Question

A gaseous mixture of $ {H_2} $ ​ and $ {N_2}O $ gas contains 66 mass % of $ {N_2}O $ . What is the average molecular mass of a mixture?

Answer 1

Hint: The average molecular mass is defined as the ratio of the total mass of the mixture or polymer and the total no. of moles of substances in the mixture/ total no. of polymer molecules. Its unit is the same as molecular mass i.e. g/mol.

Complete Step By Step Answer:
We are given a mixture of $ {H_2} $ ​ and $ {N_2}O $ gas. The % weight of $ {N_2}O $ is given as 66%. Let us assume the total weight of the mixture of $ {H_2} $ ​ and $ {N_2}O $ gas to be 100gm. Therefore, 66% of it which is equal to 66gm will be $ {N_2}O $ . We need to find the mass of $ {H_2} $ present in the mixture.
Total mass of the mixture = 100gm
Mass of $ {N_2}O $ gas = 66gm
Mass of $ {H_2} $ gas $ = (100 - 66) = 34gm $
The formula for finding the average molecular mass is given as: $ {M_{average}} = \dfrac{{Total{\text{ }}Mass}}{{Total{\text{ }}Moles}} $
The no. of moles of each gas present in the mixture can be found out by using the formula: $ Moles = \dfrac{{Mass(g)}}{{Molar{\text{ }}Mass(g/mol)}} $
First let us know the Molar Mass of each gas present in the mixture. The molar mass of $ {H_2} $ gas is 2g/mol and that of $ {N_2}O $ is 44 g/mol
The no. of moles of $ {N_2}O $ $ = \dfrac{{66}}{{44}} = 1.5mol $
The no. of moles of $ {H_2} $ $ = \dfrac{{34}}{2} = 17mol $
On substituting the values to find the average molecular mass we get: $ {M_{average}} = \dfrac{{66 + 34}}{{1.5 + 17}} $
 $ {M_{average}} = \dfrac{{100}}{{18.5}} = 5.4g/mol $
This is the required answer. The average molecular mass is 5.4 g/mol of the mixture.

Note:
There are various methods to determine the average molecular weight of a polymer in the laboratory. These include gel permeation chromatography, light-scattering measurements and viscosity measurements. There two types of average molecular weight, those are number average molecular weight and weight average molecular weight.