The Invisible Teamwork of Gases
What is Partial Pressure?
Imagine a classroom full of students. The total noise level is a combination of every individual student's voice. Similarly, the air we breathe is not a single substance but a mixture of gases, primarily nitrogen $ (N_2) $, oxygen $ (O_2) $, and others. Each of these gases contributes to the total atmospheric pressure.
Partial Pressure is defined as the pressure that a specific gas in a mixture would exert if it alone occupied the entire volume of the mixture at the same temperature.
Think of a balloon filled only with oxygen. The pressure inside that balloon is the oxygen's partial pressure. Now, imagine taking that oxygen and mixing it with nitrogen in the same sized container without changing the temperature. The oxygen molecules are still bouncing around, colliding with the walls, and trying to exert their own pressure. They haven't stopped doing their job just because another gas is present. This individual contribution is the partial pressure.
Dalton's Law: The Rule of Addition
The scientist John Dalton[1] formalized this idea in 1801. Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of the individual gases.
$ P_{total} = P_1 + P_2 + P_3 + ... $
Where $ P_1 $, $ P_2 $, etc., are the partial pressures of gases 1, 2, and so on.
This makes intuitive sense. If you have three friends pushing on a door from the same side, the total force on the door is the sum of each friend's individual push. In the same way, the total pressure in a gas mixture is the sum of all the "pushes" from each type of gas molecule.
Calculating Partial Pressure with Mole Fraction
How do we figure out what the partial pressure of a specific gas is? The key is the mole fraction[2]. The mole fraction $ (X) $ of a gas is the number of moles of that gas divided by the total number of moles of all gases in the mixture.
$ P_A = X_A \times P_{total} $
And: $ X_A = \frac{n_A}{n_{total}} $
Where $ n_A $ is the number of moles of gas A and $ n_{total} $ is the total moles of gas.
This means the more of a gas you have in a mixture (the higher its mole fraction), the greater its share of the total pressure. If a gas makes up 50% of the molecules in a mixture, it will be responsible for 50% of the total pressure.
A Practical Example: The Air We Breathe
Let's use the air around us to see these principles in action. Dry air at sea level has a total pressure of about $ 101.3 kPa $ (kilopascals). It is approximately $ 78\% $ nitrogen, $ 21\% $ oxygen, and $ 1\% $ other gases (like argon and carbon dioxide).
We can calculate the partial pressure of oxygen $ (P_{O_2}) $:
- Mole fraction of oxygen, $ X_{O_2} = 0.21 $
- Total pressure, $ P_{total} = 101.3 kPa $
- $ P_{O_2} = X_{O_2} \times P_{total} = 0.21 \times 101.3 kPa = 21.3 kPa $
This means that out of the $ 101.3 kPa $ of pressure you feel at sea level, oxygen is responsible for about $ 21.3 kPa $ of it. If we removed all other gases, the oxygen alone at the same volume and temperature would exert that pressure.
| Gas | Percentage (%) | Mole Fraction | Partial Pressure (kPa) |
|---|---|---|---|
| Nitrogen $ (N_2) $ | 78 | 0.78 | 79.0 |
| Oxygen $ (O_2) $ | 21 | 0.21 | 21.3 |
| Other Gases (Ar, COâ‚‚, etc.) | 1 | 0.01 | 1.0 |
| Total | 100 | 1.00 | 101.3 |
Why Partial Pressure Matters in the Real World
The concept of partial pressure is not just a theoretical idea; it is critical for our safety and health in several areas.
Scuba Diving: As a diver goes deeper underwater, the pressure around them increases dramatically. According to Dalton's Law, the partial pressure of every gas in the diver's air tank also increases. While our bodies are fine with oxygen at a partial pressure of $ 21 kPa $, at great depths the $ P_{O_2} $ can become high enough to cause oxygen toxicity, which can lead to seizures. Conversely, the increased partial pressure of nitrogen $ (P_{N_2}) $ can cause nitrogen narcosis, a confused state similar to being drunk. Divers must carefully manage their depth and gas mixtures to avoid these dangers.
Medical Gases: In hospitals, patients with breathing difficulties are often given oxygen through a mask. This increases the mole fraction of oxygen they are inhaling. Even if the total pressure in the lungs remains the same, a higher mole fraction means a higher partial pressure of oxygen. This increased $ P_{O_2} $ helps force more life-saving oxygen into the patient's bloodstream.
High-Altitude Physiology: At the top of a high mountain, the total atmospheric pressure is lower than at sea level. Even though the air is still $ 21\% $ oxygen, the partial pressure of oxygen is much lower. This is why it's harder to breathe at high altitudes—there is less "pressure" pushing oxygen into your lungs. Your body must work harder to get the oxygen it needs.
Important Questions
Q: Does the identity of the gas matter for its partial pressure?
A: For the calculation using Dalton's Law, the chemical identity of the gas does not matter. What matters is the number of moles of the gas. An ideal gas's pressure contribution depends only on the number of molecules, not their type. However, for how the gas interacts with our body or in chemical reactions, the identity is extremely important (e.g., oxygen vs. carbon dioxide).
Q: What happens to the partial pressure if I compress the gas mixture?
A: When you compress a gas mixture, you decrease its volume. According to Boyle's Law, if the temperature is constant, the pressure of a gas is inversely proportional to its volume. Compressing the mixture increases the total pressure. Because the number of moles of each gas hasn't changed, their mole fractions remain the same. Therefore, the partial pressure of each gas will increase proportionally. For example, if you halve the volume, you double the total pressure, and you also double every partial pressure.
Q: Can a gas have a partial pressure in a liquid?
A: Yes, this is a very important concept! Gases can dissolve in liquids (like carbon dioxide in soda). The amount of gas that dissolves is directly proportional to its partial pressure in the gas mixture above the liquid. This is known as Henry's Law[3]. This is why a sealed soda bottle is fizzy—the high partial pressure of CO₂ inside keeps the gas dissolved. When you open the bottle, the partial pressure of CO₂ above the liquid drops, and the gas comes out of the solution as bubbles.
The concept of partial pressure allows us to understand and predict the behavior of individual gases within a mixture. From the fundamental principle of Dalton's Law to its life-saving applications in diving and medicine, this idea is a cornerstone of gas physics and chemistry. By recognizing that each gas in a mixture contributes its own share to the total pressure, we can solve a wide range of practical problems, from calculating safe breathing gas for a diver to understanding why it's hard to catch your breath on a mountaintop. It is the invisible teamwork of gases, quantified.
Footnote
[1] John Dalton: An English chemist, physicist, and meteorologist. He is best known for introducing the atomic theory into chemistry and for his research into color blindness, sometimes referred to as Daltonism. His law of partial pressures was a major step in understanding gas behavior.
[2] Mole Fraction (X): A unit of concentration defined as the ratio of the number of moles of a constituent to the total number of moles in a mixture. It is a dimensionless quantity.
[3] Henry's Law: A gas law which states that at a constant temperature, the amount of a given gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium with that liquid.