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Q.

The rate constant of a reaction increases by five times on increase in temperature from $27^{0} C$ to $52^{0} C$ . The value of activation energy in kJ mol^-1 is____ (rounded-off to the nearest integer). [R=8.314 J K^-1mol^-1]

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answer is 52.

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Detailed Solution

$T_{1} = 300 K, T_{2} = 325 K, K_{2} = 5 K,$

$\begin{aligned} \ln \frac{K_{2}}{K_{1}} = \frac{E_{a}}{R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}] \\ or, \ln 5 = \frac{Ea}{8.314} [\frac{1}{300} - \frac{1}{325}] \\ or, E_{a} = 0.7 \times 2.303 \times 8.314 \times 12 \times 325 \\ = 52271 J = 52.271 kJ \end{aligned}$

Nearest integer answer will be 52 kJ

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The rate constant of a reaction increases by five times on increase in temperature from 270C to 520C . The value of activation energy in kJ mol-1 is____ (rounded-off to the nearest integer). [R=8.314 J K-1mol-1]