What is the slope of the straight line for the graph drawn between $\ln k$ and $\frac{1}{T}$, where $k$ is…
What is the slope of the straight line for the graph drawn between $\ln k$ and $\frac{1}{T}$, where $k$ is the rate constant of a reaction at temperature $T$ ?
$\frac{-E_a}{2.303 R}$
$\frac{-E_a}{R}$
$\frac{E_a}{R}$
$\frac{R}{E_a}$
Solution
Arrhenius equation is
$k=A e^{-E_a / R T}$
On taking log both sides,
$\ln k=\ln A-\frac{E_a}{R T}$
or $\quad \ln k=-\frac{E_a}{R T}+\ln A$
Since, the reaction,
$y=m x+c$
when a graph is plotted between $\ln k$ and $\frac{1}{T}$ a straight line is obtained. The slope of the straight line is equal to $-\frac{E_a}{R}$.
