# Vapour density of a volatile substance is 4 in comparison to methane $\left( {{\text{C}}{{\text{H}}_4} = 1} \right)$. Its molecular mass will be:A) 8B) 2C) 64D) 128

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Hint: The relationship between the molecular mass and the vapour density is ${\text{molecular mass = }}2 \times {\text{vapour density}}$.

The relationship between the molecular mass and the vapour density for two substances is

$\dfrac{{{\text{molecular mass of volatile substance}}}}{{{\text{molecular mass of methane}}}}{\text{ = }}\dfrac{{{\text{vapour density of volatile substance}}}}{{{\text{vapour density of methane}}}}$.

Rearrange above expression:

${\text{ }}\begin{array}{*{20}{c}} {{\text{molecular mass of}}} \\ {{\text{volatile substance}}} \end{array}{\text{ = }}\dfrac{{{\text{vapour density of volatile substance}}}}{{{\text{vapour density of methane}}}} \times {\text{ }}\begin{array}{*{20}{c}} {{\text{molecular mass}}} \\ {{\text{of methane}}} \end{array}$... ...(1)

The ratio of the vapour density of a volatile substance to that of methane is 4. The molecular mass of methane is 12+4(1)=16. Substitute values in equation (1).

${\text{molecular mass of volatile substance = }}\dfrac{{{\text{vapour density of volatile substance}}}}{{{\text{vapour density of methane}}}} \\ {\text{ }} \times {\text{ molecular mass of methane}} \\ {\text{molecular mass of volatile substance = }}\dfrac{4}{1} \times {\text{ 16}} \\ {\text{molecular mass of volatile substance = 64}} \\$
The molecular mass of volatile substances will be 64.

The correct answer is option C.

Note:
Write a correct relationship between the molecular mass and the vapour density. Avoid calculation errors. Vapour density is the density of a gas relative to that of hydrogen under identical conditions of temperature and pressure.