Question

For a first order reaction, $A \longrightarrow B$, the reaction rate at reactant concentration of $0.01\, M$ is found to be $2.0 \times 10^{-5} \, mol \, \, L^{-1} s^{-1}$. The half-life period of the reaction is

• A. 220 s
• B. 30 s
• C. 300 s
• D. 347 s

Answer 1

Answer: (D)

347 s

Answer 2

For first order reaction,
\hspace20mm A \longrightarrow B
\hspace10mm rate = k x [A]
\hspace10mm Rate =2.0 \times 10^{-5} mol \, \, L^{-1} s^{-1}
\hspace10mm [A]=0.01 M
So, $2.0 \times 10^{-5}=k \times 0.01$
\hspace10mm k=\frac{2.0 \times 10^{-5}}{0.01} s^{-1}
\hspace10mm =2.0 \times 10^{-3} s^{-1}
For first order reaction,
\hspace10mm t_{1/2}=\frac{0.693}{k}
\hspace15mm =\frac{0.693}{2.0 \times 10^{-3}}
\hspace15mm =346.5 \approx 347 s