# JEE Main & Advanced Chemistry Chemical Kinetics Arrhenius Equation

Arrhenius Equation

Category : JEE Main & Advanced

Arrhenius proposed a quantitative relationship between rate constant and temperature as,

$k=A\,{{e}^{-{{E}_{a}}/RT}}$                                                …..(i)

The equation is called Arrhenius equation.

In which constant  A is known as frequency factor. This factor is related to number of binary molecular collision per second per litre.

${{E}_{a}}$ is the activation energy.

T is the absolute temperature and

R is the gas constant

Both A and ${{E}_{a}}$ are collectively known as Arrhenius parameters.

Taking logarithm equation (i) may be written as,

$\log k=\log A-\frac{{{E}_{a}}}{2.303\,RT}$                                             …..(ii)

The value of activation energy $({{E}_{a}})$ increases, the value of k decreases and therefore, the reaction rate decreases.

When log k plotted against $1/T$,  we get a straight line. The intercept of this line is equal to log A and slope equal to $\frac{-{{E}_{a}}}{2.303\,R}$.

Therefore ${{E}_{a}}=-2.303\,R\times \text{slope}$.

Rate constants for the reaction at two different temperatures ${{T}_{1}}$ and ${{T}_{2}}$,

$\log \frac{{{k}_{2}}}{{{k}_{1}}}=\frac{{{E}_{a}}}{2.303R}\left[ \frac{1}{{{T}_{1}}}-\frac{1}{{{T}_{2}}} \right]$                                    …..(iii)

where ${{k}_{1}}$and ${{k}_{2}}$are rate constant at temperatures ${{T}_{1}}$ and ${{T}_{2}}$ respectively $({{T}_{2}}>{{T}_{1}})$.

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