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

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.