1. Understand the Relationship Between Density, Pressure, and Temperature
The ideal gas law helps us understand the relationship:
* PV = nRT
Where:
* P = pressure (in Pa)
* V = volume (in m³)
* n = number of moles
* R = ideal gas constant (8.314 J/mol·K)
* T = temperature (in K)
We can rearrange this equation to solve for density (ρ):
* ρ = (n * M) / V
* ρ = (P * M) / (R * T)
Where:
* M = molar mass of the gas (in g/mol)
2. Convert Units
* Pressure (P): 133 kPa = 133,000 Pa
* Temperature (T): 303 K (already in Kelvin)
3. Calculate the Molar Mass of Each Gas
* He: 4.00 g/mol
* Ne: 20.18 g/mol
* Ar: 39.95 g/mol
* Kr: 83.80 g/mol
* Xe: 131.29 g/mol
4. Use the Density Equation to Find the Matching Gas
Plug in the known values (pressure, temperature, R) and the molar mass (M) of each gas into the density equation. Calculate the density for each gas and see which one matches the given density (2.104 g/L).
Example Calculation (for Argon):
* ρ = (P * M) / (R * T)
* ρ = (133,000 Pa * 39.95 g/mol) / (8.314 J/mol·K * 303 K)
* ρ ≈ 2.104 g/L
Result:
The gas with a density of 2.104 g/L at 303 K and 133 kPa is Argon (Ar).
