While RPKA allows observation of rates over the course of the entire reaction, conducting only same-excess experiments does not provide sufficient information for determination of the corresponding rate constants. In order to construct enough independent relationships to solve for all of the unknown rate constants, it is necessary to examine systems with different-excess.
Consider again the simple example discussed above where the catalyst associates with substrate A, followed by reaction with B to form product P and free catalyst. Regardless of the approximation applied, multiple independent parameters (k and K in the case of pre-equilibrium; k, k, and k in the case of steady-state) are required to define the system. While one could imagine constructing multiple equations to describe the unknowns at different concentrations, when the data is obtained from a same-excess experiment [A] and [B] are not independent:
:e = [B] − [A]
Multiple experiments using different values of e are necessary to establish multiple independent equations defining the multiple independent rate constants in terms of experimental rates and concentrations. Non-linear least squares analysis may then be employed to obtain best fit values of the unknown rate constants to those equations.