Part 6: THERMODYNAMICS

This should have been a reasonably straight forward calculation, but care needs to be taken with the last part of the question.

a. Cyclohexane and trans-hex-3-ene are constitutional isomers. (1 mark)

b. C₆H₁₂ + 9 O₂ --> 6 CO₂ + 6 H₂O (1.5 marks)

c. (see figure)

DHc elements = (6 x -93.9) + (6 x -68.4) = -973.8 kcal/mol

DHf A= -973.8 - (- 938) = -35.8 kcal/mol

DHc B = -973.8 - (- 19.3) = -954.5 kcal/mol

(1.5 marks)

d.

e.
The structures are shown in the figure above (0.5 marks each)

Given the thermodynamic data in the table provided in the question, and hence the figure shown above, A is the most stable isomer (i.e. lowest energy) (1 mark)

Several factors to consider here, first the more stable isomer will be composed of more stronger covalent bonds.
The acyclic alkene has a C=C and hence 2 x sp2 C and 2 primary sp3 C atoms while the cycloalkane has 6 secondary sp3 C atoms and therefore 12 secondary sp3 C-H bonds.
The pi bond in the alkene is about 60 kcal/mol weaker than the extra C-C sigma bond in cyclohexane.
Primary C-H bonds are about 3 kcal/mol stronger than secondary C-H bonds.
Allylic C-H bonds (there are 4 in the alkene) are about 10 kcal/mol weaker than equivalent simple C-H bonds.
sp2 C-H bonds (there are 2 in the alkene) are about 10 kcal/mol stronger than sp3 C-H bonds.
All told, this approximations suggests that cyclohexane is about 20 kcal/mol more stable than the alkene

(1.5 marks)

Common errors:

• incorrect coefficients in the balanced equation
• missing signs in calculated values
• incorrect or no labelling of the most and least stable isomers based on the thermodynamic numbers. A is the most stable because it is at the lowest energy (see the figure).
• drawing structures other than cyclohexane and trans-hex-3-ene as stated in the question.
• not matching A and B to the correct structure, not drawing line diagrams as the question asked.
• incomplete or vague explanation based on bonding of why a more branched isomer is more stable. Typically students did not talk about the strengths and numbers of the bonds involved which is the key part. Some students related stablity to surface area, intermolecular forces and boiling points. They are not relevant as stability is controlled by the much stronger covalent bonds within the molecules.
• cyclohexane contains 6 secondary sp3 C atoms (no primary C or H and not sp2).
• part d : no y axis label, not showing the elemental reactents and combustio products
• part e answers based on the heats of reaction values... (that's like saying it's cold out because the thermometer says it's -25C rather than saying because an arctic front is moving through). Here for the thermodynamics question, a good answer requires a molecular level rationale (i.e. based on bond strengths).