A first order reaction takes 40 min for 30% decomposition. Calculate t 1/2 .

Question

Philoid · Accepted Answer

Given:

Time t = 40 min

When 30% decomposition is undergone, 70% is the concentration.

We know, time taken

Where, k- rate constant

[R]_° -Initial concentration

[R]-Concentration at time ‘t’

⇒

⇒ 258.23 = (2.303/k)

We know, Half-life t_1/2 = 0.693/k

Which can be written as, t_1/2 = 0.3010 × (2.303/k)

⇒ t_1/2 = 0.3010 × 258.23

⇒ t_1/2 = 77.72 min

A first order reaction takes 40 min for 30% decomposition. Calculate t1/2.