Multiple Choice
Using the integrated rate law for a first-order reaction, ln[A]t = -kt + ln[A]0, how can you determine the rate constant (k) if you have concentration data over time?
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15. Chemical Kinetics
Integrated Rate Law
Multiple Choice
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
Verified step by step guidance1
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.
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.
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].
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].
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.
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