Final answer:
To compute the mass of N₂ per unit surface area on Venus, we use the ideal gas law to calculate the density of the atmosphere. The mass of N₂ per unit surface area on Venus is approximately 4.82 kg/m². Comparing this with Earth's atmosphere, the mass of N₂ per unit surface area on Venus is approximately 5.31 times greater than on Earth.
Step-by-step explanation:
To compute the mass of N₂ per unit surface area of Venus, we need to know the density of the atmosphere. The density can be calculated using the ideal gas law, which states that the density of a gas is equal to its pressure divided by its molar mass and the gas constant (R), multiplied by the temperature.
Assuming a temperature of 750 K and a pressure of 92 bar (9200 kPa), we can calculate the density of the atmosphere. The molar mass of nitrogen gas (N₂) is 28.01 g/mol.
The density of N₂ on Venus would be:
Density = (Pressure * Molar Mass) / (Gas Constant * Temperature)
Density = (9200 * 28.01) / (8.314 * 750)
Density ≈ 137.72 kg/m³
To find the mass of N₂ per unit surface area, we need to multiply the density by the mole fraction of N₂ in the atmosphere. Since 3.5% of the atmosphere consists of N₂, the mass of N₂ per unit surface area of Venus can be calculated as:
Mass of N₂ per unit surface area = Density * Mole Fraction of N₂
Mass of N₂ per unit surface area ≈ 137.72 kg/m³ * 0.035
Mass of N₂ per unit surface area ≈ 4.82 kg/m²
Comparing this with Earth's atmosphere, which has a surface pressure of approximately 1 bar, the mass of N₂ per unit surface area on Earth can be calculated similarly using the known values of the molar mass of N₂ (28.01 g/mol) and the mole fraction of N₂ (approximately 0.7808).
Density on Earth = (1 * 28.01) / (8.314 * 298)
Density ≈ 1.164 kg/m³
Mass of N₂ per unit surface area on Earth ≈ 1.164 kg/m³ * 0.7808
Mass of N₂ per unit surface area on Earth ≈ 0.908 kg/m²
Therefore, the mass of N₂ per unit surface area on Venus is approximately 5.31 times greater than that on Earth.