Question

On the basis of Arrhenius equation, how would you determine the temperature coefficient of a reaction?

Answer 1

The temperature coefficient of a chemical reaction is defined as the ratio of the rate constant of a reaction at two different temperatures separated by 10°C. The two temperatures generally taken are 35°C (308 K) and 25°C (298 K).

Thus,

\[\ce{Temperature coefficient = \frac{k_{35^\circ C}}{k_{25^\circ C}}}\]

In general, \[\ce{Temperature coefficient = \frac{k_t + 10^\circ}{k_{t^\circ}}}\]

Where:

k_T = rate constant at temperature T

k_T + 10 = rate constant at temperature T + 10

The Arrhenius equation is

\[\ce{k = A e^{-E_a/(RT)}}\]

Take the ratio of rate constants at T and T + 10:

\[\ce{\frac{k_T + 10^\circ}{k_{T^\circ}} = \frac{Ae^{-E_a/R(T + 10)}}{Ae^{-E_a/RT}}}\]

= \[\ce{e^{\frac{E_a}{R}(\frac{1}{T} - \frac{1}{T + 10})}}\]

Now simplify:

\[\ce{Temperature coefficient = exp (\frac{E_a * 10}{RT(T + 10)})}\]

This expression shows that the temperature coefficient depends on

Activation energy E_a

Absolute temperature T