Graphic Analysis of First-Order Rate Data

Abstract

Objective

To provide an in-depth discussion of five graphs used to analyze first-order rate data. Special emphasis is given to the use of semilogarithmic graph paper and semilogarithmic plots.

Data Sources

A theoretical set of time-concentration data was generated using the equation C=C_o e^-kt. Arbitrarily chosen values of 6.0 mg/L and 0.33 h^-1 were used for C_o and k, respectively.

Study Selection

First-order rate data were plotted for subsequent graphic analysis in five different ways: concentration (C) versus time (t) (on linear graph paper), ln C versus t (on linear graph paper), log C versus t (on linear graph paper), C versus t (on commercial semilogarithmic graph paper), and C versus t (on extemporaneously prepared semilogarithmic graph paper).

Data Synthesis

Methodology for estimation of the first-order rate constant, half-life, and initial concentration from each of the five different graphs is discussed. The strengths and weaknesses of each graphing technique are presented. Fundamental equations relevant to first-order kinetics are also reviewed. Familiarity with these equations is shown to be essential to the analysis of different graphs.

Conclusions

Each of the five plots used to analyze the first-order rate data offers advantages and disadvantages. The most expedient approach is the use of commercially available semilogirithmic graph paper.