Question

The vapour density of a gas depends upon the:
A. Total number of electrons in the molecule
B. Total number of neutrons in the molecule
C. Total number of molecules
D. molecular mass of gas

Answer 1

Vapour density is defined as the ratio of density of a substance with compared to the density of the Hydrogen
$V.D = \dfrac{Density~of~sub.}{Density~of~{{H}_{2}}}$

Complete Solution :
Now, the ideal gas equation can correctly describe the relationship between Vapour density and options given above.
PV = nRT
$PV=\dfrac{m}{M}RT$
As n = no. of moles which can be written as given mass of substance/molecular mass of substance, rearranging the equation just a bit,
$PM=\dfrac{m}{V}RT$
PM = dRT, because mass/ volume is density itself.
If we assume that there is a substance whose density is ${{d}_{s}}$ and molecular mass is M, then
$PM = {{d}_{s}}RT$ …1
Now, the density of Hydrogen is ${{d}_{{{H}_{2}}}}$ and Molecular mass of hydrogen is ${{M}_{{{H}_{2}}}}$ , then
$P{{M}_{{{H}_{2}}}}={{d}_{{{H}_{2}}}}RT$ …2
Dividing both the equations, we get:
$\dfrac{M}{2} = \dfrac{{{d}_{s}}}{{{d}_{{{H}_{2}}}}}$
Because the molecular mass of hydrogen is 2 gm and we already defined the vapour density and applying these into the formula we get,
V.D= 2 x M
Which states that vapour density of a gas depends upon the molecular mass of a gas and nothing else.
So, the correct answer is “Option D”.

Note: There is always a confusion among the students about the absolute density and vapour density, therefore, vapour density is a part of absolute density. Absolute density is a ratio between density of a substance to that of density of a reference. When that reference is taken water, it becomes specific gravity and when that reference is hydrogen, it is vapour density.