Question

The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is 1.0 × 10⁻³ s⁻¹ and the activation energy E_a = 11.488 kJ mol⁻¹, the rate constant at 200 K is ______ × 10⁻⁵ s⁻¹ (Round off to the nearest integer) (Given R = 8.314 JK⁻¹ mol⁻¹).

Answer 1

The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is 1.0 × 10⁻³ s⁻¹ and the activation energy E_a = 11.488 kJ mol⁻¹, the rate constant at 200 K is 10 × 10⁻⁵ s⁻¹.

Explanation:

Given: k₁ = 1.0 × 10⁻³ s⁻¹ at T₁ = 300 K

T₂ = 200 K

E_a = 11.488 kJ mol⁻¹

R = 8.314 J K⁻¹mol⁻¹

`log  k_2/k_1 = E_a/(2.303 R) (1/T_1 - 1/T_2)`

`log  k_2/10^-3 = 11488/(2.303 xx 8.314) (1/300 - 1/200)`

= `11488/19.15 (1/300 - 1/200)`

= `600 xx ((2 - 3)/600)`

= `600 xx (-1/600)`

= 600 × 0.0016

= −0.96

`log  k_2/10^-3 = -1`

⇒ `k_2/10^-3 = 10^-1`

⇒ k₂ = 10⁻¹ × 10⁻³

k₂ = 10⁻⁴

⇒ k₂ = 10  × 10⁻⁵ s⁻¹

∴ The rate constant at 200 K is 10 × 10⁻⁵ s⁻¹

So, the required value of x = 10.