The rate of decomposition for CH3NO2 and C2H5NO2 can be given in terms of rate constant (in s^-1) K1 and K2, respectively. The energy of activation for these reactions is 152.30 and 171.39 kJ/mol and

Question

The rate of decomposition for CH3NO2 and C2H5NO2 can be given in terms of rate constant (in s^-1) K1 and K2, respectively. The energy of activation for these reactions is 152.30 and 171.39 kJ/mol and the frequency factors are 10^13 and 10^14 s^-1, respectively. The temperature (in °C) at which rate constant will be same for both decomposition reactions, is (R = 8.3 J/K-mol, ln 10 = 2.3)

Prashant Kotian · Accepted Answer

Correct answer: 0727. Setting K1 = K2 gives A1 e^(-Ea1/RT) = A2 e^(-Ea2/RT). Rearranging: A2/A1 = e^((Ea2 - Ea1)/RT). 10^14 / 10^13 = 10 = e^((171.39 - 152.30) × 1000 / 8.3T). Taking ln: ln 10 = 19090 / 8.3T. 2.3 = 19090 / 8.3T => T = 19090 / (8.3 × 2.3) = 19090 / 19.09 = 1000 K. Converting to Celsius: 1000 - 273 = 727°C. Therefore, correct answer is 0727.

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