Question

A gas has a molecular formula ${\left( {CH} \right)_n}$. If the vapor density of the gas is 39, what should be the formula of the compound?
A. ${C_3}{H_3}$
B. ${C_4}{H_4}$
C. ${C_2}{H_2}$
D. ${C_6}{H_6}$

Answer 1

Hint: Molar mass is the mass of one mole of substance. Molar mass can be calculated by the sum of atomic mass of all atoms is the compound.

Complete step-by-step answer:
We know that, the relation between molar mass and vapor density is, ${\rm{Molar}}\;{\rm{mass}} = {\rm{2}} \times {\rm{Vapor}}\;{\rm{density}}$. First we calculate the molar mass of the compound ${\left( {CH} \right)_n}$. Two elements present in the compound, carbon and hydrogen and the number of atoms of individual elements is n. So, to calculate the molar mass of the compound, we have to add the atomic mass of carbon and hydrogen and have to multiply the result with n.

$\begin{array}{c}{\rm{Molar}}\;{\rm{mass}}\;{\rm{of}}\;{\rm{compound}}{\left( {CH} \right)_n} = \left( {12\;{\rm{g}}\;{\rm{mo}}{{\rm{l}}^{ - 1}} + 1\;{\rm{g}}\;{\rm{mo}}{{\rm{l}}^{ - 1}}} \right) \times n\\ = 13n\;{\rm{g}}\,{\rm{mo}}{{\rm{l}}^{ - 1}}\end{array}$

The density of vapor in relation to hydrogen is termed as vapor density. In other terms Vapor density can be understood as the ratio of a certain volume of gas and the mass of equal volume of hydrogen.

Now, we use the relation between molar mass and vapor density to calculate the value of n. The value of vapor density given is 39.

$\begin{array}{c}{\rm{Molar}}\;{\rm{mass}} = {\rm{2}} \times {\rm{Vapor}}\;{\rm{density}}\\{\rm{13}}n = 2 \times 39\\n = \dfrac{{2 \times 39}}{{{\rm{13}}}}\\n = 6\end{array}$

So, the value of n is 6. Now, we have to substitute the value of n in the given molecule formula, that is, ${\left( {CH} \right)_n} = {\left( {CH} \right)_6}$. So, the molecular formula of the compound is ${C_6}{H_6}$.

Hence, option D is correct.

Note: Students might get confused in density and vapor density. Vapor density is the number of times a given volume of gas is heavier than the same volume of hydrogen measured and density is the ratio of mass to volume.