The thermal decomposition of oct-7-en-5-ol is investigated at different temperatures, TTT:
CH2=CHCH2CH(OH)CH2CH2CH2CH3→CH2=CHCH3+CH3CH2CH2CH2CHO\text{CH}_2=\text{CHCH}_2\text{CH(OH)CH}_2\text{CH}_2\text{CH}_2\text{CH}_3 \rightarrow \text{CH}_2=\text{CHCH}_3 + \text{CH}_3\text{CH}_2\text{CH}_2\text{CH}_2\text{CHO}CH2=CHCH2CH(OH)CH2CH2CH2CH3→CH2=CHCH3+CH3CH2CH2CH2CHO
The rate constant, kkk, is calculated at each temperature. Some of the results are shown in the table below:
T / K1/T / K−1k / s−1lnk5002.00×10−32.08×10−5−10.785101.96×10−34.30×10−5−10.05520(i)8.61×10−5(ii)5301.89×10−31.68×10−4−8.705401.85×10−33.20×10−4−8.05\begin{aligned} &T \text{ / K} && 1/T \text{ / K}^{-1} && k \text{ / s}^{-1} && \ln k \\ &500 && 2.00 \times 10^{-3} && 2.08 \times 10^{-5} && -10.78 \\ &510 && 1.96 \times 10^{-3} && 4.30 \times 10^{-5} && -10.05 \\ &520 && \mathbf{(i)} && 8.61 \times 10^{-5} && \mathbf{(ii)} \\ &530 && 1.89 \times 10^{-3} && 1.68 \times 10^{-4} && -8.70 \\ &540 && 1.85 \times 10^{-3} && 3.20 \times 10^{-4} && -8.05 \end{aligned}T / K5005105205305401/T / K−12.00×10−31.96×10−3(i)1.89×10−31.85×10−3k / s−12.08×10−54.30×10−58.61×10−51.68×10−43.20×10−4lnk−10.78−10.05(ii)−8.70−8.05
Complete the table with the missing values (i) (to 3 significant figures) and (ii) (to 2 decimal places).
Identify the piece of information in the table column headings that allows the overall order of the reaction to be deduced, and state this overall order.
A graph of lnk\ln klnk against 1T\frac{1}{T}T1 is plotted. The line of best fit has a gradient of −18200 K-18200\text{ K}−18200 K. Calculate the activation energy, EaE_{\text{a}}Ea, in kJ mol−1\text{kJ mol}^{-1}kJ mol−1. (Gas constant R=8.31 J K−1mol−1R = 8.31 \text{ J K}^{-1}\text{mol}^{-1}R=8.31 J K−1mol−1)
5-Methyloct-7-en-5-ol decomposes in a similar way to oct-7-en-5-ol to produce an alkene and a carbonyl compound. Deduce the structures of the alkene and the carbonyl compound.