Question

Air contains nitrogen and oxygen in the volume ratio of 4:1 .The average vapour density of air is :
A.30
B.28.8
C.28
D.14.4

Answer 1

Hint:Nitrogen and oxygen are present by volume , so first we will calculate the total molecular mass of air. We will then keep this valve of molecular mass in the vapour density formula and calculate the value of vapour density.

Complete step by step answer:
Nitrogen and oxygen are present in the volume ratio of 4:1 . It means 80% nitrogen and 20% oxygen are present in the gas.

Vapour Density of a gas is the relative ratio of the density of that gas to that of density of hydrogen gas. Mathematically,
Vapour density =$\dfrac{{density(gas)}}{{density({H_2})}}$.
We will use this equation to procced through the question. We will now learn to calculate density of a gas.
From ideal gas equation we have,
$
  PV = nRT \\
  PV = \dfrac{w}{M}RT \\
  \dfrac{{PM}}{{RT}} = \dfrac{w}{V} \\
 $
Where
 $
  P = pressure \\
  V = volume \\
  T = temperature \\
  n = moles \\
 $

Since ,
$\dfrac{w}{V} = density(gas)$
We can rewrite the above equation as ${d_{gas}} = \dfrac{{PM}}{{RT}}$……….(i) . This is the general equation of calculating the density of any gas. Keeping all other factors constant , density depends on molecular mass of gas i.e. $M$.
We can now write it as :
 Vapour density = $\dfrac{{{d_{gas}}}}{{{d_{{H_2}}}}} = \dfrac{{{M_{gas}}}}{{{M_{{H_2}}}}}$.
Since the molecular mass of hydrogen gas is 2. The equation gets reduced to-
$VD = \dfrac{{{M_{gas}}}}{2}$…………(ii)

We will now calculate the molecular mass of the gas.
${M_{gas}} = \dfrac{{80}}{{100}} \times m({N_2}) + \dfrac{{20}}{{100}} \times m({O_2})$
$
  {M_{gas}} = \dfrac{4}{5} \times 28 + \dfrac{1}{5} \times 32 \\
  {M_{gas}} = 22.4 + 6.4 \\
  {M_{gas}} = 28.8 \\
    \\
 $
We know the relation between density and molecular mass . Now using that:
From equation (ii),
 $
  VD = \dfrac{{{M_{gas}}}}{2} \\
  VD = \dfrac{{28.8}}{2} \\
  VD = 14.4 \\
 $
Hence, option (D) is correct.

Note: Vapour density is a unitless quantity . Vapour density is only calculated for gas and vapour. There are only 14 gases and vapour with a vapour density less than one, i.e. they are lighter than air. The density and vapour density of a gas are not the same. More the vapour density of a gas, the heavier the gas will be.