= Solution
\b[The molecular formula is $\boxed{\mathrm{C_4H_8O_2}}$, 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>:
$$
n_{\mathrm C}:n_{\mathrm H}:n_{\mathrm O}
=\frac{54.35}{12}:\frac{9.11}{1}:\frac{36.54}{16}
=4.5292:9.1100:2.2838
\simeq 2:4:1.
$$
The <empirical formula> is therefore $\mathrm{C_2H_4O}$, 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,
$$
M\simeq 3.05\times28.97\ \mathrm{g\,mol^{-1}}=88.36\ \mathrm{g\,mol^{-1}},\qquad
\frac{M}{44\ \mathrm{g\,mol^{-1}}}\simeq2.
$$
Doubling $\mathrm{C_2H_4O}$ gives $\mathrm{C_4H_8O_2}$; 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 $\mathrm{C_8H_8O_4}$. 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>.
Back to article page
