Problem 15 - Chemistry An Atoms First Approach

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?

Step-by-Step Solution

Answer

Dalton's law of partial pressures supports postulates a, c, and d of the kinetic molecular theory. It supports postulate a by demonstrating that each gas particle contributes independently to the total pressure with no dependence on the presence of other gas particles, a result of their random motion. It supports postulate c by implying that there are no intermolecular forces between the particles of different gases in the mixture. Finally, it supports postulate d by deriving the total pressure from the sum of partial pressures, which comes from the conservation of kinetic energy between the particles and container walls, suggesting elastic collisions.

Step 1: 1. Reviewing the kinetic molecular theory postulates

The kinetic molecular theory postulates are: a) Gases consist of very small particles, either atoms or molecules, that are in constant, random motion. b) The volume of gas particles is negligible compared to the volume of their container. c) There are no intermolecular forces between gas particles except during collisions. d) Collisions between gas particles and the container walls are perfectly elastic, with the conservation of kinetic energy. e) The average kinetic energy of gas particles is directly proportional to the absolute temperature of the gas.

Step 2: 2. Understanding Dalton's law of partial pressures

Dalton's law states that in a mixture of non-reacting ideal gases, the total pressure exerted by the mixture is equal to the sum of the partial pressures of each individual gas. The partial pressure of a gas is defined as the pressure that the gas would exert if it occupied the same container by itself. Mathematically, Dalton's law can be expressed as: \(P_{total} = P_{1} + P_{2} + P_{3} + ... + P_{n}\) Where \(P_{total}\) is the total pressure of the gas mixture, and \(P_{1}, P_{2}, P_{3},\dots, P_{n}\) are the partial pressures of the individual gases in the mixture.

Step 3: 3. Identifying the supported postulates

Dalton's law of partial pressures supports the following postulates of the kinetic molecular theory: - Postulate a) - Gases consist of very small particles in constant, random motion: Since the total pressure exerted by the gas mixture is the sum of the partial pressures, it implies that each gas particle contributes independently to the total pressure with no dependence on the presence of other gas particles. This is consistent with the random motion described in Postulate a. - Postulate c) - No intermolecular forces between gas particles except during collisions: Dalton's law assumes that the contributions to the total pressure of the mixture from the individual gases are independent of each other. This suggests there are no intermolecular forces between the particles of different gases, thus supporting Postulate c. - Postulate d) - Collisions between gas particles and container walls are elastic with the conservation of kinetic energy: The total pressure of a gas mixture is derived from the sum of the partial pressure contributions, which comes from the conservation of kinetic energy between the particles and container walls. This supports the idea of elastic collisions in Postulate d. In conclusion, Dalton's law of partial pressures supports postulates a, c, and d of the kinetic molecular theory.