Density Of An Ideal Gas

The ideal gas law can be manipulated to find the density of a gas if the molecular mass is known.

Problem:

What is the density of a gas with molar mass 100 g/mol at 0.5 atm and 27 °C?

Solution:

First, start with the ideal gas law:

PV = nRT

where
P = pressure
V = volume
n = number of moles of gas
R = gas constant = 0.0821 L·atm/mol&midddot;K
T = absolute temperature

To find the density, we need to find the mass of the gas and the volume. First, find the volume. Solve the equation for V.

V = nRT/P

Second, find the mass. The number of moles is the place to start. The number of moles is the mass (m) of the gas divided by its molecular mass (MM).

n = m/MM

Substitute this into the volume equation for n.

V = mRT/MM·P

Density (ρ) is mass per volume. Divide both sides by m.

V/m = RT/MM·P

Invert the equation.

m/V = MM·P/RT

ρ = MM·P/RT

Plug in the given information:

Remember to use absolute temperature for T: 27 °C + 273 = 300 K

ρ = (100 g/mol)(0.5 atm)/(0.0821 L·atm/mol·K)(300 K) ρ = 2.03 g/L

Answer:

The density of the gas is 2.03 g/L at 0.5 atm and 27 °C.