Chemical Kinetics - Result Question 54
####55. The temperature dependence of rate constant $(k)$ of a chemical reaction is written in terms of Arrhenius equation, $k=A e^{-E_a^{} / R T}$. Activation energy $(E_a^{})$ of the reaction can be calculated by plotting
[2003]
(a) $\log k$ vs $\frac{1}{\log T}$
(b) $k$ vs $T$
(c) $k$ vs $\frac{1}{\log T}$
(d) $\log k vs \frac{1}{T}$
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Solution:
(d) $k=A e^{-E_a / R T}$
or $\log T=\log A-\frac{E_a}{2.303 R T}$
Comparing the above equation with $y=m x+c$
$y=\log k, x=\frac{1}{T}$
Thus a plot of $\log _{10} k vs 1 / T$ should be a straight line, with slope equal to $-E_a / 2.303 R$ and intercept equal to $\log A$
or $E_a=-2.303 R \times$ Slope
