Elementary analysis of carboxylic acids

Exercise 1

A saturated aliphatic monocarboxylic acid contains $31.37\%\;O$ Find condensed formulas of all possible isomers.

1) One double bond, 2 O atoms: General formula: $C_nH_{2n}O_2$ $\%_O$ $=$ $\frac{32\cdot 100}{12n+2n+32}$ $\frac{3200}{14n+32}$ $=$ $31,37$ $n$ $=$ $5 $ Molecular formula: $C_5H_{10}O_2$ 2) Condensed formulas: $CH_3(CH_2)_3COOH$ $CH_3CH_2CH(CH_3)COOH$ $CH_3CH(CH_3)CH_2COOH$ $CH_3C(CH_3)_2COOH$