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# The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.

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The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature.

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From Arrhenius equation, we obtain

log $$\frac{k_2}{k_1}$$ = $$\frac{E_a}{2.303R}$$ $$\Big(\frac{T_2 - T_1}{T_1T_2}\Big)$$

It is given that, k2 = 4k1

T1 = 293 K

T2 = 313 K

Therefore, log $$\frac{4k_1}{k_2}$$ = $$\frac{E_a}{2.303 \times 8.314}$$ $$\Big(\frac{313 - 293}{293 \times 313}\Big)$$

⇒ 0.6021 = $$\frac{20 \times E_a}{2.303 \times 8.314 \times 293 \times 313}$$

⇒ Ea = $$\frac{0.6021 \times 2.303 \times 8.314 \times 293 \times 313}{20}$$

= 52863.33 J mol-1

= 52.86 kJ mol-1

Hence, the required energy of activation is 52.86 kJ mol-1.

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