Determination of first order rate constants by natural logarithm of the slope plot exemplified by analysis of Aspergillus niger in batch culture.

Finding rate constants from experimental data is often difficult because of offset and noise. A computer program was developed to average experimental data points, reducing the effect of noise, and to produce a loge of slope plot--a plot of the natural logarithm of the slope of a curve--eliminating the effect of any offset. If y-values depend exponentially on x-values the loge of slope plot is rectilinear and the slope is equal to the first order rate constant. Therefore the loge of slope plot provides easy identification of exponential sections of any experimental or calculated data, corresponding rate constants, and small changes in the rate constant as exemplified by analysis of titrant added to a batch culture of Aspergillus niger. The loge of slope plot was easily applicable and superior to conventional methods of analysis of exponential decreasing or increasing data.