Determining the Limits of Equilibrium-Constant Values in Consecutive Equilibria from a Single-Component Measurement Mitchell D. Menzmer Pacific Union College, Angwin, CA 94508 Equilibrium Constants i n Consecutive Reactions In the course of investigation of reactions that may be represented by
or, oppositely, to find values of K1 and K2 from experimentally determined equilibrium concentrations. In practice, with the analytical methods available, the equilibrium concentration of only one species [A],
it is important to understand how the values of equilibrium constants
[Bl.
[CI,
may be experimentally available. Equations 2 4 show the relationship between equilibrium constants Kl and K2 and the equilibrium concentrations of each of the species A, B, and C.
and
affect the equilibrium concentrations of A, B, and C. Treatment of these systems in terms of equilibrium is trivial provided that the equilibrium concentrations of two of the three components (Aand B, Aand C, or B and C ) can be independently determined. It is always possible to calculate the equilibrium concentration of the third species using the relationship
In this paper, using eqs 2 4 , I point out that some conclusions can be drawn regarding the values of Kl and K2 from a single ratio, either [A], (Pa=IA],
[BI. [Al,
'pb = -
where the subscripts denote initial and equilibrium concentrations. Alternatively, [A], + [Bl, + IC1. = [Ale + [Bl, + [CI. can be used when initial concentrations of B and C are not negligible. Using ExperimentallyDetermined Values
Finding Limiting Values
In such situations, it is possible either to predict how known values ofKl and Kz affect the ratios,
Equations 2-4 must first be rearranged into a form suitable for finding limiting values of the equilibrium con-
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Journal of Chemical Education
stants K l and K2,based on @.@b, , or @,Equation . 2 may be rearranged to solve for either K I or Kz. -l 1 'Pa K -' - ~ ~ + l -l 1 'Pa Kz=--1 KI
And from eq 9 it may be deduced that 1 K,>1 -- 1
(5)
(6)
(14)
9c
Using Constraints Using the constraints Kl > 0 and Kz > 0 as minimum limiting values and combining them with each of the eqs 11-14, we get the corresponding inequalities.
Equation 3 may also be rearranged to solve for either KI or Kz. 1
K1=
-I 1-K2
(7)
%
& - - I1- %
1 KI
(8)
And finally, eq 4 may be rearranged to solve for either Kl or Kz.
Kz =
Kl+l
- 11
(10)
Making Deductions With the constraint that Kl and Kz must be nonzero and nonnegative (i.e., Kl > 0 andKz > 01, limiting values for KI and Kz may be deduced from eqs 6-9.(Equations 5 and 10 allow no useful deductions.) From eq 6 the following deduction may be made. 1 K1
