\(A \rightarrow\) Product ;

given \(t_{1 / 2}=1\,hr\)

for a zero order reaction

\(t_{\text {completion}}=\frac{\left[A_{0}\right]}{k}=\frac{\text {initial} \,\operatorname{conc}}{rate\, {\text{on}}\,{\text{ stant}}}\)

\(\therefore \) \(t_{1 / 2}=\frac{\left[A_{0}\right]}{2 K}\)

or \( k=\frac{\left|A_{0}\right|}{2 t_{1 / 2}}=\frac{2}{2 \times 1}=1\,mol\,lit\)  \(^{-1}\, h r^{-1}\)

Further for a zero order reaction

\(k=\frac{d x}{d t}=\frac{\text { change in concentration }}{\text {time}}\)

\(I=\frac{0.50-0.25}{time}\)

\(\therefore \) time \(=0.25\, h r\)