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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

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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)

  Is there an error in this question or solution?
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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