Question

The rate of a reaction at 600 K is $7.5\times {10}^5$ times the rate of the same reaction at 400K. Calculate the energy of activation for the reaction.

• A. 129 KJ/mol
• B. 135 KJ/mol
• C. 113 KJ/mol
• D. none of these

Answer 1

Answer: (B)

135 KJ/mol

$k_{600}=7.5\times {10}^5\times {10}_{400}A{e}^{-E_a/R\times 600}=7.5\times {10}^5\times A{e}^{-E_a/400R}\left(\frac{-E_a}{600R}\right)=\ln (7.5\times {10}^5)+\left(\frac{-E_a}{400R}\right)\frac{E_a}{400R}-\frac{E_a}{600R}=13.5278\frac{1}{100R}\left[\frac{6E_a-4E_a}{24}\right]=13.5278E_a=13.5278\times 100R\times 12E_a=134964joules/mol{E}_a=135kJ/mol$