A first order reaction takes 40 min for `30%` decomposition. Calculate `t_(1//2)`. (Given `log 7 =0.845)`

Options

A. 77.7 min
B. 52.5 min
C. 46.2min
D. 22.7 min

Answer

A

Explanation

30% decomposition means X = 30% of `R_(0)` of `R = R_(0) - 0.3 R_(0) = 0.7 R_(0)`
For first order, `k = (2.303)/(t) "log" ([R_(0)])/([R])`
`= (2.303)/(40) "log" (10)/(7) "min"^(-1) = 8.918 xx 10^(-3) "min"^(-1)`
`t_(1//2) = (0.693)/(k) = (0.693)/(8.918 xx 10^(-3) "min"^(-1)) = 77.7 "min"`