative. The magnitude of this linear force constant can be related to the linear force constants of the interfaces concerned and thus give a new independent method for the determination of the absolute value of the tension that is manifested at the boundary limit (the edge) of each of the interfaces. Acknowledgments.-The author wishes to thank his wife, who carefully reviewed the manuscript, and Professor Arthur W. Thomas of Columbia University, who stimulated and encouraged this research.
t
‘
KINETICS OF CONSECUTIVE COMPETITIVE SECOND-ORDER REACTIONS BY P. R. WELLS’ College of Technology and Commerce, Leicester, England Received March 2SV1969
Due to the complex nature of the mathematical expressions obtained most treatments of consecutive competitive second-order reactions lack generality since simplifying conditions2 or approximationsa are employed. The following treatment is general as far as equation 8 and is essentially equivalent to those due to Higgins and Williams,‘ to Frost and Schwemer,6to McMillan6 and to Riggs,’ but yields an expression more suitable for the present purpose ( 1 ) Iowa State College, Ames, Iowa, U.S.A. (2) Cf. Jen-Yuan Chien, f. A m . Chem. Soc., 70, 2256 (1948); M. TalAt-Erben, J . Chem. P h y s . , 26, 75 (1957). (3) Cf. K. Ingold, J . Chem. SOC.,2170 (1931); F. H. Westheimer, W. A. Jones and R. A. Lad, J . Chem. Phya., 10, 478 (1942).
C.
(4) H. G. Higgina and E. J. Williams, Aust. J . Sci. Res., AS, 572 (1952). (5) A. A . Frost and W. C. Schwemer. J . A m . Chem. Soc., 74, 1268 (1952). (6) W . H. MoMillan, ibid., 79, 4838 (1957). (7) N. V. Riggs, Aust. J . Chem., 11, 86 (1958).
I
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) 8. Wideqvist, Acta Chsm. Scand., 4, 1216 (1960). (9) D. Frenah, J . A m . Chsm. Boc., 7 2 , 4806 (1950).
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).
