91Ó°ÊÓ

As per the Arrhenius concept, the rate of the reaction depends on the collision frequency, the activation energy, and the temperature.

\({\bf{Rate(R) = Z \times }}{{\bf{e}}^{{\bf{ - }}\frac{{{{\bf{E}}_{\bf{a}}}}}{{{\bf{RT}}}}}}\)

where, Z, \({{\bf{E}}_{\bf{a}}}\)_, and T are the collision frequency, activation energy, and temperature respectively.

Taking the logarithm on both the sides,

\({\bf{log}}\,{\bf{R = log}}\,{\bf{Z - 2}}{\bf{.303}}\frac{{{{\bf{E}}_{\bf{a}}}}}{{{\bf{RT}}}}\)

At different temperatures, say \({{\bf{T}}_{\bf{1}}}\), \({{\bf{T}}_{\bf{2}}}\)_, and \({{\bf{T}}_3}\); let the rate of the reaction is denoted by \({{\bf{R}}_{\bf{1}}}\), \({{\bf{R}}_{\bf{2}}}\) and \({{\bf{R}}_{\bf{3}}}\).

Thus, the equation becomes,

\(\begin{align}{}\log \,{R_1} = \log \,Z - 2.303\frac{{{E_a}}}{{R{T_1}}}\\\log \,{R_2} = \log \,Z - 2.303\frac{{{E_a}}}{{R{T_2}}}\\\log \,{R_3} = \log \,Z - 2.303\frac{{{E_a}}}{{R{T_3}}}\end{align}\)

Linear plot for reaction rates at different temperature is shown as:

Comparing this to the linear equation,

\({\bf{y = mx + c}}\)

where, m and c represent the slope and intercept in the graph. Herein, the slope gives the activation energy value

Hence, the slope of this linear plot will provide the value for the activation energy of the reaction.