Question

Dalton's law of partial pressures is based on the assumption that the gas molecules (1) are perfectly spherical (2) do not attract or repel one another (3) have the same speed (4) are small

Short answer

Gas molecules do not attract or repel one another.

Step-by-step solution

Understanding Dalton's Law of Partial Pressures

Dalton's law 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. This means each gas in a mixture exerts pressure independently.

Key Assumptions of Dalton's Law

Dalton's law assumes that gas molecules are in constant, random motion and that each gas molecule behaves as if no other gas molecules are present.

Identifying Assumptions in the Choices

(1) being perfectly spherical is not necessarily an assumption for Dalton's law. (2) not attracting or repelling one another is a key assumption, as it ensures that each gas exerts pressure independently. (3) having the same speed is not assumed because gases have a range of speeds based on temperature. (4) being small can affect behavior to some extent, but it is not as critical as (2).

Choosing the Correct Assumption

Based on the above analysis, the correct assumption crucial to Dalton's law is that gas molecules do not attract or repel one another.

Key concepts

gas behavior

To understand Dalton's Law of Partial Pressures, it's essential to grasp the basic concept of gas behavior. Gases behave quite differently compared to solids and liquids. The distinguishing factor here is the kinetic molecular theory, which suggests that gas molecules are in constant, random motion. This movement causes them to collide with each other and the container holding them.

Gas behavior is characterized by several key features:

• Expansibility: Gases expand to fill the volume of any container they are in.
• Compressibility: Gases can be compressed into a smaller volume.
• Pressure: The exerted force on the walls of their container is due to collisions of the gas molecules.
• Temperature: A measure of the average kinetic energy of gas molecules.

By understanding these principles, students can better appreciate why Dalton's Law operates under certain assumptions.

partial pressures

One of the essential principles of Dalton's Law is the concept of partial pressures. Partial pressure refers to the pressure that a single gas in a mixture would exert if it occupied the entire volume by itself. In a mixture of gases, each gas contributes a portion of the total pressure, known as partial pressure.
The total pressure in a container is the sum of the partial pressures of all gases present. This can be expressed in the equation:
\[ P_{total} = P1 + P2 + P3 + ... + Pn \]
where \( P1, P2, P3, ... \) are the partial pressures of the individual gases.

The concept of partial pressures is crucial because it explains how gases in a mixture do not interfere with each other's behavior. Each gas independently contributes to the overall pressure based solely on its proportion in the mixture. This aspect is especially significant in chemical and physical processes involving gases.

non-reacting gases

Dalton's Law assumes that the gases in question do not chemically react with each other. When gases react, they form new compounds, changing the nature and properties of the mixture. For instance, when hydrogen gas reacts with oxygen gas, water is formed, altering the initial conditions.

Non-reacting gases, on the other hand, maintain their individual identities and properties. This concept allows us to consider each gas independently, which is the foundation for Dalton's Law.

• In a mixture, each gas behaves as if it is alone.
• The individual gas pressures add up to create the total pressure.

Understanding the behavior of non-reacting gases is crucial for practical applications too. It applies to a variety of fields, such as meteorology, respiratory physiology, and industrial gas mixtures.

independent pressure

A critical point to Dalton's Law is the idea of independent pressure. Each gas in a mixture exerts pressure independently of the other gases. While the gases share the same container and temperature, they do not influence each other's pressure directly.

Here's how it works:

• Molecules move randomly and collide with the walls of the container.
• These collisions generate pressure.

Because the gases are non-reacting, these collisions behave as if other gases are not present. This is why the total pressure is simply the sum of the individual partial pressures.

The assumption that gas molecules do not attract or repel one another ensures their pressures remain independent. If they did attract or repel, the pressure dynamics would change, altering the total pressure calculation. This independence lies at the core of many scientific and engineering calculations involving gas mixtures.