Final answer:
The density of air at a pressure of 1.00 atm and a temperature of 20°C is approximately 1.21 kg/m³. The density of the atmosphere on Venus is approximately 0.657 kg/m³.
Step-by-step explanation:
The density of a gas can be calculated using the ideal gas law, which states that the density (ρ) is equal to the molar mass (M) divided by the molar volume (V). The molar mass can be found by multiplying the mass fraction of each component by its molar mass and summing them up. In this case, for air with 78% N2, 21% O2, and 1% Ar, the molar mass can be calculated as:
M = (0.78 * 28) + (0.21 * 32) + (0.01 * 40) = 28.94 g/mol
To convert the molar mass to kg/mol, divide by 1000:
M = 0.02894 kg/mol
The molar volume can be calculated using the ideal gas law:
V = (RT)/P
where R is the ideal gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and P is the pressure in Pascal. First, convert the temperature from Celsius to Kelvin:
T = 20 + 273 = 293 K
Then, convert the pressure from atm to Pascal:
P = 1.00 * 101325 = 101325 Pa
Substituting these values into the equation and solving for V:
V = (8.314 * 293) / 101325 = 0.02385 m³/mol
Finally, calculate the density:
ρ = M/V = 0.02894 / 0.02385 = 1.21 kg/m³
Therefore, the density of air at a pressure of 1.00 atm and a temperature of 20°C is approximately 1.21 kg/m³.
Similarly, for the atmosphere on Venus with 96% CO2 and 4% N₂, the molar mass can be calculated as:
M = (0.96 * 44) + (0.04 * 28) = 43.36 g/mol
Converting to kg/mol:
M = 0.04336 kg/mol
Converting the pressure from atm to Pascal:
P = 92.0 * 101325 = 9289000 Pa
Using the given temperature:
T = 737 K
Calculating the molar volume:
V = (8.314 * 737) / 9289000 = 0.066 m³/mol
Calculating the density:
ρ = M/V = 0.04336 / 0.066 = 0.657 kg/m³
Therefore, the density of the atmosphere on Venus is approximately 0.657 kg/m³.