Share

# 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? - ISC (Arts) Class 12 - Chemistry (Theory)

ConceptOrder of a Reaction Problems Based on First Order Rate Equation and Half Life Period

#### 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

2014-2015 (March) (with solutions)
Question 2.2.2 | 2.00 marks
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.
S