Final answer:
The time required for a first-order reaction to be 32% completed can be calculated using the integrated rate law for first-order reactions. In this case, the reaction will take approximately 128 seconds.
Step-by-step explanation:
A first-order reaction is a reaction in which the rate is proportional to the concentration of only one reactant. The time required for a first-order reaction to be 32% completed can be calculated using the integrated rate law for first-order reactions.
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 at time t, [A]0 is the initial concentration, k is the rate constant, and t is the time.
In this case, the reaction is 32% completed, which means [A]t = 0.32[A]0. By substituting these values into the equation, we can solve for t:
ln(0.32) = -kt
t = ln(0.32)/(-k)
Substituting the given rate constant (k = 1.5 × 10^-3 s^-1) into the equation gives:
t = ln(0.32)/(-1.5 × 10^-3)
t ≈ 128 seconds