Question

Atmospheric air has 78% N$_2$; 21% O$_2$; 0.9% Ar and 0.1% CO$_2$, by volume. What is the molecular mass of air in the atmosphere?

Answer 1

Hint : This question is based on the concept of Avogadro’s principle. In the question we are given a different volume percentage of gases. It is related to the summation of volumes with the molar mass. So, the molecular mass of air in the atmosphere can be calculated.

Complete step by step answer :
We have 78% of nitrogen gas, 21% of oxygen gas, 0.9% of argon gas, and 0.1 % of carbon-dioxide in air
As mentioned, it is related to Avogadro’s principle, it states that volume of different gas will contain equal number of molecules under the same temperature, and pressure conditions.
Thus, the molar mass of mixture of gases is related to the summation of percentage of each gas by volume multiplied with the molar mass of the individual gas.
Now, if we calculate for nitrogen gas, the molar mass of nitrogen gas is 28 (as it is in diatomic state), thus it will be $\dfrac{78}{100}$ $\times$28 = 21.84
Similarly if we calculate for oxygen it will be $\dfrac{21}{100}$ $\times$32 = 6.72

For argon gas, it is $\dfrac{0.9}{100}$ $\times$40 = 0.36

For carbon-dioxide, it is $\dfrac{0.1}{100}$ $\times$44 = 0.04

So, the total molar mass of mixture of gases in air =21.84 + 6.72 + 0.36 + 0.04 =28.96
In the last we can conclude that the molecular mass of air in the atmosphere is 28.96 u.

Note : Don’t get confused while calculating the molar mass from the given percentage volume. You have to convert the percentage into numbers by dividing to 100, and then multiply with the respective molar masses as shown, and the molar mass is calculated on the basis of their nature like oxygen exists as diatomic molecule in gaseous, so it is considered to be 32 instead of 16.