Question

For a reaction, activation energy E_a = 0 and the rate constant at 200 K is 1.6 × 10⁶ s⁻¹. The rate constant at 400 K will be ______.

[Given that gas constant, R = 8.314 J K⁻¹ mol⁻¹]

Options

• 3.2 × 10⁶ s⁻¹

• 3.2 × 10⁴ s⁻¹

• 1.6 × 10⁶ s⁻¹

• 3.2 × 10³ s⁻¹

Answer 1

For a reaction, activation energy E_a = 0 and the rate constant at 200 K is 1.6 × 10⁶ s⁻¹. The rate constant at 400 K will be 1.6 × 10⁶ s⁻¹.

Explanation:

We know that

`k = A E^(-E_a//RT)`

For two temperatures:

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

If E_a = 0:

`ln (k_2/k_1) = 0`

⇒ `k_2/k_1 = 1`

So,

k₂ = k₁

k₁ ​= 1.6 × 10⁶ s⁻¹ at T₁ = 200 K

T₂ = 400 K

Since E_a = 0:

k₂ ​= 1.6 × 10⁶ s⁻¹