Question

Calculate the vapour density of a sample containing 5 moles of ${O_2}$ and 5 moles of ${N_2}$ with respect to He.

Answer 1

Hint: Vapor density is defined as the density of vapor which is in relation with hydrogen. It is the mass of some volume of compound which is divided by the mass of hydrogen of the same volume. The vapor density is related to the molecular weight.

Complete step by step answer:
Given,
Moles of ${O_2}$ is 5 moles.
Moles of ${N_2}$ is 5 moles.
The number of moles is calculated by using the formula shown below.
The formula for calculating the moles is shown below.
$n = \dfrac{m}{M}......(i)$
Where
n is the number of moles of compound.
m is the mass of the compound.
M is the molar mass of the compound.
The molecular mass of ${O_2}$ is 32 g/mol.
The molecular mass of ${N_2}$ is 28.0134 g/mol.
To calculate the mass of ${O_2}$gas substitute the value of mole and molar mass in equation (i).
$5mol = \dfrac{m}{{32g/mol}}$
$\Rightarrow m = 160g$
To calculate the mass of ${O_2}$gas substitute the value of mole and molar mass in equation (i).
$5mol = \dfrac{m}{{28.031g/mol}}$
$\Rightarrow m = 140g$
The relation between the molar mass and vapour density is shown below.
$V.D = \dfrac{M}{2}$
Where,
V.D is the vapor density.
M is the molecular weight or molar mass.
To calculate the vapour density, substitute the values in the above equation.
$V.D = \dfrac{{160 + 140}}{4}$
$\Rightarrow V.D = \dfrac{{300}}{4}$
$\Rightarrow V.D = 75$

Therefore, the vapour density of a sample containing 5 moles of ${O_2}$ and 5 moles of ${N_2}$ with respect to He is 75. .

Note: If any gas whose value of vapor density is less than one, it will rise and flow in the air, when the value of vapour density is more than one, the gas will start to sink in the air.