Question

How does Dalton’s law of partial pressures help us with our model of ideal gases? That is, what postulates of the kinetic molecular theory does it support?

Short answer

Dalton's Law of Partial Pressures supports the first and third postulates of the Kinetic Molecular Theory. It demonstrates that individual gases in a mixture behave independently, as each gas exerts pressure on the container walls independently (Postulate 1) and their contributions to the total pressure are unaffected by the presence of other gases (Postulate 3). Thus, the total pressure of a gas mixture can be determined by summing the partial pressures of its individual components.

Step-by-step solution

Understanding Dalton's Law of Partial Pressures

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. Mathematically, it is expressed as: \[P_{total} = P_1 + P_2 + P_3 +...+ P_n\] Where \(P_{total}\) is the total pressure of the gas mixture, and \(P_1, P_2, P_3,..., P_n\) are the partial pressures of individual gases in the mixture.

Understanding the Kinetic Molecular Theory

The Kinetic Molecular Theory is a model which describes the behavior of ideal gases. The theory is based on several postulates, which include: 1. Gases consist of a large number of particles (atoms or molecules) that are in constant random motion. 2. The volume occupied by the gas particles themselves is negligible compared to the volume of the container. 3. Gas particles are neither attracted nor repelled by each other and their collisions are perfectly elastic. 4. The average kinetic energy of gas particles is directly proportional to the temperature of the gas.

Relating Dalton's Law of Partial Pressures to the Kinetic Molecular Theory

Dalton's Law of Partial Pressures supports the following postulates of the Kinetic Molecular Theory: Postulate 1: The constant random motion of gas particles in a mixture means that each gas exerts pressure on the container walls independently. This justifies the additivity of the partial pressures in Dalton's Law. Postulate 3: Since gas particles in a mixture are neither attracted nor repelled by each other, each gas behaves independently and its contribution to the total pressure is unaffected by the presence of other gases. Therefore, Dalton's Law of Partial Pressures supports the first and third postulates of the Kinetic Molecular Theory by showing that individual gases in a mixture behave independently and that their properties can be added together to determine the properties of the mixture as a whole.

Key concepts

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures is a fundamental principle in understanding gas mixtures. This law states that the total pressure exerted by a mixture of non-reacting gases is equivalent to the sum of the pressures each gas would exert if it occupied the space alone. In mathematical terms, it can be represented as:\[ P_{\text{total}} = P_1 + P_2 + P_3 + \ldots + P_n \]where \(P_{\text{total}}\) is the overall pressure of the gas mixture, and \(P_1, P_2, P_3, \ldots, P_n\) are the individual partial pressures of the gases involved.
This concept is crucial because it allows chemists to predict the pressure exerted by gas mixtures under specific conditions. It reflects the idea that gases, being "ideal," act independently even when mixed together.
Each type of gas molecule behaves as if others aren't present, maintaining their typical pressure contributions. This independence arises because ideal gases do not react with each other. Dalton's Law underlines the addition of individual pressures without mutual influence, which aligns well with the theoretical behavior of ideal gases.

Kinetic Molecular Theory

The Kinetic Molecular Theory provides a framework for understanding the physical behavior of gases. It explains gas laws through several key ideas about gas particles and their movements. These are:

• Gases comprise a large number of molecules or atoms moving in random directions. This accounts for properties like pressure, as collisions with the container walls generate force.


• The actual volume occupied by gas molecules is negligible compared to the volume of the container. This helps justify why gases are compressible and expand to fill their containers.


• There's an absence of attractive or repulsive forces among the particles, which means they move independently. This concept aligns with the idea that gas laws like Boyle's or Charles's can be applied uniformly.


• The temperature of a gas relates to the average kinetic energy of its particles. Higher temperatures mean faster particle movement, which impacts properties like pressure and volume under pressure.

This theory is the underpinning for understanding why gases behave as they do in ideal situations, and explains how changes in external conditions (like temperature and volume) affect gas behavior.

Postulates of the Kinetic Molecular Theory

The postulates of the Kinetic Molecular Theory detail the assumptions about how gases behave under ideal conditions. They provide a fundamental understanding of gas properties and behaviors, ensuring a clearer perspective on both individual gas behavior and gas mixtures: - **Constant Random Motion**: Gas particles are always moving unpredictably. This randomness ensures they exert pressure consistently within a container, as they continually collide with the container walls. Dalton's Law links here because each type of gas maintains its own pressure through such collisions. - **Elastic Collisions**: When gas particles collide, they don't lose energy. This is key because it ensures the persistent kinetic energy that maintains pressure and temperature stability across the gas. - **Negligible Interactions**: Simplifying gases to ideal conditions means assuming they neither attract nor repel each other significantly. This assumption permits Dalton's Law to function, as no gas interferes with another's pressure contribution. Overall, these postulates are instrumental in predicting how gases will behave under various conditions and highlight their independence within mixtures. They provide a ground-up view of gas properties, essential for applying concepts like Dalton's Law accurately.