Question

In the Arrhenius equation for a first order reaction, the values of ‘A’ of ‘E_a’ are 4 × 10¹³ sec⁻¹ and 98.6 kJ mol⁻¹ respectively. At what temperature will its half life period be 10 minutes?

[R = 8.314 J K⁻¹ mol⁻¹]

In the Arrhenius equation for a certain reaction, the value of A and E_a (activation energy) are 4 × 10¹³ sec⁻¹ and 98.6 kJ mol⁻¹ respectively. If the reaction is of first order, at what temperature will its half-life period be ten minutes?

Answer 1

The value of k, corresponding to t_1/2 = 10 min = 600 s, is given by

k = `0.693/t_(1//2)`

= `0.693/600`

= 1.155 ×10⁻³ s⁻¹.

Given that A = 4 × 10¹³ sec⁻¹ and E_a = 98.6 kJ mol⁻¹.

According to the Arrhenius equation,

k = `e^(-E_a//RT)`

Taking logarithm, we get

log_e k = `log_e A - E_a/(RT)`

or, log₁₀ k = `log_10 A - E_a/(2.303 RT)`

Substituting the values, we get

log10 1.155 × 10⁻³ = `log_10 4 xx 10^13 - 98.6/(2.303 xx 8.314 xx 10^-3 xx 7`

or, −2.9374 = `13.6021 - 5149.6/7`

or, `5149.6/T` = 13.6021 + 2.9374 = 16.5395

or, T = `5149.6/16.5395`

= 311.35 K