Calculating time requireed to complete a definite fraction of first order reaction : A first order reaction is `20%` complete in 10 minutes. Calculate the time taken for the reaction to go to `75%` completion.
Stratagy : First calculate the rate constant (k) using frist data and then calculate the required time to complete `75%` of the reaction by using the value of rate constant :

Explanation

According to Eq. `(4.22)` we have
`t_(f) = (2.303)/(k) log ((1)/(1-f))`
or `k= (2.303)/(t_(f)) log( (1)/(1-f))`
Substituting the values of `t_(f)(=10 min) and f(-20//100 or 0.2)`, we have
`k = (2.303)/(10 min) log ((1)/(1-0.2))`
`= (2.303)/(10 min) log ((1)/(0.8))`
`= 0.0223 min^(-1)`
Since rate constant dose not change as the reaction progresses, we can use its value to calculate the time takes for `75%` completion of the reaction. Let it be `t_(0.75)`,
`t_(0.75) = (2.303)/(0.0223 minj^(-1)) log ((1)/(1-0.75))`
`= 62.18` minutes .