Question

The rate constant for the first-order decomposition of H₂O₂ is given by the following equation.
$log \ k = 14.2 - \frac{1.0 \times 10^4}{T} K$
Calculate $E_a$ for this reaction and rate constant k, if its half-life period be 200 minutes. (Given : R = 8.314 JK⁻¹mol⁻¹)

Answer 1

Arrhenius equation is given by,

k= Ae -Ea/RT  

⇒In k = In A - Ea/RT

⇒In k = Log A - Ea/RT

⇒ Log k = Log A - Ea/2.303RT         (i)

The given equation is

Log k = 14.34 - 1.25 104 K/T             (ii)

From equation (i) and (ii), we obtain

Ea/2.303RT  = 1.25 104 K/T  

⇒ Ea  =1.25 × 104K × 2.303 × R

= 1.25 × 104K × 2.303 × 8.314 J K - 1mol - 1

= 239339.3 J mol - 1 (approximately)

= 239.34 kJ mol - 1

 

Also, when t1/2= 256 minutes,

k = 0.693 / t1/2

= 0.693  256

= 2.707 × 10 - 3 min - 1

= 4.51 × 10 - 5s - 1

It is also given that, log k= 14.34 - 1.25 × 104K/T

= 668.95 K

= 669 K (approximately)