Question

In an organic compound of molar mass $108gmo{l^{ - 1}}$ , $C,{\text{ }}H{\text{ }}and{\text{ }}N$ atoms are present in $9:1:3.5$ by weight. Molecular formula can be:
A. ${C_6}{H_8}{N_2}$
B. ${C_7}{H_{10}}N$
C. ${C_5}{H_6}{N_2}$
D. ${C_4}{H_{18}}{N_3}$

Answer 1

The molecular formula of a compound represents the exact coefficients of every element present in the compound. A mole of a compound is the amount of a compound taken which is equal to the molecular weight of the compound.

Complete step by step answer:
The molecular mass is also referred to as the molar mass of the compound. The molar mass of a compound is the mass equal to the sum total of the masses of all the atoms present. Thus the molar mass of a compound with formula ${C_a}{H_b}{N_c}$ is equal to $a{\text{ }} \times$ atomic mass of $C$ + $b{\text{ }} \times$ atomic mass of $H$ + $c{\text{ }} \times$ atomic mass of $N$.
A molecular formula is the chemical representation of a compound in terms of chemical symbols of the element with exact number of atoms of the elements. The number of the atoms is indicated by the subscript after the symbol of each element.
The molar mass of the given organic compound $108gmo{l^{ - 1}}$. The ratio of the elements in the given molecule is $9:1:3.5$. The sum of the ratios gives the total number of the atoms present in the molecule =$9 + 1 + 3.5 = 13.5$.
The mass of carbon present in molar mass $108g$ = $\dfrac{{9 \times 108}}{{13.5}} = 72g$
The mass of hydrogen present in molar mass $108g$ = $\dfrac{{1 \times 108}}{{13.5}} = 8g$
The mass of nitrogen present in molar mass $108g$ = $\dfrac{{3.5 \times 108}}{{13.5}} = 28g$
The atomic mass of carbon, hydrogen and nitrogen is $12g$, $1g$,$14g$.
The mole of a compound is the ratio of the amount of a compound and the molar mass of a compound. It is expressed as
$mole = \dfrac{{amount{\text{ }}of{\text{ }}compound}}{{molar{\text{ }}mass{\text{ }}of{\text{ }}compound}}$
Thus the moles of carbon in the compound =$\dfrac{{72g}}{{12g}} = 6$
The moles of hydrogen in the compound = $\dfrac{{8g}}{{1g}} = 8$
The moles of nitrogen in the compound =$\dfrac{{28g}}{{14g}} = 2$
Thus the ratio of the moles of each element is $C:H:N = 6:8:2$ .
Hence the molecular formula of the compound is ${C_6}{H_8}{N_2}$, i.e. option A is the correct answer.

Note:
The molecular formula is different from the empirical formula of a compound. The empirical formula is the simplest ratio of the moles of the element. For the given compound the empirical formula is ${C_3}{H_4}N$.