3.14: Combustion Energy: A Measure of Stability in Alkanes and Cycloalkanes

The low reactivity in alkanes can be attributed to the non-polar nature of C–C and C–H σ bonds. Alkanes, therefore, were initially termed as “paraffins,” derived from the Latin words: parum, meaning “too little,” and affinis, meaning “affinity.”

Alkanes undergo combustion in the presence of excess oxygen and high-temperature conditions to give carbon dioxide and water. A combustion reaction is the energy source in natural gas, liquified petroleum gas (LPG), fuel oil, gasoline, diesel fuel, and aviation fuel. The energy released during combustion, called the heat of combustion (−ΔH°), helps predict the relative stabilities in alkanes and cycloalkanes.

For straight-chain alkanes, the heat of combustion increases gradually with the sequential addition of a CH₂ group. However, in higher alkanes, the heat of combustion decreases with increased branching, suggesting that branched isomers have lower potential energies and have greater stabilities compared to straight chain (linear) alkanes.

In cycloalkanes, the relative stability depends on the strain energy, which is the combined outcome of angular, torsional, and steric strains. The strain energy is determined as the difference between the actual and the predicted heats of combustion. A study of strain energy as a function of ring size reveals that the smallest cycloalkane (C3) exhibits maximum strain due to excessive compression of its bond angles. As the ring size increases, the bond angles approach the ideal value of 109° with cyclohexane (C6) being strain-free. Further strains in higher cycloalkanes (C7 to C9) result from their non-ideal bond angles.

Alkanes exhibit low reactivity due to strong non-polar C–C and C–H σ bonds.

Combustion of alkanes in excess oxygen, under high-temperature conditions, gives carbon dioxide and water.

Combustion reactions form the basis of energy sources for heat and power.

The energy released during combustion — called the heat of combustion — helps predict the relative stabilities of alkanes and cycloalkanes.

For a series of straight-chain alkanes, the sequential addition of a CH₂ group gradually increases the heat of combustion by an average value of 658.5 kJ mol^-1.

Now, consider different isomers of octane undergoing combustion to produce identical moles of products and different experimental heats of combustion.

The straight-chain isomer has the highest negative heat of combustion. The amount of heat released marginally decreases with branching, suggesting that increased branching lowers the potential energy and increases the stability of the isomer.

In cycloalkanes, wherein several CH₂ groups are linked together by C–C bonds, the predicted heat of combustion is “n times the average combustion energy of a CH₂ group.”

For strained cycloalkanes, the actual heat of combustion is slightly higher than the predicted values. The difference between the actual and the predicted value gives the strain energy.

A plot of strain energy as a function of ring size shows that cyclopropane has maximum strain due to excessive compression of its bond angles from 109.5° to 60°.

A decrease in the energy for cyclobutane, followed by cyclopentane, is relative to their reduced overall strain, while cyclohexane is virtually strain-free.

Moderate strain energies in C7 to C9 cycloalkanes mainly result from torsional and steric strains that arise from non-ideal bond angles in their conformations.