Precision in Measurements of Activation Energies

Precision in Measurements of Activation Energies. The value of the activation energy E may be calculated from a knowledge of the specific rate constants at two different temperatures. By rearranging the Arrhenius equation we have 

It can be seen that the precision of measurement of E will depend critically on the size of the temperature interval chosen. Thus if Ti — T2 = 10 C and the mean error in T and T2 is 0.2 C it will introduce an error of 2 per cent in E. In similar fashion, errors in measuring k and will be magnified by the factor 1/ln (feAi), so that if the reaction rate does not change appreciably over the temperature interval in question, this will cause enhanced errors in E, 

Increasing the interval to 20 C decreases this error by a factor of 2, but simultaneously it decreases the chances of observing with any accuracy a variation of E with temperature. Decreasing the interval, say, to 5°C, doubles this error and simultaneously increases the error in the last term, since this term contains a factor In Qc /ki in the denominator which becomes smaller as hi approaches k.  

If ki and ki can each be estimated to dbl per cent and their ratio is about 2 for a 10°C interval, then the error in E due to the last term in Eq. (IV.6C.2) will be about =fc2.0 per cent. 

To measure E over a 10 C interval to =h0.5 per cent will generally require a temperature error of less than 0.03 0 and a measurement of k and k to within zbO.3 per cent. This latter in turn will, as we have seen, require analytical precision of dbO.l per cent over an extended range of concentration changes. 

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