Part 8: THERMODYNAMICS

How can we estimate the heat of combustion, of a methyl group, -CH3 ?
An ethane molecule, can be viewed as two methyl groups joined together : CH3CH3, so we can get an estimate for a methyl group by simply dividing the heat of combustion of hydrogen by 2 to give ΔHc (-CH3) = -373 / 2 = -186.5 kcal/mol or -1561 / 2 = -780.5 kJ/mol.

How can we estimate the heat of combustion, of a methylene group, -CH2- ?
The difference between members of the straight chain hydrocarbon series is a -CH2- . So, for example, the difference between propane and ethane is a -CH2- ......
CH3CH2CH3 - CH3CH3 = -CH2 -

ΔHc (-CH2-) = -530.4 - -373  = -157.4 kcal/mol or -2219 - -1561 = -658 kJ/mol.

(You can test the reliability of this by looking at the difference of butane and propane....)

Cyclobutane can be viewed as (CH2)4 so the estimated heat of combustion would just be 4 x ΔHc (-CH2-)

ΔHc (cyclobutane)  = 4 x -157.4 = -629.6 kcal/mol or 4 x -658 = -2632 kJ/mol

Similarly, cyclobutane can be viewed as (CH2)6 so the estimated heat of combustion would just be 6 x DHc (-CH2-)

ΔHc (cyclohexane)  = 6 x -157.4 = -944.4 kcal/mol or 6 x -658 = -3948 kJ/mol

How good are these estimates ?

First for cyclobutane, we have underestimated by 26.7 kcal/mol or 114 kJ/mol i.e. the actual reaction releases more heat than we have predicted. This is because our estimate cannot take into account the ring strain in cyclobutane.  This ring strain arises from the compressed C-C-C bond angles (about 90o) compared to the optimal 109.5o and due to the torsional strain due to the eclipsing of C-H and C-C bonds in the cyclic structure. This extra energy is released when the ring breaks open.

For cyclohexane, the estimates are very, very close to the actual value. This is because cyclohexane in the predominant chair conformation is ring strain free. The bond angles are close to the optimal 109.5o and there is no torsional strain since the bonds are staggered.