A first order reaction is 12.5 % completed in 20 minutes at 300 K. When same reaction is carried out at 315 K, it is 12.5% complete in 2.5 minute. What is the activation energy of reaction (in kcal/mol)? [Given : R = 2 cal/mol and ln 2 = 0.7 ]

Engineering

Chemistry

Arrhenius Equation

Question

A first order reaction is 12.5 % completed in 20 minutes at 300 K. When same reaction is carried out at 315 K, it is 12.5% complete in 2.5 minute. What is the activation energy of reaction (in kcal/mol)?
[Given : R = 2 cal/mol and ln 2 = 0.7 ]

None of these

26.46

35.38

17.69

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$\ln \frac{k_{2}}{k_{1}} = \ln (\frac{20}{2 .5}) = \frac{E_{a}}{R} [\frac{1}{300} - \frac{1}{315}]$

$E_{a} = \frac{(\ln 8) \times 2 \times 300 \times 315}{15} = 26 .46 kcal / mol$