Calculate the pressure and composition of air on the top of Mt. Everest, assuming that the atmosphere has a temperature of 0 degree Celsius
independent of altitude (h = 29,141 ft). Assume that air at sea level is 20%
O2 and 80% N2.
To calculate the pressure and composition of air on the top of Mt. Everest, we can use the ideal gas law and the fact that the composition of air remains constant with altitude.
1. Convert the altitude from feet to meters:
1 ft ≈ 0.3048 m
h = 29,141 ft × 0.3048 m/ft ≈ 8,848 m
2. Convert the temperature from Celsius to Kelvin:
T = 0 °C + 273.15 ≈ 273.15 K
3. Determine the molar mass of air:
Air is a mixture of oxygen (O2) and nitrogen (N2). The molar mass of O2 is roughly 32 g/mol, and the molar mass of N2 is roughly 28 g/mol.
Molar mass of air = 0.20 × (32 g/mol) + 0.80 × (28 g/mol)
= 6.4 g/mol + 22.4 g/mol
≈ 28.8 g/mol
4. Calculate the pressure using the ideal gas law:
The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and T is temperature in Kelvin.
Since we are assuming that the temperature is constant, we can rearrange the equation to solve for pressure:
P = (nRT) / V
At sea level, the composition of air is 20% O2 and 80% N2. Assuming a total air pressure of 1 atm, we can calculate the partial pressure of O2 and N2:
Partial pressure of O2 = 0.20 × 1 atm = 0.20 atm
Partial pressure of N2 = 0.80 × 1 atm = 0.80 atm
Now we can calculate the number of moles of O2 and N2 using their partial pressures, volume, and the ideal gas law:
Moles of O2 = (Partial pressure of O2 × V) / (RT)
Moles of N2 = (Partial pressure of N2 × V) / (RT)
Since the volume is not given, we can assume that the volume is the same at any given altitude (reasonable approximation for this calculation).
5. Calculate the pressure on the top of Mt. Everest:
We will use the same volume and temperature values as at sea level, but with the new number of moles generated for O2 and N2.
The total pressure at the top of Mt. Everest will be the sum of the partial pressures of O2 and N2:
P = Partial pressure of O2 + Partial pressure of N2
Therefore, calculate the partial pressures of O2 and N2 using the moles calculated in step 4:
Partial pressure of O2 = (Moles of O2 × RT) / V
Partial pressure of N2 = (Moles of N2 × RT) / V
Finally, calculate the total pressure on the top of Mt. Everest:
P = Partial pressure of O2 + Partial pressure of N2
By following these steps, you should be able to calculate the pressure and composition of air on the top of Mount Everest.