The rate of a reaction becomes four times when the temperature changes from 293 K to 313 K. Calculate the energy of activation (Ea) of the reaction assuming that it does not change with temperature. [R = 8.314 J/K mol-1, log4 = 0.6021]

We can use the Arrhenius equation in the form:

log(K2/K1) = Ea / (2.303R) * (1/T1 - 1/T2)

where:

• K1 and K2 are the rate constants at temperatures T1 and T2 respectively.
• Ea is the activation energy.
• R is the gas constant (8.314 J/K mol-1).
• T1 and T2 are the temperatures in Kelvin.

Given that the rate of reaction becomes four times, we have K2/K1 = 4. We are given T1 = 293 K and T2 = 313 K. Substituting these values into the equation, we get:

log(4) = Ea / (2.303 * 8.314) * (1/293 - 1/313)

0.6021 = Ea / (19.147) * (0.00341 - 0.00319)

0.6021 = Ea / (19.147) * (0.00022)

Ea = (0.6021 * 19.147) / 0.00022

Ea = 52863 J/mol

Converting to kJ/mol:

Ea = 52.863 kJ/mol