Question

The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction at 25°C are 3.0 × 10⁻⁴ s⁻¹, 104.4 kJ mol⁻¹ and 6.0 × 10¹⁴ s⁻¹ respectively. The value of rate constant at \[\ce{T -> \infty}\] is ______.

Options

• 2.0 × 10¹⁸ s⁻¹

• 6.0 × 10¹⁴ s⁻¹

• infinity

• 3.6 × 10³⁰ s⁻¹

Answer 1

The rate constant, the activation energy and the Arrhenius parameter of a chemical reaction at 25°C are 3.0 × 10⁻⁴ s⁻¹, 104.4 kJ mol⁻¹ and 6.0 × 10¹⁴ s⁻¹ respectively. The value of rate constant at \[\ce{T -> \infty}\] is 6.0 × 10¹⁴ s⁻¹.

Explanation:

Given: Rate constant at 25°C (298 K): k = 3.0 × 10⁻⁴ s⁻¹

Activation energy: E_a = 104.4 kJ mol⁻¹

Arrhenius pre-exponential factor: A = 6.0 × 10¹⁴ s⁻¹

\[\ce{T -> \infty}\]

The Arrhenius equation is given as:

\[\ce{k = A e^{-Ea​/RT}}\]

As \[\ce{T -> \infty}\], the exponent:

\[\ce{\frac{E_a}{RT} -> 0}\]

⇒ \[\ce{e^{-Ea​/RT}}\]

→ e⁰ = 1

So,

\[\ce{\underset{T -> \infty}{lim} k = A}\]

= 6.0 × 10¹⁴ s⁻¹