Question

The relative density of a mixture of nitrogen and oxygen is $14.4\left( {H = 1} \right)$and the relative densities of nitrogen and oxygen are $14.0$and $16.0$$\left( {H = 1} \right)$respectively. Calculate the composition of the mixture: (i) by volume and (ii) by mass.

Answer 1

Hint: Relative density is the ratio of the density of a substance to the density of the standard. It is usually water for a solid or liquid and air for gas. Density is defined as the ratio of the amount of mass in a unit volume of matter and every substance has a different density.

Complete step by step answer:
The density of a sample is the ratio of the mass of the sample divided by the volume of a sample while relative density is calculated by solving the density of a sample to the density of the known reference of substance. It is a unitless quantity and it is measured at room temperature (20 Celsius degrees) and standard atmosphere. It can also be called Specific gravity. If the value of it is less than 1, then the substance is less dense than water and would float. The value of the relative density of the earth is $5.513g/c{m^3}$.

According to the question; (i) by volume in $1ml$
The mixture of nitrogen = $\left( x \right)ml$ and the mixture of oxygen = \[\left( {1 - x} \right){\text{ }}ml.\]
By using the formula, density= mass/volume.
Mass of $\left( x \right)ml$ of ${N_2}$ = density of nitrogen $ \times $volume of nitrogen = $14 \times x = 14xg$.
Mass of \[\left( {1 - x} \right){\text{ }}ml\] of ${O_2}$ = density of oxygen $ \times $volume of oxygen =$16 \times \left( {1 - x} \right) = (16 - 16x)g$.
Total mass of the mixture = $14x + 16 - 16x = (16 - 2x)g$.
It means,$14.4 \times 1 = 16 - 2x \Rightarrow x = 0.8$.
Hence, mixture of nitrogen = $x = 0.8ml$ and oxygen = $1 - x = 1 - 0.8 = 0.2ml$ by volume.

(ii) By mass in $1g$
The mixture of ${N_2}$= $\left( x \right)g$and its volume = mass /density =$x/14$.
The mixture of ${O_2}$= $\left( {1 - x} \right)g$and its volume =$1 - x/16$.
Total volume = $x/14 + 1 - x/16 = 1/14.4$
By solving this question, we get mass by using the formula i.e. density=mass/volume
$ x = 0.7778g\left( {{N_2}} \right) \\
  1 - x = 0.2222g\left( {{O_2}} \right) \\
$
Hence, nitrogen contains \[0.7778g{\text{ }}in{\text{ }}0.8ml\] and oxygen contains \[0.2222g{\text{ }}in{\text{ }}0.2ml\].

Note:
Students should remember that the total composition of the mixture is equal to 1. Relative density is called specific gravity when the reference density is the density of water. Specific gravity will help us to know whether the object sinks or floats.