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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