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

Options

A. 77.78 min
B. 78.34 min
C. 84.36 min
D. 65.34 min

Explanation

Here,`a=100,a-x=100-30=70and t=40min`
`k(2.303)/(t)"log"(a)/((a-x))=(2.303)/(40min)"log"(100)/(70)`
`=(2.303)/(40)"log"(10)/(7)=(2.303)/(40)"log"1.428`
`k(2.303)/(40)xx0.1548=8.91xx10^(-3)min^(-1)`
`t_(1//2)=(0.693)/(k)=(0.696)/(8.91xx10^(-3)"min"^(-1))`
`t_(1//2)77.78min`