The rate of a chemical reaction doubles when its temperature is increased from 300 K to 310 K . Which of the following expressions correctly represents the activation energy ( E_a ) of the reaction in J mol ⁻¹ ? (where R is the universal gas constant)

Step-by-step solution

Given that the rate of reaction doubles, the ratio of rate constants k₂ k₁ = 2 . Initial temperature, T₁ = 300 K Final temperature, T₂ = 310 K Using the Arrhenius equation for two different temperatures: ( k₂ k₁ ) = E_a 2.303 R ( T₂ - T₁ T₁ T₂ ) Substituting the given values: (2) = E_a 2.303 R ( 310 - 300 300 310 ) (2) = E_a 2.303 R ( 10 300 310 ) Rearranging to solve for E_a : E_a = 2.303 R 300 310 2 10 Answer: 2.303 R 300 310 2 10