Question

Chemists commonly use a rule of thumb that an increase of 10 K in temperature doubles the rate of a reaction. What must the activation energy be for this statement to be true for a temperature increase from 25°C to 35°C?

Answer 1

Arrhenus equation k = A e^-Ea/RT

where k = rate of reaction

A = collision frequency

Ea = activation energy

R= universal gas constant = 8.314 J/K/mol

T = temperature

Arrhenius equation can be written as

In (k2/k1) = Ea/R (1/T1 - 1/T2)

Ea = R ln (k2/k1) / (1/T1 - 1/T2) -- Eq (1)

Given that rate of reaction is doubled when temperature raised from 25oC to 35oC.

Hence, Initial rate of rection = k1

Final rate of reaction k2 = 2k1

Initial temperature T1 = 25oC = 25 + 273 K = 298 K

Final temperature T2 = 25oC = 35 + 273 K = 308 K

substitute all these velues in eq (1),

Ea = R ln (k2/k1) / (1/T1 - 1/T2) -- Eq (1)

= (8.314 J/K/mol) [ In (2k1/k1)] / [(1/298 - 1/308)]

= 52882 J/mol

= 52.882 kJ/mol

Ea = 52.882 kJ/mol

Therefore, activation energy of the reaction = 52.882 kJ/mol