The rate law for a reaction gives us a tool for predicting how fast a reaction will go under initial concentration conditions. So it is a way of incorporating one of the important factors which affect rates into a quantitative description of reaction kinetics.
But what happens if the temperature is different from the one at which the rate law was determined? There is a provision in the rate law for the effect of temperature: the rate constant, k. Experiments reveal that the rate constant changes with temperature in a predictable (if not simple) way. Not surprisingly, higher temperatures produce larger rate constants.
The mathematical model which best describes the relationship between the rate constant and the temperature is not linear but it can be written in linear form by the use of logarithms (which we encountered in the conversion of transmittance to absorbance).