To determine the molecular formula of an unknown organic compound, first determine its composition ratio by elemental analysis, then establish the molecular formula from its molecular mass. These are frequently tested calculation problems.
Basic Knowledge
Elemental analysis by combustion (Liebig method): Completely burn the sample and collect the resulting H2O and CO2 in absorption tubes to measure their masses.
・Mass of H = (mass of H2O)×(2/18)
・Mass of C = (mass of CO2)×(12/44)
・Mass of O = mass of sample - mass of C - mass of H (when no other elements are present)
Divide the mass of each element by its atomic mass to obtain the mole ratio, then convert it to the simplest whole-number ratio to obtain the empirical formula.
Determining the molecular formula: The molecular formula is an integral multiple of the empirical formula, based on the ratio of the formula mass of the empirical formula to the molecular mass (measured by the vapor-density method, freezing-point depression, mass spectrometry, or similar methods). Example: empirical formula CH2O (formula mass 30), molecular mass 60 → molecular formula C2H4O2.
Degree of unsaturation (IDoU): CnHmNpOqXr (X is a halogen) → IDoU = (2n + 2 + p - m - r)/2. Each double bond and each ring contributes +1.
Mass of C (= mass of CO2×12/44)
Mass of H (= mass of H2O×2/18)
Empirical formula (simplest whole-number ratio, example: CH2O)
Molecular formula (= empirical formula×integer n, determined from molecular mass)
Degree of unsaturation (CnHm→(2n+2-m)/2)
Structural formula (a formula that explicitly shows the bonding arrangement of atoms)
Further Study (Principles and Applications)
Modern elemental analysis uses an automated CHNS analyzer, enabling precise measurement with only 1–3 mg of sample. Mass spectrometry (MS) can measure molecular mass to an accuracy of one atomic mass unit, and high-resolution MS can determine the molecular formula directly (for example, distinguishing C2H4O2=60.0211 from C3H8O=60.0575).
The sequence for structure determination is: ① molecular formula → ② calculate degree of unsaturation → ③ identify functional groups by IR (infrared spectroscopy) → ④ determine the H/C skeleton by NMR (nuclear magnetic resonance) → ⑤ examine fragments by MS → ⑥ determine the three-dimensional arrangement by X-ray crystallography.
In high-school entrance examinations, the common pattern is to infer the structure from the chemical reactions of functional groups (silver-mirror test, Fehling’s test, iodoform test, and so on), without using IR or NMR.
- Combustion method: calculate C from CO2 and H from H2O masses
- Mass of O = sample mass - C - H
- The empirical formula is the simplest whole-number ratio
- Molecular formula = empirical formula×n; n is determined from molecular mass
- Degree of unsaturation = (2n+2-m)/2 (CnHm)
- Degree of unsaturation 1 = one double bond or one ring
- CHNS analysis + MS is standard today
Points to Note (Common Confusions and Frequent Errors)
① In a combustion tube, the CaCl2 tube (absorbs H2O) comes first, followed by the soda lime tube (absorbs CO2). If the order is reversed, soda lime also absorbs H2O. ② When nitrogen is present, combustion produces N2 or nitrogen oxides, so another method, such as the Dumas method, is required. ③ Difference between empirical and molecular formulas: empirical formula CH2O can correspond to molecular formulas such as C2H4O2 (acetic acid) and C6H12O6 (glucose).
Practice
- When 30 mg of an organic compound consisting only of C, H, and O is completely burned, 44 mg of CO2 and 18 mg of H2O are obtained. Find its empirical formula.
- When the empirical formula of a compound with molecular mass 60 is CH2O, find its molecular formula.
- Calculate the degree of unsaturation of C4H8 and draw all possible structures.