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The molecular formula is $\boxed{{\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{O}}_2}$, interpreting the vapour density as relative to air. The organic elemental analysis first determines a simpler empirical formula; the vapor-density molar mass measurement then fixes its multiple.

Take 100 mass units of the chemical substance and divide each elemental contribution by its rounded relative atomic mass:The empirical formula is therefore ${\mathrm{C}}_2{\mathrm{H}}_4\mathrm{O}$, with empirical formula mass approximately 44. Its calculated mass percentages are 54.55% carbon, 9.09% hydrogen and 36.36% oxygen. The small discrepancies from the given organic elemental analysis are consistent with rounded experimental data; they should not be converted into large, meaningless integer subscripts.

For equal volumes of ideal gases at equal temperature and pressure, the density ratio equals the molar mass ratio. On the air convention,Doubling ${\mathrm{C}}_2{\mathrm{H}}_4\mathrm{O}$ gives ${\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{O}}_2$; its rounded relative molecular mass of 88 predicts an air-relative vapor density of approximately $88/28.97=3.04$, close to 3.05. If the stated vapor density were instead relative to hydrogen, it would imply a relative molecular mass near 6.1, smaller than the empirical formula mass and incompatible with the analysis. That interpretation cannot describe a pure, undecomposed molecular vapor with the stated composition.

Under the older equivalent weight convention $\mathrm{C}=6$, $\mathrm{O}=8$, $\mathrm{H}=1$, the same composition and formula weight could be written ${\mathrm{C}}_8{\mathrm{H}}_8{\mathrm{O}}_4$. This is a change of notation, not eight modern carbon chemical atoms in the molecule. The result specifies composition and molar mass; it does not distinguish among structural isomers, such as ethyl acetate and butyric acid.

Burn a known mass of pure, suitably dry material completely, collect the resulting carbon dioxide and water separately, calculate the carbon and hydrogen masses, and obtain oxygen by difference under the stated three-element assumption. This is organic elemental analysis, not an identification of molecular structure.

Weigh a representative portion of mass $m$ in a clean combustion boat or suitable carrier. In the classical apparatus, a heated combustion tube contains an oxidizing material such as copper(II) oxide, with a controlled stream of clean, dry oxygen-bearing gas where the arrangement requires it. The purpose is complete conversion of carbon into carbon dioxide and hydrogen into water, without unburnt material escaping. An equation for a model substrate iswith the oxygen amount understood as the net external requirement when positive.

Downstream, a preweighed water-absorption tube collects the water. A following preweighed alkaline absorber collects the carbon dioxide; the order prevents water from being incorrectly attributed to the carbon dioxide absorber. Guards exclude atmospheric moisture and carbon dioxide during handling, and a final clean-gas sweep transfers products still held in the apparatus. Let the blank-corrected mass increases be $a$ for the water collector and $b$ for the carbon dioxide collector.

Using the simple historical atomic-mass ratios $\mathrm{C}=12$, $\mathrm{H}=1$, $\mathrm{O}=16$,Consequently,Modern work uses the appropriate modern molar masses in the same ratios. No sample mass or absorption results are supplied, so no numerical percentages are justified.

The oxygen already present in the sample cannot be obtained merely by measuring the oxygen in the combustion products: the oxidant supplies additional oxygen. Difference works here only because the sample is assumed to contain exclusively carbon, hydrogen and oxygen and to be free of unaccounted water, solvent, ash and other elements. If the combustion leaves a mineral residue, that mass cannot silently be reported as oxygen. A separate check of purity and residue therefore tests an assumption of the calculation.

Incomplete combustion, escaped vapour, exhausted absorbers, moisture entering from the carrier gas, and contamination of the carbon dioxide absorber all bias the result. A blank and an independent repeat with a suitable reference material check recovery. Oxygen by difference accumulates the errors in both other determinations; forcing the percentages to sum to 100 is not independent proof that the analysis is correct.