Calculate the density of CO2 at: Laboratory conditions At STP
The Correct Answer and Explanation is:
To calculate the density of carbon dioxide (CO₂), we use the ideal gas law:
Density(ρ)=PMRT\text{Density} (\rho) = \frac{PM}{RT}
where:
- PP is pressure,
- MM is the molar mass of CO₂ (44.0144.01 g/mol),
- RR is the gas constant (0.08210.0821 L·atm/(mol·K)),
- TT is the temperature in Kelvin.
1. Density at Laboratory Conditions
Laboratory conditions vary, but assuming:
- T=25∘C=298T = 25^\circ C = 298 K
- P=1P = 1 atm
ρ=(1 atm)(44.01 g/mol)(0.0821 L\cdotpatm/(mol\cdotpK))(298 K)\rho = \frac{(1 \text{ atm}) (44.01 \text{ g/mol})}{(0.0821 \text{ L·atm/(mol·K)}) (298 \text{ K})}
ρ≈1.79 g/L\rho \approx 1.79 \text{ g/L}
2. Density at Standard Temperature and Pressure (STP)
STP is defined as:
- T=273T = 273 K
- P=1P = 1 atm
ρ=(1 atm)(44.01 g/mol)(0.0821 L\cdotpatm/(mol\cdotpK))(273 K)\rho = \frac{(1 \text{ atm}) (44.01 \text{ g/mol})}{(0.0821 \text{ L·atm/(mol·K)}) (273 \text{ K})}
ρ≈1.96 g/L\rho \approx 1.96 \text{ g/L}
Explanation
The density of a gas is influenced by temperature and pressure. When temperature increases, the gas expands, lowering its density. Conversely, at lower temperatures, gas molecules occupy a smaller volume, increasing density. At STP, CO₂ has a density of 1.96 g/L, but in laboratory conditions (typically 25°C), the density reduces to 1.79 g/L due to thermal expansion.
These calculations assume CO₂ behaves ideally. However, real gases exhibit minor deviations due to intermolecular forces, which can slightly affect density, especially at high pressures.
