Determination of the molecular formula by the percentage of elements and the molar mass

Exercise 3

   

A substance contains $40\%\; C$. $6.7\%\; H$ and $53.3\%\; O$. Find all possible molecular formulas (The smallest one is called empirical formula).

Lets take $100\;g$ of this substance : $m_C= 40\; g$ $n_C= \frac{40}{12}=3.33$ $m_H= 6.7\;g$ $n_H= \frac{6.7}{1}=6.7$ $m_O= 53.3\;g$ $n_O= \frac{53.3}{18}=3.33$ The ratio $C:H:O$ is $1:2:1$ Empirical formula: $CH_2O$; Possible molecular formulas: $CH_2O$. $C_2H_4O_2$. $C_3H_6O_3$. ...$C_nH_{2n}O_n$ (with $n$: integer)