Influence of temperature. Activation energy

Values of the activation energy E are in J/kmol in the SI system but are usually quoted in kJ/kmol (or J/mol) using these values R must then be expressed as kJ/kmol K. For most reactions the activation energy lies in the range 50,000-250,000 kJ/kmol, which implies a very rapid increase in rate constant with temperature. Thus, for a reaction which is occurring at a temperature in the region of 100°C and has an activation energy of 100,000 kJ/kmol, the reaction rate will be doubled for a temperature rise of only 10°C. 

the complete rate equation for an irreversible reaction normally has the form  

Unfortunately, the exponential temperature term exp(- E/RT) is rather troublesome to handle mathematically, both by analytical methods and numerical techniques. In reactor design this means that calculations for reactors which are not operated isothermally tend to become complicated. In a few cases, useful results can be obtained by abandoning the exponential term altogether and substituting a linear variation of reaction rate with temperature, but this approach is quite inadequate unless the temperature range is very small. 

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