QuestionJuly 8, 2025

The decomposition of N_(2)O_(5) in solution in carbon tetrachloride proceeds via the reaction 2N_(2)O_(5)(soln)arrow 4NO_(2)(soln)+O_(2)(soln) The reaction is first order and has a rate constant of 4.82times 10^-3s^-1 at 64^circ C If the reaction is initiated with 0.072 mol in a 1.00-L vessel, how many moles remain after 151 s? 0.035 moles 1.6times 10^3 moles 0.067 moles 9.6 moles 0.074 moles

The decomposition of N_(2)O_(5) in solution in carbon tetrachloride proceeds via the reaction 2N_(2)O_(5)(soln)arrow 4NO_(2)(soln)+O_(2)(soln) The reaction is first order and has a rate constant of 4.82times 10^-3s^-1 at 64^circ C If the reaction is initiated with 0.072 mol in a 1.00-L vessel, how many moles remain after 151 s? 0.035 moles 1.6times 10^3 moles 0.067 moles 9.6 moles 0.074 moles
The decomposition of N_(2)O_(5) in solution in carbon tetrachloride proceeds via the reaction 2N_(2)O_(5)(soln)arrow 4NO_(2)(soln)+O_(2)(soln) The reaction is first order and has a rate constant of 4.82times 10^-3s^-1 at 64^circ C If the reaction is initiated with 0.072 mol in a 1.00-L vessel, how many moles remain after 151 s? 0.035 moles 1.6times 10^3 moles 0.067 moles 9.6 moles 0.074 moles

Solution
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Answer

0.035 moles Explanation 1. Identify the first-order reaction formula For a first-order reaction, use the formula: **[A] = [A]_0 e^{-kt}** where [A] is the concentration at time t, [A]_0 is the initial concentration, k is the rate constant, and t is the time. 2. Substitute known values Initial concentration [A]_0 = 0.072 \text{ mol/L}, k = 4.82 \times 10^{-3} \text{ s}^{-1}, t = 151 \text{ s}. 3. Calculate remaining concentration [A] = 0.072 \times e^{-4.82 \times 10^{-3} \times 151} [A] = 0.072 \times e^{-0.72782} [A] \approx 0.072 \times 0.483 [A] \approx 0.0348 \text{ mol/L}

Explanation

1. Identify the first-order reaction formula<br /> For a first-order reaction, use the formula: **$[A] = [A]_0 e^{-kt}$** where $[A]$ is the concentration at time $t$, $[A]_0$ is the initial concentration, $k$ is the rate constant, and $t$ is the time.<br />2. Substitute known values<br /> Initial concentration $[A]_0 = 0.072 \text{ mol/L}$, $k = 4.82 \times 10^{-3} \text{ s}^{-1}$, $t = 151 \text{ s}$.<br />3. Calculate remaining concentration<br /> $[A] = 0.072 \times e^{-4.82 \times 10^{-3} \times 151}$<br /> $[A] = 0.072 \times e^{-0.72782}$<br /> $[A] \approx 0.072 \times 0.483$<br /> $[A] \approx 0.0348 \text{ mol/L}$
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