ChemicalThermodynamicseasyFE ExamCoursework

Density of an Ideal Gas

Carbon dioxide ( $M = 44\ \text{g/mol}$ ) is at $200\ \text{kPa}$ and $300\ \text{K}$ .

Take $R = 8.314\ \text{J/mol·K}$ and assume ideal gas behaviour.

Find the density.

Given

P	200 kPa	Pressure
T	300 K	Temperature
M	44 g/mol	Molar mass

Hint 1

Start from PV = nRT and substitute n = m/M to get a density.

Hint 2

ρ = PM/(RT).

Hint 3

Convert pressure to Pa and molar mass to kg/mol before substituting.

Worked solution — try the problem first

From $PV = nRT$ with $n = m/M$ :

$\rho = \frac{PM}{RT}$

Convert to base SI. Both conversions matter:

$P = 200\ \text{kPa} = 2.00\times10^{5}\ \text{Pa}, \qquad M = 44\ \text{g/mol} = 0.044\ \text{kg/mol}$

$\rho = \frac{(2.00\times10^{5})(0.044)}{(8.314)(300)} = \frac{8800}{2494.2} = 3.528\ \text{kg/m}^3$

$\boxed{\rho = 3.53\ \text{kg/m}^3}$

Sanity check. Air at ambient conditions is about 1.2 kg/m³. CO₂ is 1.5× heavier per mole than air, and this gas is at twice atmospheric pressure, so roughly $1.2 \times 1.5 \times 2 = 3.6$ kg/m³ — consistent.

Concepts:Ideal gas lawDensityUnit conversion

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