Density of Gas Formula

The formula to determine the density of a gas is given as follows:

Density of a gas (ρ) = PM/RT

Where,

“P” is the pressure of the gas,

“M” is the molar mass (g/mol),

“R” is the universal gas constant (R = 0.082 L⋅ atm⋅ K^−1⋅ mol⁻¹), and

“T” is the temperature of the gas (K)

Derivation For the Density of Gas formula 

The density of a gas is equal to the total mass of the gas to the total volume of the gas. To determine the molar mass of a gas, we have to consider the ideal gas equation.

From the ideal gas equation, we have

PV = nRT …………(1)

where,
“P” is the pressure of the gas,
“V” is the volume of the gas
“n” is the number of moles
“R” is the universal gas constant (R = 0.082 L⋅ atm⋅ K⁻¹⋅ mol⁻¹), and
“T” is the temperature of the gas

We know that, number of moles (n) = m/M 

where, 
“m” is the mass of the gas,
“M” is the molecular mass of the gas.

Now, substitute n = m/M in equation (1).

Thus, PV = mRT/M

P = mRT/MV ……….(2)

we know that density (ρ) = m/V. So, substitute the value of ρ in equation (2).

Thus, we get

P = ρ RT/M

ρ = PM/RT 

Thus, the ideal gas density formula is ρ = PM/RT.

Density is referred to as the ratio of the mass per unit of volume of a substance under specific conditions of pressure and temperature. Mathematically, it can be defined as mass divided by volume. It is generally represented by “ρ” or “D”. The density of a substance varies depending on its pressure and temperature. For example, the density of an ideal gas can be doubled as the pressure doubles or by halving its absolute temperature. That means the density of gas always increases as the pressure increases and decreases as the temperature increases. We can determine the molar mass of a substance if we know its density. Generally, the density of a substance is different for different materials. At standard conditions for temperature and pressure, osmium and iridium are the densest known elements.

Density (ρ) = m/V

Where “m” is the mass, and “V” is the volume.

The SI unit of density of a substance is kilogram per cubic meter (kg/m³). Some other units of measurement of density are kilogram per liter (kg/L), gram per milliliter (g/mL), tonne per cubic meter (t/m³), etc.