#### 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?

#### Solution

Given: Following is a 1st order reaction.

`(t_"1/2")` half-life of a reaction = 120 min

To Find :

The time required to complete 90% of the reaction

Solution:

Let the reaction constant be K

Initial concentration [`R_0`]

Now calculating constant K

`K = 0.693/t_"1/2"`

`K = 0.693/120`

`K =0.0058 "min"^"-1"`

Now time required to complete 90% of the reaction

Final concentration = `[R_0] - 0.9[R_0]`

`= 0.1[R_0]`

Now

`K = 2.303/t log [R_0]/(0.1[R_0])`

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

`t = 2.303/0.0058`

t = 397.06 min

time required to complete 90% of reaction = 397.06 min

Is there an error in this question or solution?

#### APPEARS IN

Solution 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? Concept: Order of a Reaction - Problems Based on First Order Rate Equation and Half Life Period.