Multiple Choice
What is the rate law for the elementary reaction: Cl(g) + Cl(g) + N2(g) → Cl2(g) + N2(g)?
15. Chemical Kinetics
Rate Law
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The following reaction is first order: C2H6 → 2 CH3. If the rate constant is equal to 5.5 × 10⁻⁴ s⁻¹ at 1000 K, how long will it take for 0.35 mol of C2H6 in a 1.00 L container to decrease to 0.10 mol in the same container?
A
1,818 seconds
B
3,636 seconds
C
7,272 seconds
D
5,454 seconds
Verified step by step guidance1
Identify the type of reaction and the order. This is a first-order reaction, which means the rate of reaction is directly proportional to the concentration of the reactant.
Use the first-order rate equation: \( [A] = [A]_0 e^{-kt} \), where \([A]\) is the concentration at time \(t\), \([A]_0\) is the initial concentration, \(k\) is the rate constant, and \(t\) is the time.
Substitute the given values into the equation: \([A]_0 = 0.35\) mol/L, \([A] = 0.10\) mol/L, and \(k = 5.5 \times 10^{-4}\) s\(^{-1}\).
Rearrange the equation to solve for \(t\): \(t = \frac{-1}{k} \ln \left( \frac{[A]}{[A]_0} \right)\).
Calculate \(t\) using the rearranged equation, ensuring to use natural logarithms (ln) for the calculation.
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