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Sia

青州's Question
Chemistry
Posted 11 months ago

8) Acetaldehyde, CH3CHO\mathrm{CH}_{3} \mathrm{CHO}, decomposes to CO\mathrm{CO} and CH4\mathrm{CH}_{4} in the gas phase. Find the rate law of the reaction from the following data on initial rates:
\begin{tabular}{|c|c|}
\hline PCH3CHO\mathbf{P}_{\mathrm{CH} 3 \mathrm{CHO}} (atm) & Initial Rate (atm/sec) \\
\hline 0.213 & 1.34×1031.34 \times 10^{-3} \\
\hline 0.416 & 3.79×1033.79 \times 10^{-3} \\
\hline 0.107 & 4.77×1044.77 \times 10^{-4} \\
\hline
\end{tabular}
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Answer from Sia
Posted 11 months ago
Solution
1
Identify the reaction: The reaction given is the decomposition of acetaldehyde (CH3CHO\mathrm{CH}_{3} \mathrm{CHO}) into carbon monoxide (CO\mathrm{CO}) and methane (CH4\mathrm{CH}_{4})
2
Write the general rate law: The rate law for the reaction can be expressed as Rate=k[CH3CHO]n \text{Rate} = k [\mathrm{CH}_{3} \mathrm{CHO}]^n , where kk is the rate constant and nn is the order of the reaction with respect to CH3CHO\mathrm{CH}_{3} \mathrm{CHO}
3
Use the given data to determine the order of the reaction: We have the following data: \begin{align*} P_{\mathrm{CH}_{3} \mathrm{CHO}} & \text{(atm)} & \text{Initial Rate (atm/sec)} \\ 0.213 & 1.34 \times 10^{-3} \\ 0.416 & 3.79 \times 10^{-3} \\ 0.107 & 4.77 \times 10^{-4} \end{align*} To find nn, we can use the method of initial rates
4
Calculate the reaction order: \begin{align*} \frac{\text{Rate}_2}{\text{Rate}_1} &= \left(\frac{[\mathrm{CH}_{3} \mathrm{CHO}]_2}{[\mathrm{CH}_{3} \mathrm{CHO}]_1}\right)^n \\ \frac{3.79 \times 10^{-3}}{1.34 \times 10^{-3}} &= \left(\frac{0.416}{0.213}\right)^n \\ 2.83 &= (1.95)^n \\ n &\approx 1.5 \end{align*} Thus, the reaction order nn is approximately 1.5
5
Write the rate law: The rate law for the decomposition of acetaldehyde is Rate=k[CH3CHO]1.5 \text{Rate} = k [\mathrm{CH}_{3} \mathrm{CHO}]^{1.5}
Answer
The rate law for the decomposition of acetaldehyde is Rate=k[CH3CHO]1.5 \text{Rate} = k [\mathrm{CH}_{3} \mathrm{CHO}]^{1.5} .
Key Concept
Rate law determination
Explanation
The rate law is determined by comparing the initial rates of reaction at different concentrations of the reactant. By using the method of initial rates, we can find the order of the reaction with respect to the reactant.

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