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In a compound carbon, hydrogen and nitrogen are present in $9:1:3.5$ by weight. If the molecular weight of the compound is$108$, then the molecular formula of the compound is.
A)${C_2}{H_6}{N_2}$
B)${C_3}{H_4}N$
C) ${C_6}{H_8}{N_2}$
D) ${C_9}{H_{12}}{N_3}$


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Last updated date: 19th Jun 2024
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Answer
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Hint:We all know that the empirical formula of a compound is the simplest whole number ratio of each type of atom in a compound. An empirical formula is calculated from information about the mass of each element in a compound or from the percentage composition.

Complete step by step answer:
The mass ratio of carbon, hydrogen and nitrogen are present in $9:1:3.5$
The molecular weight of the substance can be calculated as,
The atomic weight of carbon is $12$.
The atomic weight of hydrogen is $1$.
The molecular weight of nitrogen is $14$.
Molar ratio of $C:H:N = \dfrac{9}{{12}}:\dfrac{1}{1}:\dfrac{{3.5}}{{14}} = 0.75:1:0.25$
The smaller ratio is$0.25$.
The integer ratio is $ = \dfrac{{0.75}}{{0.25}}:\dfrac{1}{{0.25}}:\dfrac{{0.25}}{{0.25}} = 3:4:1$
Thus the empirical formula of the compound is ${C_3}{H_4}N$
The empirical weight of the compound is $54g$.
The molecular formula is the expression of the number of atoms of each element in one molecule of a compound if the molar mass value is known the molecular formula is calculated by the empirical formula.
${\text{n}} = \dfrac{{{\text{Molar mass}}}}{{{\text{Mass of the empirical formula}}}}$
Substituting the values we get,
$ \Rightarrow $${\text{n}} = \dfrac{{108}}{{54}} = 2$
The molecular formula of the compound is ${C_6}{H_8}{N_2}$.
Therefore option C is correct.

Note: Now discuss about the steps for determining the empirical formula of a compound as follows:
The mass of each element present in grams has to be calculated.
The number of moles of each atom present has to be found.
The number of moles of each element has to be divided by the smallest number of moles.
The numbers of moles have to be converted to whole numbers. The set of whole numbers are the subscripts in the empirical formula.