The relative molecular mass of an alkanoic acid with the empirical formula of CH\(_2\)O is [ H = 1, C = 12, O = 16 ]

Answer Details

An alkanoic acid (carboxylic acid) has the general formula \(\text{C}_n\text{H}_{2n}\text{O}_2\). The task is to find the molecular formula whose empirical formula is CH\(_2\)O and whose molecular formula fits the alkanoic acid pattern.

First, calculate the empirical formula mass of CH\(_2\)O:

\[12 + 2(1) + 16 = 30\]

The molecular formula must be a whole-number multiple of the empirical formula: \((\text{CH}_2\text{O})_n\). To satisfy the alkanoic acid general formula \(\text{C}_n\text{H}_{2n}\text{O}_2\), we need 2 oxygen atoms, which requires \(n = 2\):

\[(\text{CH}_2\text{O})_2 = \text{C}_2\text{H}_4\text{O}_2\]

This is ethanoic acid (acetic acid, CH\(_3\)COOH), a well-known alkanoic acid.

The relative molecular mass is:

\[2(12) + 4(1) + 2(16) = 24 + 4 + 32 = 60\]

The answer is 60.