The following reaction has a rate constant of 3.7 × 10^–3 M•s^–1 at 25°C:
A → B + C
Calculate the concentration of C after 2.7 × 10^–3 sec where [A]₀ was 0.750 M at 25°C; assume [C]₀ = 0 M.

• A. 0.75 M
• B. 9.99×10^–6 M
• C. 3.7×10^–3 M
• D. 7.5×10^–6 M

Answer: (B)

Verified step by step guidance

1. Identify the type of reaction: The given reaction A → B + C is a first-order reaction because the rate constant is given in units of M•s–1, which is typical for first-order reactions.
2. Write the integrated rate law for a first-order reaction: The integrated rate law for a first-order reaction is [A] = [A]₀e^(-kt), where [A] is the concentration of A at time t, [A]₀ is the initial concentration of A, k is the rate constant, and t is the time.
3. Calculate the concentration of A at time t: Substitute the given values into the integrated rate law equation. Use [A]₀ = 0.750 M, k = 3.7 × 10^(-3) M•s^(-1), and t = 2.7 × 10^(-3) s to find [A].
4. Determine the concentration of C: Since the reaction is A → B + C, the concentration of C formed is equal to the decrease in concentration of A. Therefore, [C] = [A]₀ - [A].
5. Substitute the calculated concentration of A into the equation for [C]: Use the value of [A] obtained from the previous step to find the concentration of C at time t.