of error, rate constants and rate laws can be determined by these differential methods with significantly lower uncertainty than by the construction of graphical rate equations (above.) Different-excess experiments 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 (k2 and K1 in the case of pre-equilibrium; k1, k−1, and k2 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. Graphical rate laws Kineticists have historically relied on linearization of rate data to extrapolate rate constants, perhaps best demonstrated by the widespread use of the standard Lineweaver–Burk linearization of the Michaelis–Menten equation. Linearization techniques were of particular importance before the advent of computing techniques capable of fitting complex curves, and they remain a staple in kinetics due to their intuitively simple presentation. It is important to note that linearization techniques should NOT be used to extract numerical rate constants as they introduce a large degree of error relative to alternative numerical techniques. Graphical rate laws do, however, maintain that intuitive presentation of linearized data, such that visual inspection of the plot can provide mechanistic insight regarding the reaction at hand. The basis for a graphical rate law rests on the rate (v) vs. substrate concentration ([S]) plots discussed above. For example, in the simple cycle discussed with regard to different-excess experiments a plot of vs. [B] and its twin vs. [A] can provide intuitive insight about the order of each of the reagents. If plots of vs. [B] overlay