Question

The empirical formula of a compound is $C{H}_2$. The mass of 1 liter of this gas is exactly equal to that of 1 liter of nitrogen under similar conditions. The molecular formula of the gas is:

• A. $C_2{H}_4$
• B. $O_3{H}_6$
• C. $C_6{H}_{12}$
• D. $C_4{H}_8$

Answer 1

The correct option is A $C_2{H}_4$

Empirical formula of a compound is CH2. The mass of 1 litre of this gas is exactly equal to that of 1 litre of nitrogen under similar conditions.
Under similar conditions, same volume of two gases corresponds to same number of moles of two gases. The number of moles of two gases are same and the mass is also same. This means that molecular weight of two gases is same. Thus, the molecular weight of the compound is equal to the molecular weight of nitrogen. It is equal to 28 g/mol. Hence, the molecular formula of the gas is $C_2{H}_4$
Note: Atomic weights of C and H are 12 g/mol and 1 g/mol respectively. Hence the molecular weight of $C_2{H}_4$ will be $2\left(12\right)+4\left(1\right)=28$ g/mol.