Question

Why can we use a gas mixture, such as air, to study the general behavior of an ideal gas under ordinary conditions?

Short answer

Under ordinary conditions, each component of air behaves independently and approximates the behavior of an ideal gas.

Step-by-step solution

- Understanding Ideal Gas Behavior

First, remember that an ideal gas is a hypothetical gas whose particles are considered to have no intermolecular forces and occupy no volume. The behavior of an ideal gas is described by the Ideal Gas Law: \[ PV = nRT \]

- Properties of Air

Next, recognize that air is a mixture of gases, primarily nitrogen (\( N_2 \)) and oxygen (\( O_2 \)), with small amounts of other gases. Despite being a mixture, each component behaves largely independently under ordinary conditions.

- Application of Dalton's Law

Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure is the sum of the partial pressures of individual gases: \[ P_{total} = P_1 + P_2 + ... + P_n \] This allows us to treat air, and other gas mixtures, similarly to single-component ideal gases.

- Real Gases Approximating Ideal Behavior

Under ordinary conditions (low pressure and high temperature), real gases (like the components of air) behave very similarly to ideal gases because the interactions between molecules are negligible and the volume of the molecules themselves is very small compared to the total volume.

- Conclusion

Given the independent behavior of each component in the mixture, along with the conditions where real gases approximate the ideal gas law, we can use air to study the general behavior of an ideal gas.

Key concepts

Ideal Gas Law

To understand why we use air to study ideal gas behavior, we need to start with the Ideal Gas Law. This law is expressed as \[ PV = nRT \] where

• \(P\) represents pressure
• \(V\) is volume
• \(n\) is the number of moles of gas
• \(R\) is the universal gas constant
• \(T\) is temperature in Kelvin.

The Ideal Gas Law describes the relationship between these variables. It assumes that gas particles do not attract or repel each other (no intermolecular forces) and that they occupy no volume themselves. Though this is a simplification, it works well under many conditions.

Dalton's Law of Partial Pressures

Air is a mixture of gases such as nitrogen, oxygen, and trace amounts of other gases. Dalton's Law of Partial Pressures helps us understand how these gases contribute to the total pressure of air. According to this law: \[ P_{total} = P_1 + P_2 + ... + P_n \] This means the total pressure exerted by air is the sum of the pressures of its individual components. Each component of the gas mix behaves independently. Therefore, we can treat air (a mixture) similarly to a single-component ideal gas when studying its behavior.

Real Gases Approximation

Real gases don't always follow ideal gas behavior perfectly but tend to approximate it under certain conditions. At low pressures and high temperatures:

• The intermolecular forces between gas molecules are negligible.
• The volume occupied by gas molecules themselves is very small compared to the volume of the container.

These conditions make the real gases behave similarly to ideal gases. Because ordinary conditions often fall within these ranges, real gases like those in air can be approximated using the Ideal Gas Law.

Gas Mixtures

When examining gas mixtures, each component's behavior can be studied as if it were alone in the container. This is because gases in a mixture do not react with one another, and the behavior of one gas does not significantly impact the others. This principle is a cornerstone in using real-world gas mixtures, such as air, to model ideal gas behavior. By combining the Ideal Gas Law and Dalton's Law, we can predict how the whole mixture will respond to changes in pressure, volume, and temperature.

Air Composition

Air primarily consists of nitrogen ( \(N_2\) ) and oxygen ( \(O_2\) ), with smaller amounts of other gases like argon and carbon dioxide. Despite being a mixture with multiple components, everyday atmospheric air behaves predictably and in line with the Ideal Gas Law under ordinary conditions. This reliability makes air an excellent representative sample when studying gaseous behavior in general. This is due to the consistency in the proportion of gases and the predictable nature of their interactions, or lack thereof.