Research into the influence of temperature

If the temperature is not a separate variable, a possible temperature coefficient is of little interest to us as it has many chances to be a function of all the rate variables concentrations, time, etc. 

When a model hypothesis is available, various modes of the expression of the rates-concentrations can be deduced. These expressions usually involve rate coefficients from elementary steps and, eventually, equilibrium constants. At this stage, Arrhenius law can be applied to the rate coefficients, with an activation energy for each. For the equihbrium constants, van t Hoffs law, which involves reaction enthalpy, can be applied and written as  

It is only after introducing these substitutions that the rate law according to the temperature can be obtained. Arrhenius law can thus be checked to see whether the theory is correct. If this is the case, a physics-based definition can be given to the temperature coefficient as a function of the activation energies and enthalpy of the elementary steps. 

If the temperature coefficient has several values according to the temperature, we will determine whether the changes in the Arrhenius curve correlate with a change of mode, especially a change in the rate-limiting steps with temperatirre. 

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