Combustion Analysis Calculator

Article — Combustion Analysis Calculator

Combustion Analysis Calculator: Empirical Formula from CO₂ and H₂O Masses

Combustion analysis determines the empirical formula of an organic compound by burning a measured mass of sample in excess oxygen, then weighing the CO₂ and H₂O products. Each mole of CO₂ contains one mole of carbon from the sample; each mole of H₂O contains two moles of hydrogen. Mass of oxygen is calculated by difference: m_O = m_sample − m_C − m_H. A typical worked example: 0.255 g of an unknown produces 0.561 g CO₂ and 0.306 g H₂O. That gives 12.74 mmol of C, 33.96 mmol of H, and 4.23 mmol of O (by difference). Divide each by the smallest (5.94 mmol) to get a 3: 8: 1 ratio, which rounds to CH₂O × 2 → C₃H₈O, the formula of ethanol. If you also know the molar mass (46 g/mol), the molecular formula is the same as the empirical formula in this case.

This calculator returns the empirical formula directly from CO₂, H₂O, and sample masses, including percent compositions of C, H, and O. Provide the molar mass and it converts the empirical formula to the molecular formula automatically.

What is combustion analysis

Combustion analysis is a classic analytical technique for determining the elemental composition of an organic compound by completely burning a known mass in excess oxygen. The products — CO₂ and H₂O for carbon-hydrogen-oxygen compounds, plus N₂ and SO₂ for nitrogen and sulfur — are trapped by selective absorbents and weighed. From the trapped masses, the moles of each element in the original sample are calculated, then converted to an empirical formula.

Antoine Lavoisier introduced the technique in the 1780s. Justus von Liebig refined it in the 1830s into the standard Kaliapparat apparatus that defined organic analytical chemistry for over a century. Modern CHN analysers automate the process down to 5-minute runs on 1 to 5 mg of sample.

Combustion analysis formula step by step

The combustion analysis formula proceeds step by step: convert CO₂ mass to moles of C (one C per CO₂), convert H₂O mass to moles of H (two H per H₂O), then compute oxygen by mass difference. Atomic masses are C = 12.011, H = 1.008, O = 15.999, CO₂ = 44.009, H₂O = 18.015 g/mol.

Step 1: n_CO₂ = m_CO₂ / 44.009 → n_C = n_CO₂. Step 2: n_H₂O = m_H₂O / 18.015 → n_H = 2 × n_H₂O. Step 3: m_C = n_C × 12.011, m_H = n_H × 1.008. Step 4: m_O = m_sample − m_C − m_H, n_O = m_O / 15.999. Step 5: divide every mole count by the smallest, round to whole numbers, write the empirical formula.

Empirical vs molecular formula

The empirical formula is the simplest whole-number ratio of atoms; the molecular formula is the actual count per molecule. Glucose has the empirical formula CH₂O and the molecular formula C₆H₁₂O₆ — the same ratio, six times. Acetic acid has empirical CH₂O and molecular C₂H₄O₂. Formaldehyde, the simplest of the three, is CH₂O in both forms.

To convert empirical to molecular, you need the molar mass from an independent measurement (mass spectrometry, freezing-point depression, vapour density). Divide the actual molar mass by the empirical mass to get the multiplier n, then scale every subscript: (CH₂O)_n.

Combustion analysis of organic compounds with oxygen

Combustion analysis of organic compounds with oxygen always determines oxygen by difference, never directly. The reason: the CO₂ and H₂O traps cannot distinguish O atoms that came from the sample from O atoms that came from atmospheric O₂. Mass conservation lets us solve: anything not in the trapped C or H must be O (or other elements added by separate analysis).

This makes combustion analysis very sensitive to sample mass accuracy. A 1% error in sample weight propagates to a much larger error in oxygen percentage if O is small relative to C and H.

Combustion analysis with nitrogen or sulfur

Combustion analysis with nitrogen or sulfur requires extra traps or a separate measurement. Nitrogen is determined by the Dumas method: burn the sample, reduce all NOₓ to N₂, separate gases by chromatography, and quantify with a thermal-conductivity detector. Sulfur is oxidised to SO₂ and trapped by oxidising solutions or measured by IR. Halogens (Cl, Br, I) require Schöniger or Wickbold combustion with absorption in alkaline solution.

Modern CHN vs classic Liebig combustion analysis

Modern CHN analysers automate the classic Liebig combustion in a closed instrument. A few milligrams of sample drops into a hot oxygen-pulsed combustion tube, the products pass through copper to reduce NOₓ, then through gas chromatography with thermal conductivity detection. Carbon (as CO₂), hydrogen (as H₂O), and nitrogen (as N₂) are quantified simultaneously in about 5 minutes per sample. Modern instruments achieve ±0.3% absolute accuracy on each element.

Worked combustion analysis examples

Worked combustion analysis examples make the procedure concrete. Example 1 — ethanol: 0.230 g of unknown gives 0.440 g CO₂ and 0.270 g H₂O. n_C = 10.00 mmol, n_H = 30.00 mmol. m_C = 0.1201 g, m_H = 0.030 g. m_O = 0.230 − 0.150 = 0.080 g, n_O = 5.0 mmol. Ratio 2: 6: 1 → C₃H₈O, the formula for ethanol. Example 2 — glucose: a 0.150 g sample yields 0.220 g CO₂ and 0.090 g H₂O. n_C = 5.0 mmol, n_H = 10.0 mmol, n_O (by diff) = 5.0 mmol. Ratio 1: 2: 1 → empirical CH₂O. With molar mass 180.16, n = 6, so the molecular formula is C₆H₁₂O₆.

Common combustion analysis mistakes

The most common combustion analysis mistake is incomplete combustion, which leaves carbon as soot or CO instead of CO₂. The carbon count comes out low and the empirical formula skews wrong. Modern analysers add a Cu or Pt catalyst to ensure full oxidation. Second mistake: forgetting the multiplication by 2 for hydrogen (each water molecule has two hydrogens). Third: trying to determine oxygen by direct trapping — it cannot be distinguished from the atmospheric oxygen used to burn the sample.