Question

Ideal gas particles are assumed to be volumeless and to neither attract nor repel each other. Why are these assumptions crucial to the validity of Dalton's law of partial pressures?

Short answer

The assumptions that ideal gas particles are volumeless and neither attract nor repel each other are crucial to the validity of Dalton's law of partial pressures because they ensure that the pressures of the component gases in a mixture are independent of each other. The volumeless assumption prevents particles from affecting the pressure exerted by other gases. The lack of intermolecular forces allows each gas to behave independently, avoiding the distortion of pressures caused by interactions. These assumptions, therefore, ensure the total pressure in a gas mixture is simply the sum of the individual partial pressures, as described by Dalton's law.

Step-by-step solution

Definition of Ideal Gas:

An ideal gas is a hypothetical gas whose particles obey some simplified assumptions. These assumptions are: 1. Gas particles are in constant, random motion. 2. Collisions between gas particles, and between particles and container walls, are elastic collisions, meaning no energy is lost. 3. Gas particles are assumed to be volumeless, i.e., they occupy no space themselves. 4. There are no intermolecular forces between gas particles, i.e., they neither attract nor repel each other. 5. The average kinetic energy of a gas particle is directly proportional to its temperature in kelvins.

Dalton's Law of Partial Pressures:

Dalton's law states that the total pressure of a gas mixture is the sum of the partial pressures of its individual component gases. Mathematically, this is expressed as: \[ P_{total} = P_1 + P_2 + \cdots + P_n \] Where \(P_{total}\) is the total pressure of the gas mixture, and \(P_1, P_2, \cdots, P_n\) are the partial pressures of the n component gases in the system.

Connection between Ideal Gas Assumptions and Dalton's Law:

The assumption that ideal gas particles are volumeless is important so that the particles of one gas do not affect the pressure exerted by the particles of another. If the gas particles were to occupy space, it would alter the pressure exerted by each component gas and thus distort the partial pressures in the mixture. The assumption that gas particles neither attract nor repel each other is crucial because it allows each component gas to behave independently of the others. If there were interactions between gas particles, the force exerted by one gas on the other could cause the total pressure to be different than the sum of their individual pressures. This would invalidate the equation for Dalton's law. In summary, these two assumptions are crucial for Dalton's law because they ensure that the pressures of the component gases in a mixture are independent of each other, allowing the total pressure to be simply the sum of their individual partial pressures.