Half life period of first order reaction is 20 minutes. How long will it take to 75% completion?

CONCEPT:

• Half-life: The half-life of a chemical reaction can be defined as the time taken for the concentration of a given reactant to reach 50% of its initial concentration. It is denoted by the symbol ‘t1/2’ and is usually expressed in seconds.
• The half life period of first order reaction may be calculated as given below:

​N = N0 / 2n

Where, n = no. of half-lives

n  = Total time (t) / Half-life period (t½)

N0 = Initial concentration of the substance           

N = Amount of radioactive substance left after n- half-live

Calculations:

Given:  t½ = 20 min ; Let N0 = x ;

After completion 75% remaining amount of reactant

N = 25% of x = x / 4

To find: t =?

We know, N = N0 / 2n

 ⇒ x / 4 = x / 2n

 ⇒ 2n = 4   (·.· 22 = 4)

 ⇒  n = 2 

Also, n = Total time (t) / Half-life period (t½)

⇒ 2 = t / 20

⇒ t = 40 min

Hence, first order reaction takes 40 minutes to 75% completion.