# Variation of the rate constant with temperature for the first-order reaction

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Variation of the rate constant with temperature for the first-order reaction:
$$\displaystyle{2}{N}_{{2}}{O}_{{5}}{\left({g}\right)}\to{2}{N}_{{2}}{O}_{{4}}{\left({g}\right)}+{O}_{{2}}{\left({g}\right)}$$
is given in the following table. Determine graphically the activation energy for the reaction.
$$\begin{array}{|l|l|}\hline T(K)&K(s^{-1})\\\hline298&1.74\cdot10^{-5}\\\hline308&6.61\cdot10^{-5}\\\hline318&2.51\cdot10^{-4}\\\hline328&7.59\cdot10^{-4}\\\hline338&2.40\cdot10^{-3}\\\hline\end{array}$$

2021-03-13

Plot a graph of lnk vs $$\displaystyle{\frac{{{1}}}{{{T}}}}$$ with the help ofdata given such that u get a slope which is equal to $$\displaystyle{\frac{{-{E}_{{a}}}}{{{R}}}}$$
Then plot a graph like this:

according to the equation
$$\displaystyle{\ln{{k}}}={\left({\frac{{-{E}_{{a}}}}{{{R}}}}\right)}{\left({\frac{{{1}}}{{{T}}}}\right)}+{\ln{{A}}}$$
sloope $$\displaystyle={\left({\frac{{-{E}_{{a}}}}{{{R}}}}\right)}$$
$$\displaystyle{E}_{{a}}=$$ -slope $$\cdot R$$

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