Linear or Nonlinear Least-Squares Analysis of Kinetic Data?

Abstract

Abstract. The disadvantages of the usual linear least-squares analysis of first-and second-order kinetic data are described, and nonlinear least-squares fitting is recommended as an alternative. Keywords. Kinetics, Graduate Education/Research, ReactionsA common task in chemical kinetics is to extract the rate constant from the time dependence of concentrations. We first consider a reaction where reactant A is converted to product B, as in eq 1, and where the rate of reaction (rate of product formation or rate of reactant disappearance) is proportional to the concentration of reactant A, as in eq 2. Such a reaction is said to follow firstorder kinetics, because the rate is proportional to only one concentration.Alternatively, the rate may also be proportional to the concentration of another species C with proportionality constant k', as in eq 3. However, if C is a catalyst, so that its concentration remains constant, or if C is in large excess, so that its depletion is negligible, its concentration does not deviate from its initial concentration [C] 0 , and eq 3 can be simplified to eq 2 by setting k'[C] 0 equal to k. Such a reaction is said to follow pseudo-first-order kinetics, and k is often called a rate coefficient, rather than a rate constant, because its value changes with [C] 0 . In either case the solution to eq 2 is given by eq 4, where [A] 0 is the initial concentration of A.

What is the role of acid–acid interactions in asymmetric phosphoric acid organocatalysis? A detailed mechanistic study using interlocked and non-interlocked catalysts

“…17 Time-resolved data were obtained by NMR-spectroscopy. Rate constants were determined by both nonlinear tting 19 and linear tting of the conversion plots, which gave almost identical results (ESI Tables S4-S7 ‡ and chapter 9). We also performed reaction progress kinetic analysis (RPKA) based on different and same excess measurements.…”

Human cytochrome P450 11B2 produces aldosterone by a processive mechanism due to the lactol form of the intermediate 18-hydroxycorticosterone

“…The absorbance difference between 390 and 420 nm was found at each time point and exported to generate mixing transients. These transients were then fit by nonlinear regression in GraphPad Prism to avoid the heteroskedasticity that occurs with linear fits (47). The fitting Equation 4 assumes that the enzyme and substrate are initially at the same equation and is shown below.…”

Slow Formation of Pseudorotaxanes in Water

“…Rate constants and reaction orders were determined by nonlinear least-squares fitting of time dependent concentrations. [42] Initial experiments were conducted with equimolar concentrations (0.5 mM) of the rods (1 or 2) and the cyclophane 4 in D 2 O. Interestingly, the expected second order formation kinetic was only observed for the isophthalate terminated rod 2, while for the complexation of 1, a reasonable fit of the data was only possible for a first order kinetic. Attempts to vary the host/guest ratio of 2/4 to a point where a transition to a pseudo first-order reaction occurs was not possible due to signal broadening.…”

“…The formation kinetics of the pseudorotaxanes 1⊂4 and 2⊂4 were monitored by time‐dependent 1 H‐NMR spectroscopy (Figure ). Rate constants and reaction orders were determined by nonlinear least‐squares fitting of time dependent concentrations . Initial experiments were conducted with equimolar concentrations (0.5 m m ) of the rods ( 1 or 2 ) and the cyclophane 4 in D 2 O. Interestingly, the expected second order formation kinetic was only observed for the isophthalate terminated rod 2 , while for the complexation of 1 , a reasonable fit of the data was only possible for a first order kinetic.…”