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A first order reaction is 20% complete i...

A first order reaction is 20% complete in 5 minutes. Calculate the time taken for the reaction to be 60% complete

Text Solution

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For first order reaction, `k = (2.303)/(t) log""(a)/(a-x)`
To calculate the first order rate constant,
At 20% completion, `a = 100, (a-x) = (100 - 20) = 80`
Rate constant, `k = (2.303)/("5 min") log""(100)/(80) = (2.303)/("5 min") log 1.25`
`= 0.4464 "min"^(-1)`
At 6% completion, a = 100, (a-x) = (100 - 60) = 40
Time taken for 60% completion, `t = (2.303)/(k)log""(100)/(40) = (2.303)/(0.0446 "min"^(-1)) log ""(100)/(40)`
`t = (2.303)/(0.0446 "min"^(-1)) log 2.5 = 20.53 "min"`
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