The rate constant of first-order reaction is 3 × 10–6 per second. The initial concentration is 0.10 M. The initial rate is:
Answer & explanation
Correct answer: option 1
To determine the initial rate of a first-order reaction, we can use the rate equation:
\[ \text{Rate} = k[A] \]
where:
\(\text{Rate}\) is the rate of the reaction,
\(k\) is the rate constant,
\([A]\) is the concentration of the reactant.
Given that the rate constant (\(k\)) is \(3 \times 10^{-6}\) per second and the initial concentration (\([A]_0\)) is \(0.10 \, \text{M}\), we can substitute these values into the rate equation to find the initial rate (\(\text{Rate}_0\)):
\[ \text{Rate}_0 = k \times [A]_0 \]
\[ \text{Rate}_0 = (3 \times 10^{-6} \, \text{per second}) \times (0.10 \, \text{M}) \]
\[ \text{Rate}_0 = 3 \times 10^{-7} \, \text{M} \, \text{s}^{-1} \]
Therefore, the correct answer is \((1) \, 3 \times 10^{-7} \, \text{M} \, \text{s}^{-1}\).