At 25^$\circ$C the rate constant for the first-order decomposition of a pesticide solution is 6.40 *10^-3 min^-1. If the starting concentration of pesticide is 0.0314 M, what concentration will remain after 62.0 min at 25^$\circ$C

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Quizplus · Accepted Answer

For a first-order reaction, the concentration of the reactant at any time, $t$, can be calculated using the formula: $[A]_t = [A]_0 e^{-kt}$, 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. Given $k = 6.40 \times 10^{-3} \text{ min}^{-1}$, $[A]_0 = 0.0314 \text{ M}$, and $t = 62.0 \text{ min}$, substituting these values into the formula gives $[A]_t = 0.0314 \text{ M} \times e^{-(6.40 \times 10^{-3} \text{ min}^{-1})(62.0 \text{ min})}$, which calculates to approximately $2.11 \times 10^{-2} \text{ M}$, matching choice D.

At 25 ∘\circ∘ C the Rate Constant for the First-Order Decomposition of a Decomposition

At 25^$\circ$C the Rate Constant for the First-Order Decomposition of a Decomposition