Question

The empirical formula of a gaseous compound is $C{H_2}$. The density of the compound is $1.25{\text{ }}gm/{\text{ }}lit.$.at S.T.P. The molecular formula of the compound is:
A. ${C_2}{H_4}$
B. ${C_3}{H_6}$
C. ${C_6}{H_{12}}$
D. ${C_4}{H_8}$

Answer 1

In chemistry, the empirical formula of a compound can be calculated with the molecular by converting it into the simplest whole-number ratio. Thus, the molecular formula of the compound can be determined by equating the mass of nitrogen gas to the mass of the compound.

Complete step by step answer:
Here in the question, the empirical formula is given as $C{H_2}$ and the volume of this gas is exactly equal to the volume of nitrogen gas. So, under similar conditions, if the volumes of the two gases are the same, then the number of moles of the gases will be equal. It implies that the mass of both the gases are the same. So, the molecular mass of the nitrogen gas will be equal to the molecular mass of the compound. We know that the molecular mass of nitrogen gas is (N) is $28$g/mol
Calculation:
n =$\dfrac{Molecular\; mass}{empirical\; formula\; mass}$

$$n = {\text{ }}28.02{\text{ }}/{\text{ }}14 \\\ n = 2$$

Molecular formula = n (empirical formula)
Molecular formula =2($C{H_2}$)
Molecular formula = ${C_2}{H_4}$.

So, the correct answer is Option A.

Note: We should remember that the molecular formula of a compound is the chemical formula that tells the true formula of the compound or molecule. It refers to the actual number of atoms of various elements present in a molecule. The molecular formula is calculated by multiplying the number of moles with the empirical formula, where the number of moles is always an integer value. The empirical formula is the chemical formula that tells the simplest whole-number ratio of the atoms of all elements present in one molecule which is deduced by – (a) percentage composition of elements. (b) atomic masses.