05 Alkanes and Radical Reactions

Alkane structure and conformations

Alkanes are saturated hydrocarbons: their carbon atoms are connected by single bonds, and each carbon has four bonds overall. Acyclic alkanes follow the general formula $\mathrm{C_nH_{2n+2}}$. Each carbon is approximately tetrahedral, with bond angles near $109.5^\circ$. Carbon–carbon and carbon–hydrogen bonds are sigma bonds, written $\sigma$.

Rotation around a carbon–carbon single bond changes a molecule’s three-dimensional arrangement without changing which atoms are connected. These different spatial arrangements are conformations, and they usually interconvert rapidly rather than existing as separate, isolable compounds.

A Newman projection makes it easier to compare arrangements by showing the molecule viewed along a chosen carbon–carbon bond. The front carbon is drawn as a dot, and the rear carbon as a circle.

Takeaway: Alkane bonds connect atoms in a fixed framework, while rotation around single bonds changes the framework’s conformation.

Comparing conformational energy

The relative positions of bonds and groups affect conformational energy. In ethane, a staggered conformation, with the front and rear carbon–hydrogen bonds offset, is lower in energy than an eclipsed conformation, where those bonds line up. The energy difference is called torsional strain.

In butane, a Newman projection along the central carbon–carbon bond shows two important staggered arrangements. The anti conformation places the methyl groups $180^\circ$ apart and is lower in energy than the gauche conformation, which places them $60^\circ$ apart. Gauche is higher in energy mainly because the closer methyl groups experience steric repulsion.

A practical way to compare conformations is to stagger bonds where possible and, when possible, place the largest groups anti to one another.

The radical halogenation chain

Alkanes are relatively unreactive, but chlorine or bromine can replace an alkane hydrogen under light, written $h\nu$, or heat. This reaction is called radical halogenation:

Here, $\mathrm{X}$ is usually $\mathrm{Cl}$ or $\mathrm{Br}$. The reaction proceeds through a chain mechanism with three stages:

1. Initiation: Light or heat breaks the halogen–halogen bond homolytically, giving one electron to each atom and producing two halogen radicals:

   $$\mathrm{X_2 \rightarrow 2X\cdot}$$

2. Propagation: A halogen radical abstracts hydrogen from the alkane, producing hydrogen halide and an alkyl radical. The alkyl radical then reacts with another halogen molecule, forming the product and regenerating a halogen radical:

   $$\mathrm{X\cdot + R-H \rightarrow H-X + R\cdot}$$
   $$\mathrm{R\cdot + X_2 \rightarrow R-X + X\cdot}$$

3. Termination: Two radicals combine, removing radicals from the chain. For example:

   $$\mathrm{R\cdot + X\cdot \rightarrow R-X}$$

Single-headed, or fishhook, arrows show the movement of one electron in radical mechanisms.

Takeaway: Initiation creates radicals, propagation continues the chain, and termination removes radicals by combining them.

Product mixtures and reaction energy

Radical halogenation can produce mixtures because different kinds of hydrogen may be substituted, and further substitution can occur. More substituted alkyl radicals are generally more stable, so radical stability helps compare possible substitution sites. However, the amounts of products also depend on how many equivalent hydrogens are available, as well as on the halogen and reaction conditions.

Bond energies help estimate whether a reaction step absorbs or releases energy. Breaking a bond requires energy, while forming a bond releases energy. Bond dissociation energy is the energy required to break a bond homolytically into two radicals in the gas phase. A rough estimate of reaction enthalpy is:

A negative $\Delta H$ indicates an exothermic reaction; a positive $\Delta H$ indicates an endothermic reaction. For hydrogen abstraction, compare the alkane carbon–hydrogen bond broken with the hydrogen–halogen bond formed.

Reaction energy diagrams distinguish overall energy change from activation energy. The overall change compares product energy with reactant energy. Activation energy is the barrier from the reactants to the transition state; a smaller barrier generally means a faster reaction. A favorable overall energy change alone does not establish that a reaction will be fast.

Takeaway: Bond energies help estimate the energy change of a step, while activation energy helps explain its rate.