# According to the Arrhenius equation, how does temperature affect the rate constant?

May 8, 2016

#### Answer:

The Arrhenius equation provides a relationship between the rate constant $k$ and temperature $T$.

#### Explanation:

The Arrhenius equation provides a relationship between the rate constant $k$ and temperature $T$.

The Arrhenius equation is: $k = z p {e}^{- \frac{E a}{R T}}$

where,
$k$ is the rate constant,
$z$ is the collision factor,
$p$ is the steric factor,
$E a$ is the activation energy,
$R = 8.3245 \frac{J}{m o l . K}$ is the ideal gas constant
and $T$ is the temperature.

The activation energy by definition, is the minimum energy (or threshold energy) required for two particles of reactants upon collision to form products.

The Arrhenius equation could also be written as: $k = A {e}^{- \frac{E a}{R T}}$,

where, $A = z p$ is the Arrhenius factor.

Taking the natural logarithm of both parties, we get:

$\ln k = - \frac{E a}{R} \left(\frac{1}{T}\right) + \ln A$

Assuming that $A$ is independent of temperature, when $T$ is increased, the equilibrium constant $k$ will also increase and therefore, the rate of the reaction will also increase .

Here is a video that fully explain this topic:
Chemical Kinetics | A Model for Chemical Kinetics & Catalysis.