Reactions Involving a Prior Equilibrium S. A. Chimatadar and J. R. Rajul Karnatak University, Dharwad-580003, India
Reactions of the type
m e Results Reaction
where C is a steady state intermediate and kz and ka are not widely different are encountered quite often. Recent examples of such mechanism include the Cr(V1) oxidation of Lcysteine (I), the reduction (2) of NiL2+ nickel(1V) oxime complex by Fez+,V02+,and NiCyclam2+ and the reaction of aqueous Eu(I1) ion with pyruvic acid (3). all a t constant acidity. Noncomplementary redox reactions generally follow this mechanism for which the rate law is given by
Conditions
kr(M1s-')
k2/k3
TI(iiikFe(ii)
[HCIO,] = 1 M p = 1.785 With NaClOd: 30%:
0.20
4 . 4
TI(ll1)-V(iV)
[H2S041 = 1 M p = 5.0 (with Na.SO,): 70% 2[Ti(lll) = [V(IV)] = 0.02
0.066
-2.5
Ce(iV)-Cfliil)
[HCiO,] = 1 M + = 1.5 (with NaCIO,); 26% 3[Cr(lil)] = [Ce(lV)] = 0.003 to 0.033 M
to 0.08 M 3.54
The integrated form (4) of eq 1 can be used only with a knowledge of the ratio kzIk3 and generally such reactions are studied by the use of an inverse form (5) of eq 1, which procedure is not entirely free from error. A more dependable method is described here that involves the use of equivalent concentrations of reactants with no product present initially. Thus in the case where A and B are 2:l equivalent reactants, with equivalent concentrations (2A = B = a), the integrated form of eq 1is
With x = a12 a t time = tllz, the form (214 = k,tl12+ constant
(3)
is attained (4b) from which kl, the forward reaction rate constant of the first step, can be obtained. Aplot of half-lives for B series of equivalent initial concentrations withno product present initially willlead to kl. However, if kz is very high compared to ka, the denominator of the right-hand side of eq 1 will approximate to the term in kz only, thus effectively -
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114
Journal of Chemical Education
Graph of half-life against reciprocal of halt initial concentration
-20
leading to a different rate equation. Such a case obtains, for example, in the Cr(V1) oxidation of V(1V) (6). Equation 3 is a special case of the general relation
where t , is the time required for the completion of a definite fraction m of the reaction. By puttingx = ma (with m < 1)in eq 2, eq 4 results. Since k l is obtainable from eq 3, the ratio k z l k 3 is ascertainable from eq 4 from a knowledge of the times t , required for completion of a definite fraction m of reaction of a series of initial equivalent concentrations. Thus for the completion of 75%of the reaction, a plot of 410 versus t814will lead to k z l k 3 from
We have calculated k t and the ratio k2/kafor three reactions, namely Tl(II1)-Fe(II), Tl(II1)-V(IV), and Ce(1V)Cr(II1) for which, except the first case where kz and k 3 have been determined (7),k l and k z I k 3 are not known. The reac-
tions were followed by hack titration of excess cerium(1V) with iron(II), by titration of vanadium(1V) with Ce(1V) and by spectrophotometry, respectively. Each of the above reactions follows a rate law of the type under discussion and can be appropriately treated as discussed above. Thus, kl was found from plots of t l j 2 versus 2/a for a series of equivalent initial concentrations with no pioduct present initially. Utilizing the kl values thus obtained, k2/k3ratio could be found from eq 4 from the data available from runs carried out already (to obtain k l ) with no additional effort. The results are shown in the table and the plots of t l j z versus 2Ia are shown in the figure. Literature Cited
(41 (a1 A s h ~ m tK. , G.; Higginson,W.C. E.J Chem.Sm. 1353,3044: ( b )Chlmstadar, S. A PhDThaa. Kamatak Unirerslfy. ISSO. ( 5 ) SF., for example. Dikrhifulu. I.S. A.: Vmi. P.; Hanumantha Rae, V. J. lnarg. Nucl. Chem. 1981,43.1261. (61 Davies, K.M . ; Espenwo, J.H. II A m r . Chem. Sac. LWO, 92,1891. (71 Fsleinella, 1.8.; Felgate, P.D.: Laurena, 0. S.J. Chem. Sm. (Dolton) 1975,l
Volume 63
Number 2
February 1986
115
