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 For the first order reaction \mathrm{X \rightarrow Y+Z} carried out at \mathrm{127^{\circ} \mathrm{C}}. If \mathrm{1.9 \times 10^{-16} \%} of the reactant molecules exist in the activated state, the activation energy of the reaction is almost?

Option: 1

135.7\, \mathrm{kJmol}^{-1}


Option: 2

100\, \mathrm{kJmol}^{-1}


Option: 3

150\, \mathrm{kJmol}^{-1}


Option: 4

175.8\, \mathrm{kJmol}^{-1}


Answers (1)

best_answer

e^{-\frac{E_{a}}{R T} }\times 100=1.9 \times 10^{-16}
e^{-\frac{E_{a}}{R T} }=1.9 \times 10^{-18}

-\frac{E_{a}}{R T} =\ln 1.9-18 \ln 10

\mathrm{E_{a} =(18 \times 2.303-\ln 1.9) 8.314 \times 400 \mathrm{~K} }
\mathrm{E_{a} =135724.8 \, \mathrm{Jmol}^{-1} }

\mathrm{E_{a} =135.7\, \mathrm{kJmol}^{-1} }

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Nehul

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