The measured rate constant of a certain reaction is 53 M^-1 S^-1 at a temperatur

Question

The measured rate constant of a certain reaction is 53 M^-1 S^-1 at a temperature of 25 degree C and 9594 M^-1 S^-1 a temperature of 100 degree C. The gas constant is 8.314 J mol^-1 K^-1. The Arrhenius equation for the of the rate constant on the temperature is ln(k_2/k_1) = (E_a/R) (l/T_1 - 1/T_2). The gas constant J mol^-1 K^-1. The activation energy of the reaction is: 9.3 10^2 J mol^-1 1.4 10^3 J mol^-1 7.7 10^3 J mol^-1 2.8 10^4 J mol^-1 4.4 10^4 J mol^-1 6.4 10^4 J mol^-1 1.1 10^5 J mol^-1 None of the above; the correct activation energy is _____ J mol^-1

Explanation / Answer

K = 53 T = 25° = 298

K = 9594 T = 100|C = 373

R = 8.314

Apply ahrrenius for Ea

ln(K2/K!) = E/R*(1/T1-1/T2)

ln(9594/53) = E/8.314*(1/295 - 1/373)

E = ln(9594/53)*8.314 / ((1/295 - 1/373))

E = 60972.3275 J/mol

E = 6.1*10^4

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