A substance X decomposes in solution following the first order kinetics Flask (I) contains 500 mL of 1 M solution of X and flask (II) contains `1.5` L of `0.8` M solution of X After 5 hours concentration of X in flask (I) becomes `0.25` M what will be the time for concentration of X in flask (II) to become `0.4` M

Options

A. `2.5` hours
B. `1.5` hours
C. `1.75` hours
D. unpredictable as rate constant is not given

Answer

A

Explanation

For flast (I)
`k=(2.303)/("5 hrs")"log"(1)/(0.25)=(2.303)/("5 hrs")log4`....(i)
For flask (II)
`k=(2.303)/(t)"log"(0.8)/(0.4)=(2.303)/(t)log2`....(ii)
From (i) and (ii)
`(1)/("5 hrs")log4=(1)/(t)log 2or (2log2)/("5 hrs")=(1)/(t)log2`
or `t=("5 hrs")/(2)=2.5` hours.