ChemistryOrganic Chemistry

Degree of Saturation Formula? Calculate Organic Degrees of Unsaturation

For OpenStax Problem 7-2, DBE = (2C + 2 + N − H − X)/2 gives 5, 5, 3, 1, 6 and 5. Oxygen is ignored; halogens count like hydrogen.

Question

Calculate the degree of unsaturation in each of the following formulas:

(a) C6H5N\mathrm{C_6H_5N}

(b) C6H5NO2\mathrm{C_6H_5NO_2}

(c) C8H9Cl3\mathrm{C_8H_9Cl_3}

(d) C9H16Br2\mathrm{C_9H_{16}Br_2}

(e) C10H12N2O3\mathrm{C_{10}H_{12}N_2O_3}

(f) C20H32ClN\mathrm{C_{20}H_{32}ClN}

Answer

In organic structure problems, the quantity intended by “degree of saturation formula” is usually the degree of unsaturation, also called DBE or IHD. For the neutral, ordinary-valence formulas in this exercise,

DBE=2C+2+NHX2,\mathrm{DBE}=\frac{2C+2+N-H-X}{2},

where C,H,NC,H,N count carbon, hydrogen and nitrogen atoms, and XX counts all halogens. Oxygen does not enter this expression.

Calculate each formula

PartMolecular formulaSubstitution into the formulaDBE
(a)C6H5N\mathrm{C_6H_5N}(12+2+15)/2(12+2+1-5)/25
(b)C6H5NO2\mathrm{C_6H_5NO_2}(12+2+15)/2(12+2+1-5)/25
(c)C8H9Cl3\mathrm{C_8H_9Cl_3}(16+293)/2(16+2-9-3)/23
(d)C9H16Br2\mathrm{C_9H_{16}Br_2}(18+2162)/2(18+2-16-2)/21
(e)C10H12N2O3\mathrm{C_{10}H_{12}N_2O_3}(20+2+212)/2(20+2+2-12)/26
(f)C20H32ClN\mathrm{C_{20}H_{32}ClN}(40+2+1321)/2(40+2+1-32-1)/25

Thus the ordered answers are 5, 5, 3, 1, 6, 5.

What these numbers establish

Each ring contributes one DBE, each double bond contributes one, and each triple bond contributes two. For example, the value 1 in (d) allows one ring or one double bond; the molecular formula alone does not distinguish them. The exercise requests the six counts, not a unique structure.

This organic-chemistry calculation is not the soil-mechanics degree of saturation S=Vw/VvS=V_w/V_v, which measures the fraction of void space occupied by water. Nor should the neutral-formula DBE expression be applied blindly to ions or unusual valence states.

Evidence boundary

The six formulas and their order are from OpenStax Problem 7-2. This page interprets the search phrase in its organic-chemistry context as degree of unsaturation, not soil saturation. The results count rings and multiple-bond equivalents for ordinary neutral formulas; they do not determine unique molecular structures or establish aromaticity.

Sources

These references support the concepts and methods used in the explanation above.

Degree of Saturation Formula? Calculate Organic Degrees of Unsaturation | Verla