A first order reaction is 25% completed in 20 minutes at 300 K. When same reaction is carried out at 320 K, it is 25% complete in 5 minute. What is the activation energy of reaction (in kJ/mol)? [Take : R = 8 J/K mole and ln 2 = 0.7 ]

Engineering

Chemistry

Arrhenius Equation

Question

A first order reaction is 25% completed in 20 minutes at 300 K. When same reaction is carried out at 320 K, it is 25% complete in 5 minute. What is the activation energy of reaction (in kJ/mol)?

[Take : R = 8 J/K mole and ln 2 = 0.7 ]

13.44 kJ

26.88 kJ

None of these

53.76 kJ

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$\ln \frac{k_{2}}{k_{1}} = \ln (\frac{20}{5}) = \frac{E_{a}}{R} [\frac{1}{300} - \frac{1}{320}]$

$E_{a} = \frac{(\ln 4) \times 8 \times 300 \times 320}{20} = 53 .76 kJ$