The ideal gas law can be manipulated to find the density of a gas if the molecular mass is known.
What is the density of a gas with molar mass 100 g/mol at 0.5 atm and 27 °C?
First, start with the ideal gas law:
PV = nRT
P = pressure
V = volume
n = number of moles of gas
R = gas constant = 0.0821 L·atm/mol·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
The density of the gas is 2.03 g/L at 0.5 atm and 27 °C.