Temperature on Precision

Influence of Temperature on Precision. The dominant variable in a reaction is the temperature. Thus to measure k with any precision, the temperature must be controlled fairly accurately. We can calculate the influence of temperature from the differential form of the Arrhenius equation  

For most reactions in their experimentally accessible range E/RT is found to be about 35. Thus to reduce the expected error in k to 0.1 per cent, T must be known to be about 0.003 per cent. For T = 300°K (room temperature) this means a precision of 0.01 C, and for T = 600°K a control of 0.02°C (something well nigh impossible experimentally at 600 K). 

To reduce the error in k to 1.0 per cent, T must be known to 0.1 C at 300°K (practical) and to 0.2°C at 600°K (difficult). This places a lower limit on the precision with which reaction rates may be measured at the higher temperatures. Above 600°K it is difficult to obtain temperature control to better than 1 C with a consequent error of 5 per cent in fc, which in turn means about a 7 to 10 per cent error in E (for a 20 C interval). 

This does not imply, however, that there may not exist gradients of the order of magnitude of a few degrees in gas-reaction vessels containing a fast reaction sufficiently endo- or exothermic. Only direct experiments can justify such assumptions.  

In the case of liquid systems the solvent is able to act as an effective thermostat because it usually exceeds the quantity of reactants in a mole ratio of from 100 to 1000 or more.  

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