Question

A typical air sample in the lungs contains oxygen at \(100 \mathrm{mmHg}\), nitrogen at \(573 \mathrm{mmHg}\), carbon dioxide at \(40 \mathrm{mmHg}\), and water vapor at \(47 \mathrm{mmHg}\). Why are these pressures called partial pressures?

Short answer

Partial pressures are the individual contributions of each gas in a mixture to the total pressure.

Step-by-step solution

Understanding Partial Pressure

Partial pressure refers to the pressure exerted by a single type of gas in a mixture of gases. It is the force that the gas would exert if it occupied the entire volume by itself.

Identifying Components in the Air Sample

In the given air sample, each gas (oxygen, nitrogen, carbon dioxide, and water vapor) has a specific pressure value (part of the total pressure). These values represent the individual contributions of each gas to the total pressure exerted by the air mixture in the lungs.

Summing the Individual Pressures

To find the total pressure in the lungs, sum the partial pressures of all gases: oxygen: 100 mmHg,nitrogen: 573 mmHg,carbon dioxide: 40 mmHg,water vapor: 47 mmHg Total Pressure = 100 + 573 + 40 + 47 = 760 mmHg.

Conclusion on Partial Pressures

Since the total pressure is the sum of the pressures exerted by each gas, these individual pressures are called partial pressures. They represent each gas's contribution to the total pressure in the mixture.

Key concepts

gas mixtures

In the study of gases, we often encounter samples that consist of different types of gases mixed together. These combinations are known as gas mixtures. Each gas retains its own properties, and they all occupy the available space together. An essential characteristic of gas mixtures is that each component exerts its own pressure independently, contributing to the overall behavior and properties of the mixture.
Understanding gas mixtures helps in comprehending how gases behave in various settings, such as the air we breathe, which is a mixture of oxygen, nitrogen, carbon dioxide, and more. For example, in lung air samples, these gases function in harmony to maintain our respiratory system and support life.

Dalton's Law

Dalton's Law, or Dalton's Law of Partial Pressures, states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases. John Dalton, the English chemist, formulated this law in the early 19th century. Dalton's Law can be mathematically expressed as: \[ P_\text{total} = P_1 + P_2 + P_3 + \ldots + P_n \] where \( P_\text{total} \) is the total pressure of the mixture and \( P_1, P_2, P_3, \ldots, P_n \) are the partial pressures of the gases in the mixture.
This law is crucial for understanding how different gases coexist and interact within the same volume. For example, in the lungs, oxygen, nitrogen, carbon dioxide, and water vapor all contribute to the total lung pressure following the principles of Dalton's Law.

individual gas pressures

In a gas mixture, each gas exerts its own pressure as if it were alone in the volume. This pressure is known as the partial pressure of the gas. The concept of individual gas pressures is vital for explaining the behavior of gas mixtures.
Partial pressure is calculated based on the gas's proportion and conditions such as temperature and volume. For example, in a lung air sample, oxygen may exert a partial pressure of 100 mmHg, nitrogen 573 mmHg, carbon dioxide 40 mmHg, and water vapor 47 mmHg. Each of these values represents the pressure that the respective gas would exert if it occupied the entire volume by itself.
These individual partial pressures help to determine the total pressure in a gas mixture. By summing them up, as shown below, we get the total pressure exerted by the mixture:
\[ P_\text{total} = P_\text{O2} + P_\text{N2} + P_\text{CO2} + P_\text{H2O} = 100 + 573 + 40 + 47 = 760 \text{ mmHg} \]

lung air sample

In the context of human physiology, the air we inhale and exhale is a mixture known as a lung air sample. It comprises various gases, each contributing to our breathing process. Some key gases in a typical lung air sample include oxygen, nitrogen, carbon dioxide, and water vapor.
The air pressure in our lungs is known as the partial pressure of each gas. For example, oxygen might have a partial pressure of 100 mmHg, nitrogen 573 mmHg, carbon dioxide 40 mmHg, and water vapor 47 mmHg, as mentioned in the exercise. The sum of these partial pressures gives us the total pressure in the lungs, which is essential for the exchange of gases during respiration.
This concept is particularly important in medical and respiratory studies, where understanding the contribution of each gas to the total lung pressure aids in diagnosing and treating respiratory conditions. It helps medical professionals to make precise decisions based on the pressure values of each gas.