viii. The rate constant for the first order reaction is given by log10 k = 14.34 – 1.25 × 104 T. Calculate activation energy of the reaction. (239.3 kJ/mol)
The given rate constant equation is
log10k = 14.34 – 1.25 × 104 T ...(1)
Arrhenius equation is
k = "Ae"^((-Ea)/(RT))
Therefore, In k = In A - (Ea)/(2.303 RT) ...(2)
Comparing (1) and (2),
(Ea)/(2.303 RT) = 1.25 × 104 T
Therefore, (Ea)/(2.303 R) = 1.25 × 104
Therefore, (Ea)/(2.303 × 8.314) = 1.25 × 104
Therefore, Ea = 1.25 × 104 × 2.303 × 8.314 = 239339 K mol-1 = 239.3 kJ mol-1
The energy of activation of the reaction is 239.3 kJ mol-1