Question

The vapour density of a gas is $11.2$, at N.T.P. how much volume will occupy
A. \[1.12{\text{ }}liters\]
B. \[0.112{\text{ }}liters\]
C. \[11.2{\text{ }}liters\]
D. \[12{\text{ }}liters\]

Answer 1

Hint:From the question it is quite evident to us that we need to understand the basics of vapor density to solve this question. As we know, vapour density is defined as the density of a vapour that is related to that of hydrogen. Mathematically, vapour density is equal to half of the molar mass of a substance.

Complete step by step answer:

We know that, mathematically vapour density is defined as the mass of a certain volume of a substance divided by mass of the same volume of hydrogen.
Thus, Vapour density = $\dfrac{{mass\;of\;n\;molecules\;of\;gas}}{{mass\;of\;n\;molecules\;of\;hydrogen}}$
Also, vapour density = $\dfrac{1}{2}$ × molar mass.
So, molar mass = 2 × Vapour density
 Thus, molecular weight will be equal to two times of the vapour density of a substance.
Molecular weight = 2 $ \times $ Vapour Density (V.D.)
Here, we will substitute the values from the question.
Molecular weight = $11.2 \times 2$ =$22.4g$
So, number of moles = $n = \dfrac{{molecular\;weight}}{{vapour\;density}}$ = $\dfrac{{22.4}}{{11.2}}$
Thus, number of moles =\[\;n{\text{ }} = {\text{ }}0.5{\text{ }}moles\].
At STP, 1 mole of the gas occupies \[22.4{\text{ }}L\].
Volume occupies at STP is \[0.5{\text{ }}\times{\text{ }}22.4{\text{ }} = {\text{ }}11.2{\text{ }}liters\]

Hence option C is correct.


Note:
We need to understand the basic difference between density and vapour density. Density is the ratio of mass of a substance to its volume. And vapour density is the ratio of weight of a certain volume of gas. Also, we need to remember that when the vapor density of a gas is less than one it will rise in air and when it is greater than one the gas will sink in air.