In a first order reaction, the concentration of the reactant decreases form `0.8 M` to `0.4 M` in `15 min`. The time taken for the concentration to change form `0.1 M` to `0.025 M` is

Options

A. 30 minutes
B. 60 minutes
C. `7.5` minutes
D. 15 minutes

Answer

A

Explanation

Decrease in concentration from `0.8M` to `0.4M` means that half of the reactant is consumed. Thus, `t_(1//2)=15` minutes. Decrease from `0.1M` to `0.025` involves two half-lives:
`0.1Moverset(t_(1//2))(rarr)0.05Moverset(t_(1//w))(rarr)0.025M`
Since `t_(1//2)` for a first order reaction is independent of concentration of reactant, the time taken will be
`2xxt_(1//2)`
`=2xx15` minutes
`=30` minutes.