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# A First Order Reaction Takes 20 Minutes for 25% Decomposition. Calculate the Time When 75% of the Reaction Will Be Completed. (Given : Log = 2 = 0·3010, Log 3 = 0·4771, Log 4 = 0·6021) - CBSE (Science) Class 12 - Chemistry

ConceptIntegrated Rate Equations First Order Reactions

#### Question

A first order reaction takes 20 minutes for 25% decomposition. Calculate the time when 75% of the reaction will be completed.

(Given : log = 2 = 0·3010, log 3 = 0·4771, log 4 = 0·6021)

#### Solution

For a first order reaction

t = 2.303/k log  [R]_0/[R]

k = 2.303/"20 min" log  100/(100 - 25)

= 2.303/"20 min" log 4/3

= 2.303/"20 min" (log 4 - log 3)

= 2.303/"20 min" (0.6021 - 0.4771)

= 1.44 x 10-2 min-1

The time when 75% of the reaction completed can be calculated as

t = 2.303/k log  100/(100 - 75)

= 2.303/(1.44 xx 10^(-2)) log 4

= 2.303/(1.44 xx 10^(-2)) (0.6021)

= 96.3 min (approximately)

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#### APPEARS IN

Solution A First Order Reaction Takes 20 Minutes for 25% Decomposition. Calculate the Time When 75% of the Reaction Will Be Completed. (Given : Log = 2 = 0·3010, Log 3 = 0·4771, Log 4 = 0·6021) Concept: Integrated Rate Equations - First Order Reactions.
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