Final answer:
The density of the atmosphere at STP is calculated using the composition of the gases and the ideal gas law. The average molecular weight of air is worked out from the percentages of nitrogen, oxygen, and argon. The correct density at STP is approximately 1.225 kg/m³, which corresponds to option b.
Step-by-step explanation:
We are asked to find the density of the atmosphere at Standard Temperature and Pressure (STP). To do this, we need to calculate the average molecular weight of air based on its composition and then use the ideal gas law to find the density.
To calculate the average molecular weight (M) of the atmosphere, we use the formula:
M = (0.78 × MN₂) + (0.21 × MO₂) + (0.01 × Mar)
Where MN₂, MO₂, and Mar are the molar masses of nitrogen, oxygen, and argon, respectively:
- MN₂ = 28.0 g/mol (for N₂)
- MO₂ = 32.0 g/mol (for O₂)
- Mar = 39.9 g/mol (for Ar)
Calculating the weighted average, we get:
M = (0.78 × 28.0 g/mol) + (0.21 × 32.0 g/mol) + (0.01 × 39.9 g/mol) = 29.0 g/mol
Hence, the average molecular weight of air is 29.0 g/mol, and the density of air at STP can be found using the ideal gas law, ρ = PM/RT, where P is the pressure, M is the molar mass, R is the universal gas constant, and T is the temperature. At STP (P = 1 atm and T = 273.15 K), the density (ρ) can be calculated to be approximately:
ρ = (1 atm × 29.0 g/mol) / (0.0821 L·atm/mol·K × 273.15 K)
After converting g/mol into kg/mol (by dividing by 1000) and L into m³ (by multiplying by 1000), we find the density of the atmosphere at STP to be approximately 1.225 kg/m³, which corresponds to option (b).