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# A First Order Reaction Takes 30 Minutes for 50% Completion. Calculate the Time Required for 90% Completion of this Reaction. - CBSE (Science) Class 12 - Chemistry

ConceptIntegrated Rate Equations Half-life of a Reaction

#### Question

A first order reaction takes 30 minutes for 50% completion. Calculate the time required for 90% completion of this reaction.

(log 2 = 0.3010)

#### Solution

For the given firstorder reaction, the rate constant for 50% completion is given by

k=2.303/t

Here,

t=Time taken for 50% completion=30 min

[R]o=Initial concentration of the reactant

[R]=Final concentration of the reactant

Let [R]0 be 100 and due to 50% completion of reaction, [R] will be 10050, i.e. 50.

Putting values in (i), we get

k=2.303/30

=2.303/30

For the same reaction, the time required for 90% completion of the reaction can be computed using the expression

k=2.303/t

Here,

[R]=Final concentration of reactant=10090=10

0.023=2.303/t

rArrt=2.303/0.023

=100.13

Therefore, the time required for 90% completion of the given firstorder reaction is 100.13 min.

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Solution A First Order Reaction Takes 30 Minutes for 50% Completion. Calculate the Time Required for 90% Completion of this Reaction. Concept: Integrated Rate Equations - Half-life of a Reaction.
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