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

Exercise 4

   

A substance contains $77.4\%\; C$. $7.5\%\; H$ and $15.1\%\; N$. Find all possible molecular formulas (The smallest one is called empirical formula).

Lets take $100\;g$ of this substance : $m_C= 77.4\; g$ $n_C= \frac{77.4}{12}=6.45$ $m_H= 7.5\;g$ $n_H= \frac{7.5}{1}=7.5$ $m_N= 15.1\;g$ $n_N= \frac{15.1}{14}=1.08$ The ratio $C:H:N$ is $6:7:1$ because: $\frac{6.45}{1.08}$ $\approx$ $6$ $\frac{7.5}{1.08}$ $\approx$ $7$ Empirical formula: $C_6H_7N$; Possible molecular formulas: $C_{6n}H_{7n}N_n$ (with $n$: integer)