Explain the effect of an increase in temperature on the rate of reaction and the rate constant.

(N/A) Most chemical reactions are accelerated by an increase in temperature.
Example: In the decomposition of $N_{2}O_{5}$,the time taken for half of the original amount of material to decompose is as follows:

Temperature	$50^{\circ}C$ | $25^{\circ}C$ | $0^{\circ}C$
$t_{1/2}$	$12 \ min$ | $5 \ h$ | $10 \ d$

The temperature dependence of the rate of a chemical reaction can be accurately explained by the Arrhenius equation:
$k = A e^{-\frac{E_{a}}{RT}}$
Where $k$ is the rate constant,which is proportional to the rate of reaction.
$A$ is the Arrhenius factor or frequency factor (also called the pre-exponential factor),which is a constant specific to a particular reaction.
$R$ is the gas constant $(8.314 \ J \ K^{-1} \ mol^{-1})$.
$E_{a}$ is the activation energy $(J \ mol^{-1})$.
Taking the natural logarithm of both sides of the equation:
$\ln k = -\frac{E_{a}}{RT} + \ln A$ or $\log k = -\frac{E_{a}}{2.303 RT} + \log A$
From the equation,$\ln k \propto \frac{1}{T}$.
An increase in temperature leads to an increase in the rate of reaction and an exponential increase in the rate constant.