Final answer:
The density of xenon gas at a pressure of 742 mmHg and a temperature of 45 degrees Celsius is approximately 3.94 g/L. This calculation is based on the ideal gas law after converting units appropriately and using xenon's molar mass.
Step-by-step explanation:
To calculate the density of xenon gas at a pressure of 742 mmHg and a temperature of 45 degrees Celsius, we will use the ideal gas law: PV = nRT. In this case, density (ρ) is equal to the mass (m) divided by the volume (V), and the ideal gas law can be rearranged to solve for m/V, which is density.
First, we need to convert the temperature from Celsius to Kelvin by adding 273.15: T(K) = 45 °C + 273.15 = 318.15 K.
We also need to convert the pressure from mmHg to atmospheres, since the ideal gas constant (R) value is typically in terms of atmospheres: P(atm) = 742 mmHg × (1 atm / 760 mmHg) ≈ 0.976 atm.
Now that we have the pressure and temperature in the correct units, we can use the ideal gas constant R = 0.0821 L·atm/K·mol, and the molar mass of xenon (Xe) which is about 131.29 g/mol.
The equation to find the density is:
ρ = PM / RT
Where ρ is density, P is pressure, M is molar mass, R is the ideal gas constant, and T is temperature in Kelvin.
Substituting the values in, we get:
ρ = (0.976 atm)(131.29 g/mol) / (0.0821 L·atm/K·mol)(318.15 K)
ρ = ≈ 3.94 g/L
Thus, the density of xenon gas at the given conditions is approximately 3.94 g/L.