At high altitude where total atmospheric pressure is 0.50 atm, air still contains 21% oxygen by moles. A climber measures the partial pressure of O₂. What is it, and why is this clinically significant?
A0.21 atm — the same as at sea level, since the mole fraction is unchanged
B0.42 atm — doubling because less total gas is present
C0.105 atm — half the sea-level value, because partial pressure scales with total pressure
D0.21 atm, but it acts differently at altitude because of lower air density
P_O₂ = χ_O₂ × P_total = 0.21 × 0.50 atm = 0.105 atm — exactly half the sea-level value of ~0.21 atm. The mole fraction is unchanged, but oxygen availability to biological systems depends on partial pressure, not mole fraction. At lower partial pressure, less oxygen dissolves in blood plasma and less is available to bind hemoglobin. This is why altitude sickness occurs even though the air is 'still 21% oxygen' — the common misconception that something about the air's composition changes at altitude. The composition is the same; the partial pressure is what drives gas exchange.
Question 2 Multiple Choice
Hydrogen gas is collected by water displacement in an inverted bottle. The total pressure inside equals atmospheric pressure (1.00 atm) and water vapor pressure at the experiment temperature is 0.031 atm. What is the partial pressure of dry hydrogen gas?
A1.031 atm — adding the water vapor to atmospheric pressure
B0.969 atm — subtracting the water vapor pressure from total pressure
C1.00 atm — the water vapor is negligible and can be ignored
D0.031 atm — only the water vapor needs to be measured directly
By Dalton's law, P_total = P_H₂ + P_H₂O. So P_H₂ = P_total − P_H₂O = 1.00 − 0.031 = 0.969 atm. The collected gas is a mixture: any gas sample collected over water includes water vapor at its equilibrium vapor pressure for that temperature. This water vapor contributes to total pressure, so it must be subtracted to find the pure gas pressure. Failing to account for water vapor pressure is a common source of error in stoichiometry calculations involving gas collection.
Question 3 True / False
At high altitude, the percentage of oxygen in the atmosphere decreases compared to sea level, which is why climbers experience hypoxia.
TTrue
FFalse
Answer: False
The mole fraction (percentage) of oxygen in dry air is approximately 21% at all altitudes — it does not decrease. What decreases is the total atmospheric pressure (and therefore the partial pressure of oxygen). Since P_O₂ = χ_O₂ × P_total, halving total pressure halves P_O₂ even if χ_O₂ stays constant. Hypoxia at altitude results from reduced partial pressure, not reduced percentage. This distinction matters: supplemental oxygen works by increasing total pressure available to the lungs (in pressure masks) or by increasing χ_O₂ to nearly 1.0 in the supplied gas, both of which restore adequate P_O₂.
Question 4 True / False
If the mole fraction of nitrogen in a gas mixture is 0.78 and the total pressure is 1.00 atm, then the partial pressure of nitrogen is 0.78 atm.
TTrue
FFalse
Answer: True
Directly from Dalton's law: P_A = χ_A × P_total = 0.78 × 1.00 atm = 0.78 atm. This relationship is the quantitative backbone of the topic. Note that all mole fractions must sum to 1, so the remaining 0.22 atm of pressure is contributed by other gases in the mixture. The relationship P_A = χ_A × P_total follows from the ideal gas law: if n_A/n_total = χ_A, and P ∝ n at constant V and T, then P_A/P_total = χ_A.
Question 5 Short Answer
A scuba diver breathing normal air (21% O₂, 78% N₂) at 30 meters depth, where total pressure is approximately 4 atm, experiences increased dissolved nitrogen in the blood. Explain why, even though the composition of the air supply has not changed.
Think about your answer, then reveal below.
Model answer: At 4 atm total pressure, P_N₂ = 0.78 × 4 atm = 3.12 atm — four times the sea-level value of ~0.78 atm. By Henry's law (which you will study next), the amount of a gas that dissolves in a liquid is proportional to its partial pressure. So even though the air is still 78% nitrogen, the much higher partial pressure of nitrogen drives far more nitrogen into dissolution in the diver's blood and tissues. This is why decompression sickness (the bends) occurs: ascending too quickly causes dissolved nitrogen to come out of solution as bubbles.
This problem illustrates the chain from Dalton's law to Henry's law: composition (mole fraction) is fixed, total pressure increases with depth, partial pressure = mole fraction × total pressure increases, and dissolved gas content scales with partial pressure. The diver's air supply remains 21%/78%, but the effective 'dose' of each gas increases with depth because partial pressures increase. This is why gas management at depth is critical in diving medicine.