Chlorine dioxide (ClO₂) is used as a disinfectant in municipal water-treatment plants. It decomposes in a first-order reaction with a rate constant of 0.0714 s^-1. If the initial concentration were 0.12 M, what would the concentration be after 14.0 s has elapsed?

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The concentration after a given time in a first-order reaction is 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 $k = 0.0714 \, \text{s}^{-1}$, $[A]_0 = 0.12 \, \text{M}$, and $t = 14.0 \, \text{s}$, we can calculate $[A]_t$ as follows:$[A]_t = 0.12 \, \text{M} \cdot e^{-0.0714 \cdot 14.0}$$[A]_t \approx 0.12 \, \text{M} \cdot e^{-0.9996}$$[A]_t \approx 0.12 \, \text{M} \cdot 0.368$$[A]_t \approx 0.044 \, \text{M}$Therefore, the concentration of chlorine dioxide after 14.0 seconds would be approximately 0.044 M.

Chlorine Dioxide (ClO2) Is Used as a Disinfectant in Municipal

Chlorine Dioxide (ClO₂) Is Used as a Disinfectant in Municipal