Final answer:
To determine the rate constant for a first-order reaction, we can use the integrated rate law. The integrated rate law for a first-order reaction is given by the equation ln([A]t/[A]0) = -kt, where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration, k is the rate constant, and t is the time.
Step-by-step explanation:
To determine the rate constant for a first-order reaction, we can use the integrated rate law.
The integrated rate law for a first-order reaction is given by the equation ln([A]t/[A]0) = -kt, where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration, k is the rate constant, and t is the time.
We are given that the reaction is 34.5% complete in 49 minutes at 298 K.
This means that [A]t/[A]0 = 0.345. Plugging this value into the integrated rate law, we get ln(0.345) = -k * 49.
Solving for k, we find that the rate constant is approximately -ln(0.345)/49 = 0.0159 min^-1.