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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 : |
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Answer» 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 . |
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