A first-order reaction has a half-life of 20.0 minutes. Starting with 1.00 × 10²⁰ molecules of reactant at time t = 0, how many molecules remain unreacted after 100.0 minutes?

Question

Quizplus · Accepted Answer

For a first-order reaction, the number of molecules remaining after a certain time can be calculated using the formula $N = N_0 \times (1/2)^{(t/t_{1/2})}$, where $N_0$ is the initial number of molecules, $t$ is the time elapsed, and $t_{1/2}$ is the half-life of the reaction. Given a half-life of 20.0 minutes and a time of 100.0 minutes, the number of half-lives is $100.0 / 20.0 = 5$. Therefore, the fraction of molecules remaining is $(1/2)^5 = 1/32$. Starting with $1.00 \times 10^{20}$ molecules, the number remaining after 100.0 minutes is $1.00 \times 10^{20} / 32$, which does not match any of the provided options exactly, indicating that the correct answer is "None of these choices are correct."

A First-Order Reaction Has a Half-Life of 20