Q. The rate constant for a reaction doubles when the temperature increases from 27°C to 37°C. The activation energy for this reaction is approximately:

जब तापमान 27°C से 37°C तक बढ़ जाता है तो प्रतिक्रिया के लिए दर स्थिरांक दोगुना हो जाता है। इस प्रतिक्रिया के लिए सक्रियण ऊर्जा लगभग है:

13.8 kJ/mol
13.8 केजे/मोल

27.6 kJ/mol
27.6 केजे/मोल

51.9 kJ/mol
51.9 केजे/मोल

103.8 kJ/mol
103.8 केजे/मोल

Using Arrhenius equation simplified:

\ln \frac{k_2}{k_1} = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Given:

k_2 = 2k_1

Temperatures in Kelvin:

T_1 = 27 + 273 = 300 K, \quad T_2 = 37 + 273 = 310 K

\ln 2 = \frac{E_a}{8.314} \left(\frac{1}{300} - \frac{1}{310}\right)

0.693 = \frac{E_a}{8.314} \times \frac{310 - 300}{300 \times 310} = \frac{E_a}{8.314} \times \frac{10}{93000} = \frac{E_a}{8.314} \times 1.075 \times 10^{-4}

E_a = \frac{0.693}{1.075 \times 10^{-4}} \times 8.314 = 5360 \times 8.314 = 44584 \text{ J/mol} \approx 44.6 \text{ kJ/mol}

Since 51.9 kJ/mol is closest and typically accepted value is ~50 kJ/mol for doubling every 10°C, answer is 51.9 kJ/mol.

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