Question

The time for half-life period of a certain reaction, $A \longrightarrow$ products is $1 h$. When the initial concentration of the reactant ' $A$ ' is $2.0 \,mol \,L ^{-1}$, how much time does it take for its concentration to come from $0.50$ to $0.25 \, mol \,L ^{-1}$, if it is a zero-order reaction?

• A. $4 h$
• B. $0.5 h$
• C. $0.25 h$
• D. $1 h$

Answer 1

Answer: (C)

Half-life for a zero-order reaction is given by
$ t _{1 / 2}=\frac{\left[ A _0\right]}{2 k } $
$ \text { [where }\left[ A _0\right]=\text { initial concentration of reactan }$
$ \Rightarrow k _0=\frac{[ A ]_0}{2 t _{1 / 2}}=\frac{2.0 \, mol \, L ^{-1}}{2 \times 1 \, h }=1.0 \, mol \, L ^{-1} \, h ^{-1}$
Rate constant for a zero-order reaction is given by
$ \left. k =\frac{1}{ t }\left[ A _0\right)-( A )\right] $
$ \Rightarrow t =\frac{1}{ k }\left[\left( A _0\right)-( A )\right] $
$ t =\frac{(0.50)-(0.25) \, mol \, L ^{-1}}{1 mol \, L ^{-1} \, h ^{-1}} $
$ \Rightarrow t =0.25 \, h$