Question

We know that for a given reaction when the temperature increases from 100 k to 200 k the rate constant doubles. What is the activation energy in kj/mol

Answer 1

Answer:

The activation energy of the reaction is 1.152 kJ/mol.

Explanation:

Activation energy is the minimum amount which is absorbed by the reactant molecules to undergo chemical reaction.

Initial temperature of reaction = $T_1=100 K$

Final temperature of reaction = $T_2=200 K$

Initial rate of the reaction at 100 k = $K_1=k$

Final rate of the reaction at 200 k = $K_2=2k$

Activation energy is calculated from the formula:

$\log\frac{K_2}{K_1}=\frac{E_a}{2.303\times R}(\frac{T_2-T_1}{T_1T_2})$

R = Universal gas constant = 8.314 J/ K mol

$\log\frac{2k}{k}=\frac{E_a}{2.303\times 8.314 J/K mol}(\frac{200 K-100K}{200 K\times 100K})$

$E_a=1,152.772 J/mol=1.152 kJ/mol$