Consider the following plots of log of rate constant k( k) vs 1 ~T...

Consider the following plots of log of rate constant

\mathrm{k}(\log \mathrm{k})

\frac{1}{\mathrm{~T}}

for three different reactions. The correct order of activation energies of these reactions is
Consider the following plots of log of rate constant k( k) vs 1 ~T for three different reactions. The correct order of

Consider the following plots of log of rate constant k( k) vs 1 ~T for three different reactions. The correct order of

Options

A $\mathrm{Ea}_2 \gt \mathrm{Ea}_1 \gt \mathrm{Ea}_3$
B $\mathrm{Ea}_1 \gt \mathrm{Ea}_3 \gt \mathrm{Ea}_2$
C $\mathrm{Ea}_1 \gt \mathrm{Ea}_2 \gt \mathrm{Ea}_3$
D $\mathrm{Ea}_3 \gt \mathrm{Ea}_2 \gt \mathrm{Ea}_1$

Correct answer

A. $\mathrm{Ea}_2 \gt \mathrm{Ea}_1 \gt \mathrm{Ea}_3$

Step-by-step solution

\begin{aligned}<br />& \mathrm{K}=\mathrm{A} \mathrm{e}^{-\mathrm{E} a \mathrm{RT}} \\<br>& \operatorname{logk}=\log \mathrm{A}-\frac{\mathrm{Ea}}{2.303 \mathrm{RT}}<br />\end{aligned}

For graph between logk with

\frac{1}{\mathrm{~T}}

\mid \text{ Slope\text{ of } curve } \left\lvert\,=\frac{\mathrm{Ea}}{2.303 \mathrm{R}}\right.

From given graph
Magnitude of slope

\Rightarrow(2) \gt (1) \gt (3)

Hence \mathrm{Ea}_2

\gt

\mathrm{Ea}_1 \gt \mathrm{Ea}_3$

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