Final answer:
To find the time for 15.9% of a reactant to remain in a first-order reaction with a rate constant of 0.0720 s-1, we use the first-order kinetics integrated rate law. The calculation yields a time of approximately 24.671 seconds.
Step-by-step explanation:
The question relates to the first-order reaction and the determination of the time required for a certain percentage of reactant to remain. To calculate the time (t) when 15.9% of the reactant remains, we can use the first-order kinetics integrated rate law:
ln([A]_t/[A]_0) = -kt
Where [A]_t is the concentration of reactant at time t, [A]_0 is the initial concentration, k is the rate constant, and t is the time.
Since 15.9% remains, 84.1% has reacted, and thus [A]_t/[A]_0 = 0.159. We can substitute the values into the equation and solve for t:
ln(0.159) = -0.0720 s-1 • t
t = ln(0.159) / (-0.0720 s-1)
t ≈ 24.671 seconds
The time after which 15.9% of the reactant will remain is approximately 24.671 seconds.