Calculate the half life of a first order reaction from their rate constants given below:

(i) 200 s^-1 (ii) 2 min^-1 (iii) 4 years^-1

Half life of first order reaction is, t_1/2 = ln2/K where t_1/2 is half life of first order reaction, K is rate constant of First order reaction.

(i) t_1/2 = ln2/200 s^-1

⇒ t_1/2 = 0.693/200 s^-1 (∵ ln2 = 0.693)

⇒ t_1/2 = 0.003465 sec.

(ii) t_1/2 = ln2/2 min^-1

⇒ t_1/2 = 0.693/2 min^-1 (∵ ln2 = 0.693)

⇒ t_1/2 = 0.3465 min

(iii) t_1/2 = ln2/4 year^-1

⇒ t_1/2 = 0.693/4 years ^-1 (∵ ln2 = 0.693)

⇒ t_1/2 = 0.17325 year.

Half life of 3 reactions are 0.003465 sec, 0.3465 min, 0.17325 year respectively.