A first-order reaction has a half-life of 1.10 s .If the initial concentration of reactant is 0.384 M,How long will it take for the reactant concentration to reach 0.00100 M?
A) 9.45 s
B) 0.106 s
C) 4.10 s
D) 1.52 s
E) 0.244 s

Question

Quizplus · Accepted Answer

For a first-order reaction, the time $t$ required for the concentration of a reactant to change from an initial concentration $[A]_0$ to a final concentration $[A]$ can be calculated using the formula $t = \frac{0.693}{k}\ln\left(\frac{[A]_0}{[A]}\right)$, where $k$ is the rate constant and can be found using the half-life formula for a first-order reaction: $t_{1/2} = \frac{0.693}{k}$. Given the half-life $t_{1/2} = 1.10$ s, we can find $k$ and then calculate $t$ for the concentration to decrease from 0.384 M to 0.00100 M. The calculation confirms that option A, 9.45 s, is the correct time it takes for the concentration to reach the specified level.

A First-Order Reaction Has a Half-Life of 1