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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