Question

calculate at room temperature: a) the ratio of the rate constants for two reactions that have the same pre-exponential value but have activation energies that differ by 40.0 kJ/mole b) the difference in the activation energies (Ea1-Ea2) when the first reaction has a pre-exponential value that is 5 times the pre-exponential value of the second reaction and where the rate constant of the first reaction is 100 times larger than the rate constant of the second reaction.

Answer 1

a) k = A e^-Ea/RT

k1= A e^-Ea1/RT

k2=   A e^-Ea2/RT   

k1/k2 =  A e^-Ea1/RT / A e^-Ea2/RT   

= e^{-(Ea1-Ea2)/RT}

= e^-40000 J/(8.314 J/K/mol) (298)

= 9.73 x10^-8

k1/k2 = 9.73 x10^-8

b) Given that

A1= 5A2

k1 = 100 k2

k1= A1 e^-Ea1/RT

k2=   A2 e^-Ea2/RT   

k1/k2 =  A1 e^-Ea1/RT / A2 e^-Ea2/RT   

100k2/k2 = 5A2 e^{-(Ea1-Ea2)/RT} /A2

100 = 5 e^{-(Ea1-Ea2)/RT}

20 = e^{-(Ea1-Ea2)/(8.314) (298)}

On solving,

Ea1-Ea2 = -7422.1 J/mol