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A first order reaction takes 20 minutes ...

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, log3 = 0.4771 log4 = 0.6021 )

Text Solution

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A first order reaction takes 20 minutes for 25% decomposition.
`thereforek=(2.303)/(20)log(([A]_(0))/(0.75[A]_(0)))=(2.303)/(20)log((4)/3)`
`=(2.303)/(20)(log4-log3)`
`=(2.303)/(20)(0.6021-0.4771)=(2.303xx0.125)/(20)`
= `0.01439 min^(-1)`
Therefore , for 75% completion,
`t=(2.303)/(0.1439)log(([A]_(0))/(0.25[A]_(0)))=(2.303)/(0.01439)log4`
`=(2.303xx0.6021)/(0.01439)=96.36min`
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