Density (kg/m³) = mass (kg) / Volume (m³)
d = m/V (1)
Ideal gas law,
PV = nRT (2)
Where, P is the pressure of the gas (Pa), V is the volume of the gas (m³), n is the number of moles of gas (mol), R is the universal gas constant ( 8.314 J mol⁻¹ K⁻¹) and T is temperature in Kelvin.
n = m/M (3)
Where, n is number of moles, m is mass and M is molar mass.
From (2) and (3),
PV = (m/M) RT
By rearranging,
P = (m/VM)RT (4)
From (1) and (4)
P = (dRT) / M
P = standard pressure = 1 atm = 101325 pa
d = ?
R = 8.314 J mol⁻¹ K⁻¹
T = Standard temperature = 273 K
M = 44 g/mol = 44 x 10⁻³ kg/mol
By substitution,
101325 Pa = (d x 8.314 J mol⁻¹ K⁻¹ x 273 K) / 44 x 10⁻³ kg/mol
d = (101325 Pa x 44 x 10⁻³ kg/mol) / (8.314 J mol⁻¹ K⁻¹ x 273 K)
d = 1.96 kg m⁻³ = 1.96 g/L
Hence, the density of the CO₂ at STP is 1.96 g/L
Assumption made is "CO₂ gas has an ideal gas behavior".