Final answer:
The mass density of the ideal oxygen gas after it is heated to 390 K in a sealed 62 m³ tank with 9000 moles of gas is 4.645 kg/m³.
Step-by-step explanation:
The question asks for the mass density of an ideal oxygen gas after it has been heated from an initial temperature of 270 K to a final temperature of 390 K. The gas is in a sealed 62 m3 tank and the amount of gas is 9000 moles. The atomic mass of oxygen is 16.0 g/mol, making the molar mass of diatomic oxygen 32.0 g/mol. To find the mass density (ρ), which is mass per unit volume, we need to first determine the mass of 9000 moles of oxygen gas.
Using the molar mass:
Mass = moles × molar mass
Mass = 9000 moles × 32.0 g/mol = 288000 g or 288 kg
Now, we can calculate the mass density by dividing the mass by the volume of the tank:
ρ = mass / volume
ρ = 288 kg / 62 m3 = 4.645 kg/m3 (to three significant figures)