Absolute Gas Density

Density is a quantity that can be calculated from the relationship between body mass and volume. This also applies in the case of gases:

d_gas = m_gas
V_gas

The unit of gas density is usually g/L.

It is known that in CNTP (Normal Conditions of Temperature and Pressure) 1 mol of any gas always occupies a volume of 22.4 L. Thus, the density for gases under these conditions can be calculated from the relationship between the molar mass and this volume in mols:

d_gas = ___M_____
22.4 L. mol^-1

But this formula can only be used if the gas is in the CNTP. If we want to calculate the absolute density for any gas, we can use another formula that we find using the equation of state for gases:

pV = nRT

Since n = m/M, we substitute “n” in the gas state equation:

pV = mRT
M
m = pM
V RT

As density is mass over volume, then we have:

d = pM
RT

This equation shows us that the absolute density of a gas depends on pressure and temperature where the gas is; this is not because of the mass, as it does not depend on pressure and temperature, but the volume does.

Notice that the density of the gas is inversely proportional to its temperature. This is the principle that explains how the practice of ballooning works: the air in the balloon is the atmospheric air that, when heated, decreases in density and, in this way, rises to the sky. The more the air contained in the balloon is heated, the lower its density will be and the higher the balloon will rise.

Here's an example of how to use this formula to find the density of a gas:

Example: What is the absolute density of oxygen gas (O₂) at 600 mmHg and 127 °C? (Atomic mass: O = 16)

Resolution:

Data:

Molar mass: O₂: 2. 16 = 32 g/mol;
p=600 mmHg;
R = 62.3 mmHg. L. mol^-1. K^-1
T = 127 °C → 127 + 273 = 400 K

d =  PM
RT
d =  _600. 32__
62,3. 400
d = 0.774 g/L

Since in CNTP the pressure is equal to 1 atm, the temperature is 273 K and R is equal to 0.082 or 22.4/273, we have:

d =  PM

RT
d = ___1. M_____
(22,4/273). 273
d = ___M_____
22.4 L. mol^-1

We come back to the formula mentioned above for gases in CNTP. Let's look at an example of how to use this formula:

Example: What is the molecular mass of a gas whose absolute density in CNTP is 1.96 g/L?

Resolution:

d = ___M_____
22.4 L. mol^-1

M = 22.4. d
M = (22.4 L/mol). (1.96 g/L)
M = 43.90 g/mol

By Jennifer Fogaça
Graduated in Chemistry

Source: Brazil School - https://brasilescola.uol.com.br/quimica/densidade-absoluta-dos-gases.htm