Question

The rate constant for the first order decomposition of a certain reaction is described by the equation

log k(s^-1) = 14.34 - (1.25 x 10⁴K)/T

(i) What is the energy of activation for the reaction? 

(ii) At what temperature will its half-life period be 256 min

Answer 1

The rate constant for the first order decomposition of a certain reaction is described by the equation

Comments

this answer is wrong please upload the correct one

Answer 2

Arrhenius equation is given by, 

k = Ae  -E_a/RT 

⇒ In k = In A - E_a/RT 

⇒ In k = Log A - E_a/RT 

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

The given equation is 

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

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

E_a/2.303RT  = 1.25 x 10⁴ K/T 

⇒ E_a  = 1.25 x 10⁴ K x 2.303 x R 

= 1.25 x 10⁴ K x 2.303 x 8.314 J K^-1 mol^-1 

= 239339.3 J mol^-1 (approximately) 

= 239.34 kJ mol^-1

Also, when t_1/2= 256 minutes, 

k = 0.693 / t_1/2 

= 0.693 / 256 

= 2.707 x 10^-3 min^-1 

= 4.51 x 10^-5 s^-1 

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

= 668.95 K 

= 669 K (approximately)