The rate constant ( k ) of a reaction is measured at different...

The rate constant $( k )$ of a reaction is measured at different temperature $( T )$ , and the data are plotted in the given figure. the activation energy of the reaction in ${kJmol}^{- 1}$ is : $( R$ is gas constant)

The rate constant ( k ) of a reaction is measured at different temperature ( T ) , and the data are plotted in the

Options

A $2 / R$
B $1 / R$
C $R$
D $2R$

Correct answer

D. $2R$

Step-by-step solution

$k = {Ae}^{- Ea / RT}$
In $k = InA - \left(\dfrac{{E}_{a}}{R}\right)\dfrac{1}{T}$

In $k = InA - \left(\dfrac{{E}_{a}}{R \times {10}^{3}}\right)\dfrac{{10}^{3}}{T}$

Slope of graph

$= \dfrac{- {E}_{a}}{R \times {10}^{3}} = \dfrac{- 10}{5}$

${E}_{a} = 2R \times {10}^{3}J$

${E}_{a} = 2R \times kJ$

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