C/P 06 · Gas laws and respiratory gas exchange
Gas in a Syringe and Gas in the Lungs
Apply Boyle’s law, gas pressure–temperature relationships and partial pressures to a syringe and to the lungs.
Passage
The behavior of a gas is described by the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, T is the absolute temperature in kelvin, and R is the gas constant. For a fixed amount of gas at constant temperature, the product PV does not change (Boyle’s law). For a fixed amount of gas at constant volume, the pressure is proportional to the absolute temperature. In a mixture of gases, each gas exerts a partial pressure equal to its mole fraction times the total pressure (Dalton’s law), and each gas diffuses independently from regions of higher partial pressure to regions of lower partial pressure.
Part 1. A student traps 0.25 mol of air in a syringe that is held at a constant temperature in a water bath. She changes the volume by moving the plunger and reads the pressure from a gauge. Table 1 shows the results.
Table 1. Pressure and volume of a fixed amount of air at constant temperature.
| Volume (mL) | Pressure (kPa) |
|---|---|
| 60 | 100 |
| 30 | 200 |
| 20 | 300 |
The student waits several minutes after each change so that the air in the syringe reaches the temperature of the bath, and she checks that the gauge reads absolute pressure, not the pressure above the atmosphere. The plunger moves without noticeable leaking.
Part 2. The student then seals the syringe so that the volume cannot change and heats the water bath in steps. Table 2 shows the pressure at several temperatures.
Table 2. Pressure of a fixed volume of air at different temperatures.
| Temperature (K) | Pressure (kPa) |
|---|---|
| 300 | 100 |
| 360 | 120 |
| 450 | 150 |
Part 3. Breathing moves air into and out of the lungs because the volume of the chest cavity changes. During quiet inhalation, the diaphragm contracts and the chest expands, which enlarges the space in which the lungs sit. Air then flows in until the pressure inside the lungs equals the pressure outside. In the alveoli, oxygen and carbon dioxide are exchanged between the air and the blood by diffusion across a thin barrier. Table 3 shows approximate partial pressures of gases in dry inspired air at sea level, where the total pressure is 760 mmHg, and in the air of the alveoli, which is saturated with water vapor at body temperature.
Table 3. Approximate partial pressures (mmHg) of gases.
| Gas | Inspired air (dry) | Alveolar air | Mixed venous blood |
|---|---|---|---|
| O₂ | 160 | 100 | 40 |
| CO₂ | 0 | 40 | 46 |
| N₂ | 600 | 573 | — |
| H₂O | 0 | 47 | — |
The partial pressure of a gas in blood is the pressure of that gas in the air that would be in equilibrium with the blood. The student wants to use Table 3 to reason about which way each gas moves across the alveolar wall, and also to predict how the partial pressures would change in a different environment, such as the top of a high mountain.
Questions
Question 1 of 6
What would the pressure be if the student compressed the gas in Part 1 to 15 mL?
This would be correct if pressure were proportional to volume. Pressure and volume are inversely related.
This is the pressure at 20 mL. Compressing further must raise the pressure.
This would be the result of halving the volume twice. 15 mL is one fourth of 60 mL, not one eighth.
Why the answer is what it is
In Table 1, PV is constant at 6000 (kPa·mL): 60 × 100, 30 × 200, 20 × 300. At 15 mL, P = 6000 ÷ 15 = 400 kPa.
Review: Kinetic Molecular Theory & Gas Laws · Respiratory Physiology · Thermodynamics
Question 2 of 6
The student heats the sealed syringe in Part 2 to 600 K. What pressure would she expect?
This is the pressure at 450 K. At 600 K the pressure should be higher still.
This would be correct if the pressure had tripled, which would need 900 K. Pressure is proportional to the absolute temperature.
This would require a temperature of 1200 K.
Why the answer is what it is
At constant volume, P is proportional to T in kelvin. The ratio P/T is 100/300 = 1/3 kPa/K in every row. At 600 K, P = 600 × 1/3 = 200 kPa.
Review: Kinetic Molecular Theory & Gas Laws · Respiratory Physiology · Thermodynamics
Question 3 of 6
During inhalation, the diaphragm contracts and the volume of the chest cavity increases. Which statement correctly describes the result?
Air flows from higher to lower pressure. If the lung pressure were higher, air would flow out.
Air is not pulled by muscles. The flow occurs because the pressure changes.
The pressure change from the volume change, as in Boyle’s law, is the cause of the flow.
Why the answer is what it is
By Boyle’s law, increasing the volume of a fixed amount of gas lowers its pressure. The alveolar pressure falls below atmospheric pressure, so air flows in.
Review: Kinetic Molecular Theory & Gas Laws · Respiratory Physiology · Thermodynamics
Question 4 of 6
A climber reaches a mountaintop where the total air pressure is 380 mmHg. The composition of dry air has not changed. What is the approximate partial pressure of oxygen in the dry air there?
This is the partial pressure of oxygen in mixed venous blood, not in air.
This is the sea-level value. The fraction of oxygen is the same, but the total pressure is halved.
This is the total pressure of the air, not the pressure of oxygen alone.
Why the answer is what it is
The fraction of O₂ in air (about 21%) is the same, so its partial pressure is proportional to the total pressure. With the total pressure cut in half, from 760 to 380 mmHg, the partial pressure of O₂ falls from 160 to about 80 mmHg.
Review: Kinetic Molecular Theory & Gas Laws · Respiratory Physiology · Thermodynamics
Question 5 of 6
The partial pressure of oxygen is lower in alveolar air (100 mmHg) than in inspired air (160 mmHg). Which explanation is best supported by Table 3?
Gases are not converted into one another in the lungs.
The alveolar air also has a total pressure of 760 mmHg: 100 + 40 + 573 + 47 = 760.
Table 3 does not suggest this, and the water vapor in the air does not take up oxygen.
Why the answer is what it is
The alveolar total is still 760 mmHg. Water vapor adds 47 mmHg, CO₂ adds 40 mmHg, and oxygen continually leaves the alveolar air for the blood, so the share of the total pressure that is O₂ is smaller.
Review: Kinetic Molecular Theory & Gas Laws · Respiratory Physiology · Thermodynamics
Question 6 of 6
Based on Table 3, which statement describes the net movement of gases across the alveolar wall?
Each gas moves according to its own partial-pressure gradient, not according to the total pressure.
This is the reverse. Each gas moves from its higher partial pressure to its lower one.
The partial pressures of O₂ and CO₂ differ between alveolar air and venous blood, so they are not at equilibrium.
Why the answer is what it is
O₂ is at 100 mmHg in the alveoli and 40 mmHg in venous blood, so it moves into the blood. CO₂ is at 46 mmHg in venous blood and 40 mmHg in the alveoli, so it moves into the alveolar air.
Review: Kinetic Molecular Theory & Gas Laws · Respiratory Physiology · Thermodynamics
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