Question

The specific rate constant for a particular reaction is 2.34 × 10⁻³ mol L⁻¹ s⁻¹ at 370 K and 7.50 × 10⁻² mol L⁻¹ s⁻¹ at 400 K. Calculate the activation energy for the reaction. (R = 8.314 JK⁻¹ mol⁻¹).

Answer 1

To calculate the activation energy (E_a​) of a reaction using the rate constants at two different temperatures, you can apply the Arrhenius equation in its two-point form:

`ln(k_2/k_1) = E_a/R (1/T_1 - 1/T_2)`

Where:

k₁ = 2.34 × 10⁻³ mol L⁻¹ s⁻¹ at T₁ = 370 K

k₂ = 7.50 × 10⁻² mol L⁻¹ s⁻¹ at T₂ = 400 K

R = 8.314 J K⁻¹ mol⁻¹

∴ `ln((7.50 xx 10^-2)/(2.34 xx 10^-3)) = E_a/8.314 (1/370 - 1/400)`

∴ `ln(32.05) = E_a/8.314 ((400 - 370)/(370 xx 400))`

∴ `ln(32.05) = E_a/8.314 ((30)/(148000))`

∴ `3.467 = E_a/8.314 xx 2.027 xx 10^-4`

`E_a = (3.467 xx 8.314)/(2.027 xx 10^-4)`

= `28.83/(2.027 xx 10^-4)`

= 142228 J/mol

E_a = 142.2 kJ/mol