On the earth, air is essential for every living being to lead a life. But other than that, air also plays a vital role in the world of chemistry. If you are a chemistry student, then you will get a chance to learn about the properties of air, the molar mass of air, and many interesting things related to it. Even for your chemistry assignments, your instructors may ask you to write answers to questions like what is the molar mass of air, how to calculate the molecular weight of air, and so on. In case, you have no idea about molar mass and the ways to find the molar mass of air, continue reading this blog. From here, you will learn complete details about the molecular weight of dry air in the aspects of chemistry.
What is Air?
Air in the Earth’s atmosphere is a mixture of invisible, tasteless, and odorless gases. It is predominantly made up of 21% of oxygen and 78 % of nitrogen that surrounds the earth. Also, air contains gaseous water called water vapor in addition to small traces of other gases such as argon, carbon dioxide, neon, methane, hydrogen, helium, krypton, and xenon.
What is the Molar Mass of Air?
Before we get to know about the molar mass of air, it is important to know what molar mass means. In simple terms, molar mass, also represented by ‘M’ is defined as the mass of one mole of any substance. The molar mass of a chemical compound is the ratio between the mass of the chemical compound and the amount of substance measured in moles.
Since air is a mixture of various gases, in chemistry, there is no formula for air. However, by considering the molecular weight of the constituents present in air, the average molar mass of air is found to be 28.96 g/mol.
Understand How to Calculate the Molecular Weight of Air
So, typically, a molar mass or molecular weight is the sum of the atomic weights of the atoms in the molecule. Atomic weight is nothing but an element’s average weight about all of its isotopes and their proportional abundances. Do you know how to find the molecular weight of air? If you have no idea, take a look below. Here, we have shared the steps for calculating the molecular weight of air.
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The Formula to Calculate the Molecular Weight of Air
The most dominant components in dry air are Nitrogen (N2) and Oxygen (O2). The air also contains traces of Carbon dioxide (CO2) and Argon (Ar). In air, the proportion of oxygen is 21%, nitrogen is 78%, argon is 0.934% and carbon dioxide is 0.03%.
Therefore, the formula for the molecular weight of air M = [(2 x Atomic Weight of O2 x 0.21) + ( 2 x Atomic Weight of N2 x 0.78)+(Atomic weight of C+ Atomic Weight of O2)0.0003+( Atomic Weight of Ar x 0.00934)]
Calculation
The atomic weights of
Oxygen= 15.9994 g/mol; O2= 2 x 15.994= 31.9988 g/mol
Nitrogen= 14.0067 g/mol ; N2= 2 x 14.0067= 28.0134 g/mol
Carbon dioxide = 44.01 g/mol
Argon= 39.948 g/mol
Apply the values of atomic weights in the formula to calculate the molar mass of air
M= [(31.9988x 0.21) + (28.0134 x 0.78)+( 44.01x 0.0003)+( 39.948 x 0.00934)]
= [6.71+ 21.85+0.013+0.373]
=28.956
= 28.96u approx
The molecular weight of air is 28.96g/mol.
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Other Ways to Calculate the Molar Mass of Air
Remember, you can also calculate the molar mass of air by adding the weight of each gas. To determine the molar mass of gas, you can use the ideal gas equation PV= [m/M]RT.
Here,
P is the pressure of the gas
V is the volume of gas
m is the Mass of gas
M is the number of moles present in the gas
R = 8.3145 J/(mol ∙ K) is the universal gas constant
T is the absolute gas temperature
So, to calculate the molar mass of air, the ideal gas equation can be rewritten as
M= [m/PV]RT
Calculating the Molar Mass of Air with the Volume of Gases
To determine the molar mass of air, it is necessary to know the values of m, P, V, and T.
It is difficult to determine the mass of gas if the measurement errors of P, V, and T in any experiment do not exceed 1%. Moreover, it is impossible even with modern engineering tools to remove the gas completely from the vessel.
So, there is another method in which we can determine M by slightly changing the mass and without removing the gas from the vessel. Say, if there is a vessel with volume V that contains a gas of mass m1 under pressure P1 and at temperature T, then the equation of state for this gas will be
P1V = [m1/M] RT
Without changing the temperature, let us pump out a part of the gas from the vessel. After evacuation, the partial pressures and the mass of gas in the vessel will decrease. Let us denote them as m2 and P2 and rewrite the equation as
P2V = [m2/M] RT
From these two equations, we get
M= (m1-m2) RT/ (P1-P2) V
By using this equation, you can determine M, if you know the values of the change in mass of the gas, in pressure, the temperature, and the volume.
The air is a mixture of nitrogen, oxygen, carbon dioxide, argon, water vapor, and other gases. Therefore, the above formula will help you in finding out the Molar mass of the mixture of gases. In this scenario, the identified value of M represents the gas mixture’s average or effective molar mass.
Theoretical Method to Calculate the Molar Mass of Air
If you know the values of the relative content and molar mass of each of the gases present in the mixture, then you can theoretically find out the molar mass of air.
The formula for theoretical calculation,
M= 1 divided by [ (m1/m) (1/M1)+ (m2/m) (1/M2)+….. (mn/m) (1/Mn)]
Here,
m1/m, m2/m are the relative fractions of the content of each gas
M1 and M2 are molar masses of gases in the air.
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Calculating the Molar Mass of Air with the Volume of Gases in the Mixture
What would be the molar mass of air, if it has the following compositions- 21% O2, 78% N2, 0.5% Ar, and 0.5% CO2?
Since the volumes of gases are proportional to their amounts (Avogadro’s law), the average molar mass of a mixture may be stated in terms of both volumes and substance quantities:
Mav = (M1 · V1 + M2 · V2 + M3 · V3 +) / (V1 + V2 + V3 + …) (1)
Mav = (M1 ν1 + M2 ν2 + M3 ν3 +) / (ν1 + ν2 + ν3 + …) (2)
For 1 mol of air, then v (O2) = 0.21 mol, v (N2) = 0.78 mol, v (Ar) = 0.005 mol and v (CO2) = 0.005 mol. By substituting these values into the formula, we will receive
Mav (air) = (0.21x 32 + 0.78 x 28 + 0.005 x 40 + 0.005 x 44) / (0.21 + 0.78 + 0.005 + 0.005)
Mav (air) = 29 g/mol.
The average molar mass of air is always considered to be 29 g/mol in several computational issues involving the relative density of gases in air.
Conclusion
Hopefully, by now, you will have learned how to calculate the molar mass of air. In case, you have any queries regarding it or if you need an expert to help you with your chemistry assignments on molar mass calculation, reach out to us quickly.
