Two first order reactions have half lives in the ratio 3:2. If `t_(1)` and `t_(2)` are the time periods for 25% and 75% completion for the first and second reactions respectiely find `t_(1):t_(2)`

Options

A. `0.311:1`
B. `0.420:1`
C. `0.273:1`
D. `0.119:1`

Answer

A

Explanation

1st:100% `overset(t_(1//2)=3)(to)50%overset(t_(1//2)=3)(to)25%2nd, 100%overset(t_(1//2)=2)(to)50%overset(t_(1//2)=2)(to)25%`
`impliesK_(1)xxt_(25)=2.303log(100/75)impliesK_(2)xxt_(75)=2.3031log(100/25)`
`((0.693/3))/((0.693/2))xx(t_(1))/(t_(2))=("log"4/3)/(log4),2/3xx(t_(1))/(t_(2)),2/3xx(t_(1))/(t_(2))=(log4-log3)/(log4),(t_(1))/(t_(2))=3/2xx((log4)/(log4)-(log3)/(log4))`
`=3/2xx(1-0.4771/0.6020)=3/2xx(1-0.7925)=3/2xx0.207475=0.311`