A Graphical Solution of the Second-Reaction Rate Constant of a Two-step Consecutive First-Order Reaction P. A. B. Marasinghe and L. M. Wirth Moorhead State University, Moorhead, MN 56563
For consecutive reactions of the type
the determination of the second-reaction rate constant kp is not as easy or as direct as the determination of the firstorder rate constant kl. The methods commonly used follow the concentration of the component B or C over time. The concentration of B at a given time t (in which the initial wncentration [Bl. = 0) for the general case in which
Since this is a graphical approach, a spreadsheet could be used advantageously to estimate this with ease. It may be noted that, with the use of the curve-fitting utility of spreadsheet programs, the frst-reaction rate constant kl can be estimated to a higher degree of accuracy as well. Method
Substituting for kz in eq 1in terms of K and k l , yields eq 4, which upon differentiation.
k l * kz
is given (I)by the following analytical equation.
and equating to zero yields the point at which [Bl is at its maximum value. At that point, we get the identity
where the initial concentration of A = [A],. In general, when [BI peaks at B, as in the case described in eq 1, we get
k --. p ~ I - K l [Al,
(3)
where the dimensionless quantity K is described by
Solving for K using eq 3 involves the iterative, successive approximation method. Spreadsheet Application
Many computer programs (2-5).which vary in their degree of sophistication, are designed to perform kinetic analysis. They can also be used to estimate k2. Most methods available use the nonlinear least-squares method (6,7) to obtain the best fit to the nonlinear function, eq 1. Further, it has also been shown that for k l >> k2 or k l
