Question

A substance decomposes by following first order kinetics. If 50% of the compound is decomposed in 120 minutes, how long will it take for 90% of the compound to decompose?

Answer 1

Given: Following is a first-order reaction.

(t_1/2) half-life of a reaction = 120 min

To Find: The time required to complete 90% of the reaction = ?

Calculation: Let the reaction constant be K

Initial concentration [R₀]

Now calculating constant K

k = `0.693/t_(1/2)`

k = `0.693/120`

K = 0.005775 min⁻¹

Now time required to complete 90% of the reaction

Final concentration = [R₀] − 0.9[R₀]

= 0.1[R₀]

Now

K = `2.303/t log  [R_0]/(0.1[R_0])`

t = `2.303/0.0058 log [1/0.1]`

= `2.303/0.005775 log (10)`

= `2.303/0.005775 xx 1`

= 398.8 min

= 399 min

∴ The time required to complete 90% of reaction = 399 min