To calculate the density of air at the specified conditions, we can use the ideal gas law, which is given by the formula:
PV = nRT
Where:
- P = pressure in atm
- V = volume in liters
- n = number of moles of gas
- R = ideal gas constant (0.0821 L·atm/(K·mol))
- T = temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15 = 30 + 273.15 = 303.15 K
Next, we express the number of moles (n) in terms of density (ρ) and molar mass (M):
n = ρV / M
Substituting for n in the ideal gas law gives us:
P * V = (ρV / M) * R * T
We can simplify this by canceling V:
P = (ρ / M) * R * T
Rearranging to find the density (ρ) yields:
ρ = (PM) / (RT)
Now, we can substitute the values:
- P = 1.00 atm
- M = 29.0 g/mol
- R = 0.0821 L·atm/(K·mol)
- T = 303.15 K
Plugging in these values:
ρ = (1.00 atm * 29.0 g/mol) / (0.0821 L·atm/(K·mol) * 303.15 K)
Calculating the right side gives:
ρ ≈ (29.0 g/mol) / (24.916 L/mol) ≈ 1.16 g/L
Thus, rounding to appropriate significant figures, the density of air at 1.00 atm and 30 degrees Celsius is approximately 1.17 g/L.
The correct answer is e) 1.17 g/L.