Elements of Unsaturation

Elements of Unsaturation

(1) Elements of Unsaturation in Hydrocarbons

– Alkenes are said to be unsaturated because they are capable of adding hydrogen in the presence of a catalyst.

– The product, an alkane, is called saturated because it cannot react with any more hydrogen.

– The presence of a pi bond of an alkene (or an alkyne) or the ring of a cyclic compound decreases the number of hydrogen atoms in a molecular formula.

– These structural features are called elements of unsaturation.

– Each element of unsaturation corresponds to two fewer hydrogen atoms than in the “saturated” formula.

– Consider, for example, the formula C₄H₈.

– A saturated alkane would have a C_nH_(2n+2) formula, or C₄H₁₀.

– The formula C₄H₈ is missing two hydrogen atoms, so it has one element of unsaturation, either a pi bond or a ring.

– There are five constitutional isomers of formula C₄H₈:

– When you need a structure for a particular molecular formula, it helps to find the number of elements of unsaturation.

– Calculate the maximum number of hydrogen atoms from the saturated formula, C_nH_(2n+2) and see how many are missing.

– The number of elements of unsaturation is simply half the number of missing hydrogens.

– This simple calculation allows you to consider possible structures quickly, without always having to check for the correct molecular formula.

(2) Elements of Unsaturation with Heteroatoms

– Heteroatoms (hetero, “different”) are any atoms other than carbon and hydrogen.

– The rule for calculating elements of unsaturation in hydrocarbons can be extended to include heteroatoms.

– Let’s consider how the addition of a heteroatom affects the number of hydrogen atoms in the formula.

Halogens

– Halogens simply substitute for hydrogen atoms in the molecular formula.

– The formula C₂H₆ is saturated, so the formula C₂H₄F₂ is also saturated.

– C₄H₈ has one element of unsaturation, and C₄H₅Br₃ also has one element of unsaturation.

– In calculating the number of elements of unsaturation, simply count halogens as hydrogen atoms.

Oxygen

– An oxygen atom can be added to the chain (or added to a C-H bond to  make a C-OH group) without changing the number of hydrogen atoms or carbon atoms.

– In calculating the number of elements of unsaturation, ignore the oxygen atoms.

Nitrogen

– A nitrogen atom can take the place of a carbon atom in the chain, but nitrogen is trivalent, having only one additional hydrogen atom, compared with two hydrogens for each additional carbon atom.

– In computing the elements of unsaturation, count nitrogen as half a carbon atom.

– The formula C₄H₉N is like a formula with 4.5 carbon atoms, with saturated formula C_4.5H₉₊₂

– The formula C₄H₉N has one element of unsaturation, because it is two hydrogen atoms short of the saturated formula.

Solved Problem

Draw at least four compounds of formula C₄H₆NOCl.

Solution:

– Counting the nitrogen as 1/2 carbon, ignoring the oxygen, and counting chlorine as a hydrogen shows the formula is equivalent to C_4.5H₇.

– The saturated formula for 4.5 carbon atoms is C_4.5H₁₁, so C₄H₆NOCl  has two elements of unsaturation.

– These could be two double bonds, two rings, one triple bond, or a ring and a double bond.

– There are many possibilities, four of which are listed here.