Question: 88: For a first order reaction \mathrm{A} \rightarrow Products, initial concentration of A is 0.1 M , which becomes 0.001 M after 5 minutes. Rate constant for the reaction in \min ^{-1} is
(1) 0.4606
(2) 0.2303
(3) 1.3818
(4) 0.9212
Answer: Option (4)
Explanation:
For a first order reaction, the rate constant is given by the integrated rate law
k=\frac{2.303}{t}\log\frac{[A]_0}{[A]_t}Here, the initial concentration is [A]_0=0.1\ \mathrm{M}, the concentration after time t is [A]_t=0.001\ \mathrm{M}, and the time is t=5\ \mathrm{min}.
Substituting the values,
k=\frac{2.303}{5}\log\frac{0.1}{0.001} k=\frac{2.303}{5}\log 100 k=\frac{2.303}{5}\times 2 k=0.9212\ \min^{-1}Therefore, the rate constant for the reaction is 0.9212\ \min^{-1}.