Density‌ ‌of‌ ‌Air‌

The density of a body is the mass of the body per unit volume. Therefore, density of air is the mass of air contained in a unit volume of a container. There are some factors that the density of the air depends upon. In the case of the atmosphere, the density of air varies from place to place. 

Here, we will discuss how to calculate the value of air density at different temperatures and pressures using the density of air formula. 

Amedeo Avogadro

Lorenzo Romano Amedeo Carlo Avogadro (9 August 1776 – 9 July 1856) was an Italian scientist best known for his contribution to molecular theory, which is now known as Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Amadeo Avogadro, discovered it in the early 1800s. In layman's terms, he discovered that no matter what gas is in the container, a fixed volume of gas, say one cubic metre, at the same temperature and pressure, will always have the same number of molecules. The majority of first-year chemistry textbooks describe how this works.

What is Density of Air ?

The density of air is defined as the mass per unit volume of air. The S.I unit of density of air is kg/m3. Consider an air taken in a container of volume 1 m3, then the mass of the air inside that container having volume 1 m3 is equal to the density of air.There are some factors that the density of air depends upon. 

Variation of Density of Air at Different Altitudes

As we know the density of air in the atmosphere changes its value from place to place. As we are moving up away from the sea level, the density of air decreases. So the density of air is maximum at sea level. That is why mountaineers carry oxygen cylinders because the density of air is less at higher altitudes. So they need oxygen cylinders for easy breathing. 

Derivation of Density of Air Formula

To derive the density of air formula , we use the ideal gas equation given by

$\Rightarrow PV=nRT$ …(1)

Where,

P- Pressure of the the gas

V- Volume of the gas

n - Number of moles of the gas

R - Universal gas constant

T - Temperature of the gas.

The formula to calculate the number of moles is given by ,

$\Rightarrow n=\dfrac{M}{M_0}$

Where,

n- Number of moles of the the gas

M- Mass of the the gas

M0- Molecular mass of the gas.

Substitute the equation for number of moles (n) in the ideal gas equation(1) and simplify

$\Rightarrow PV=nRT$

$\Rightarrow PV=\dfrac{M}{M_0}RT$

$\Rightarrow PM_0=\left(\dfrac{M}{V}\right)RT$…(2)

The formula to calculate the density of air  is given by,

$\Rightarrow D=\dfrac{M}{V}$

Where,

D - Density of the the gas

M- Mass of the the gas

V- Volume of the the gas

So, we can substitute density of the gas (D) for the expression M/V in the equation (2) and simplify to get the formula for density of the gas.

$\Rightarrow PM_0=DRT$

$\Rightarrow \dfrac{PM_0}{RT}=D$

$\Rightarrow D=\dfrac{PM_0}{RT}$

So, we obtain the air density formula as,

$\Rightarrow D=\dfrac{PM_0}{RT}$

Effect of Temperature and Pressure on Density of air

We have derived the air density formula given by, 

$\Rightarrow D=\dfrac{PM_0}{RT}$

So, whenever the pressure and temperature of air changes, the density of the air changes. The density of air is inversely proportional to the temperature of the air. Therefore, whenever the temperature of the air increases, the density of the air decreases and whenever the temperature of the air decreases,

From the air density formula, we can understand that density of the air is directly proportional to the pressure of the gases. That means that when the pressure of the air increases, then the air density value also increases. Also, when the pressure of the air decreases, the density of the air decreases.

The density of air at standard temperature and pressure STP ( 00 C and 1 atm ) is equal to 1.293 kg/m3. 

Density of Air at Room Temperature

Let us calculate the air density value at room temperature using the air density formula at sea level. The room temperature is taken as 25oC and the atmospheric pressure is taken as 110325 Pa. The formula to calculate the density of the air is given by,

$\Rightarrow D=\dfrac{PM_0}{RT}$

Where,

D- Density of the the gas

M0- Molecular mass of the air 

P- Pressure of the the gas

R - Universal gas constant

T - Temperature of the gas.

The molecular mass of air is 28.96 g/mol and the value of universal gas constant is 8.314 JK-1mol-1.

Substitute each value in the air density formula to calculate the density of air.

$\Rightarrow D=\dfrac{PM_0}{RT}$

$\Rightarrow D=\dfrac{110325 ~Pa \times 28.96~ g/mol \times 10^{-3}}{8.314 ~J/Kmol \times 298~ K}$

$D=1.289~kg/m^3$

Example:

1. What is the density of air at 320 K and 2105 Pa? The molecular mass of the air is taken as 28.96 g/mol.

Sol: The formula to calculate the density of air is given by,

$\Rightarrow D=\dfrac{PM_0}{RT}$

Where,

D- Density of the the gas

M0- Molecular mass of the air 

P- Pressure of the the gas

R - Universal gas constant

T - Temperature of the gas.

The value of the universal gas constant is 8.314 JK-1mol-1. Substitute the values for the terms in the air density formula and simplify to calculate the density of air.

$\Rightarrow D=\dfrac{PM_0}{RT}$

$\Rightarrow D=\dfrac{2\times10^5~Pa \times 28.96~ g/mol \times 10^{-3}}{8.314 ~J/Kmol \times 320~ K}$

$D=2.178~kg/m^3$

2. What is the density of air when the pressure of the air is doubled keeping the temperature constant?

Sol: We know the relationship between density of air and pressure given by the formula,

$\Rightarrow D=\dfrac{PM_0}{RT}$

Where,

D- Density of the the gas

M0- Molecular mass of the air 

P- Pressure of the the gas

R - Universal gas constant

T - Temperature of the gas.

Therefore , density of air is directly proportional to the pressure of the air.So, when the the pressure of the air is doubled keeping the temperature constant, then the new density of air is given by,

$\Rightarrow D'=\dfrac{(2P)M_0}{RT}$

Where, 

D’ - the new density of air when pressure is doubled at constant temperature.

$\Rightarrow D'=2\times\dfrac{PM_0}{RT}$

Therefore, the new density of the air becomes doubled when the pressure of the air is doubled keeping the temperature constant.

Interesting Facts

• Objects traveling through denser, or "heavier," air will slow down more because the object must, in effect, push away more or heavier molecules.

• The term for this type of air resistance is "drag," and it increases as air density rises. Home runs travel farther in the less dense air in high-altitude Denver than in lower-altitude ballparks, according to baseball players. Reduced drag causes the ball to slow down more slowly, allowing it to go further. 

• A race car is slowed by cool, dense air, yet some race cars benefit from it. Cars built from the ground up for racing are essentially upside-down airplane wings that push down on the track as the air drives them around turns, improving their grip. The more dense the air, the harder it pushes them down.

• When the density of the air falls, aircraft pilots perform worse than baseball players.

Conclusion

The density of air is the mass of the air for a unit volume. The density of air depends upon the temperature and pressure of the air. When the temperature of the air increases, the density of the air decreases. The density of air increases when the pressure of the air increases. The density of air at room temperature and normal  atmospheric pressure is 1.289 kg/m3.