8) Acetaldehyde, $\mathrm{CH}_{3} \mathrm{CHO}$, decomposes to $\mathrm{CO}$ and $\mathrm{CH}_{4}$ in the gas phase. Find the rate law of the reaction from the following data on initial rates:
\begin{tabular}{|c|c|}
\hline $\mathbf{P}_{\mathrm{CH} 3 \mathrm{CHO}}$ (atm) & Initial Rate (atm/sec) \
\hline 0.213 & $1.34 imes 10^{-3}$ \
\hline 0.416 & $3.79 imes 10^{-3}$ \
\hline 0.107 & $4.77 imes 10^{-4}$ \
\hline
\end{tabular}

Question

8) Acetaldehyde, $\mathrm{CH}_{3} \mathrm{CHO}$, decomposes to $\mathrm{CO}$ and $\mathrm{CH}_{4}$ in the gas phase. Find the rate law of the reaction from the following data on initial rates:
\begin{tabular}{|c|c|}
\hline $\mathbf{P}_{\mathrm{CH} 3 \mathrm{CHO}}$ (atm) & Initial Rate (atm/sec) \
\hline 0.213 & $1.34 	imes 10^{-3}$ \
\hline 0.416 & $3.79 	imes 10^{-3}$ \
\hline 0.107 & $4.77 	imes 10^{-4}$ \
\hline
\end{tabular}

Accepted Answer

∻Solution∻ ‖ 1 ⋮ **Identify the reaction**: The reaction given is the decomposition of acetaldehyde ($\mathrm{CH}_{3} \mathrm{CHO}$) into carbon monoxide ($\mathrm{CO}$) and methane ($\mathrm{CH}_{4}$). ‖ ‖ 2 ⋮ **Write the general rate law**: The rate law for the reaction can be expressed as $ ext{Rate} = k [\mathrm{CH}_{3} \mathrm{CHO}]^n $, where $k$ is the rate constant and $n$ is the order of the reaction with respect to $\mathrm{CH}_{3} \mathrm{CHO}$. ‖ ‖ 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}} & ext{(atm)} & ext{Initial Rate (atm/sec)} \ 0.213 & 1.34 imes 10^{-3} \ 0.416 & 3.79 imes 10^{-3} \ 0.107 & 4.77 imes 10^{-4} \end{align*} To find $n$, we can use the method of initial rates. ‖ ‖ 4 ⋮ **Calculate the reaction order**: \begin{align*} \frac{ ext{Rate}_2}{ ext{Rate}_1} &= \left(\frac{[\mathrm{CH}_{3} \mathrm{CHO}]_2}{[\mathrm{CH}_{3} \mathrm{CHO}]_1} ight)^n \ \frac{3.79 imes 10^{-3}}{1.34 imes 10^{-3}} &= \left(\frac{0.416}{0.213} ight)^n \ 2.83 &= (1.95)^n \ n &\approx 1.5 \end{align*} Thus, the reaction order $n$ is approximately 1.5. ‖ ‖ 5 ⋮ **Write the rate law**: The rate law for the decomposition of acetaldehyde is $ ext{Rate} = k [\mathrm{CH}_{3} \mathrm{CHO}]^{1.5} $. ‖ ∻Answer∻ ⚹ The rate law for the decomposition of acetaldehyde is $ ext{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. ⚹◊What is the rate law for the decomposition of acetaldehyde to carbon monoxide and methane based on the given data on initial rates?⍭ Generate me a similar question◊

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