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青州's Question
Chemistry
Posted 6 months ago

7) The compound CH3CH2Cl\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl} decomposes to C2H4\mathrm{C}_{2} \mathrm{H}_{4} and HCl\mathrm{HCl} at elevated temperatures. Find the rate law for this reaction from the following rate data.
\begin{tabular}{ll} 
PCH3CH2Cl_{\mathrm{CH} 3 \mathrm{CH} 2 \mathrm{Cl}} & Initial rate (atm/sec) \\
1.8×1021.8 \times 10^{-2} & 7.5×1047.5 \times 10^{-4} \\
4.3×1024.3 \times 10^{-2} & 1.8×1031.8 \times 10^{-3} \\
7.8×1027.8 \times 10^{-2} & 3.3×1033.3 \times 10^{-3}
\end{tabular}
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Answer from Sia
Posted 6 months ago
Solution
1
Identify the reaction: The given reaction is the decomposition of mathrmCH3mathrmCH2mathrmCl\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl} to mathrmC2mathrmH4\\mathrm{C}_{2} \\mathrm{H}_{4} and mathrmHCl\\mathrm{HCl}
2
Write the general rate law: The rate law for the reaction can be written as textRate=k[mathrmCH3mathrmCH2mathrmCl]n\\text{Rate} = k [\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}]^n, where kk is the rate constant and nn is the order of the reaction with respect to mathrmCH3mathrmCH2mathrmCl\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}
3
Use the given data to determine the order of the reaction: - For PmathrmCH3mathrmCH2mathrmCl=1.8times102P_{\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}} = 1.8 \\times 10^{-2} atm, the initial rate is 7.5times1047.5 \\times 10^{-4} atm/sec. - For PmathrmCH3mathrmCH2mathrmCl=4.3times102P_{\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}} = 4.3 \\times 10^{-2} atm, the initial rate is 1.8times1031.8 \\times 10^{-3} atm/sec. - For PmathrmCH3mathrmCH2mathrmCl=7.8times102P_{\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}} = 7.8 \\times 10^{-2} atm, the initial rate is 3.3times1033.3 \\times 10^{-3} atm/sec. To find nn, we can use the ratio of the rates and the concentrations: fractextRate2textRate1=left(frac[mathrmCH3mathrmCH2mathrmCl]2[mathrmCH3mathrmCH2mathrmCl]1right)n\\frac{\\text{Rate}_2}{\\text{Rate}_1} = \\left(\\frac{[\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}]_2}{[\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}]_1}\\right)^n Using the first two data points: frac1.8times1037.5times104=left(frac4.3times1021.8times102right)n\\frac{1.8 \\times 10^{-3}}{7.5 \\times 10^{-4}} = \\left(\\frac{4.3 \\times 10^{-2}}{1.8 \\times 10^{-2}}\\right)^n 2.4=left(2.39right)n2.4 = \\left(2.39\\right)^n Taking the logarithm of both sides: log(2.4)=nlog(2.39)\\log(2.4) = n \\log(2.39) napprox1n \\approx 1 Thus, the reaction is first order with respect to mathrmCH3mathrmCH2mathrmCl\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}
4
Write the rate law: The rate law for the reaction is textRate=k[mathrmCH3mathrmCH2mathrmCl]\\text{Rate} = k [\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}]
Answer
The rate law for the decomposition of mathrmCH3mathrmCH2mathrmCl\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl} is textRate=k[mathrmCH3mathrmCH2mathrmCl]\\text{Rate} = k [\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}].
Key Concept
Rate law determination
Explanation
The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. By comparing the initial rates and concentrations, we determined that the reaction is first order with respect to mathrmCH3mathrmCH2mathrmCl\\mathrm{CH}_{3} \\mathrm{CH}_{2} \\mathrm{Cl}.

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