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 J mol⁻¹ K⁻¹)

Options

• 10

• 20

• 30

• 40

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:

`log  "K"_2/"K"_1 = "E"_"a"/(2.303 "R")[1/"T"_1 - 1/"T"_2]`

`log  (1.0 xx 10^-6)/"K"_1 = (11.488 xx 1000)/(2.303 xx 8.314) [1/200 - 1/300]`

`log  10^-3/"K"_1 = (6000 xx 3 - 2)/600`

`log  10^-3/"K"_1` = 1

10 = `10^-3/"K"_1`

K₁ = 10⁻⁴

So, x × 10⁻⁵ = 10⁻⁴

x = 10⁻⁴