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 kinetic molecular theory by emphasizing that gas particles are in constant, random motion, do not interact with each other, and that the pressure each gas exerts depends only on its partial pressure. This law demonstrates that the total pressure of a non-reactive gas mixture results from the sum of the individual pressures, without considering any interactions between the gases.

Step-by-step solution

Understanding Dalton's Law of Partial Pressures

Dalton's law of partial pressures states that in a mixture of non-reactive gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. Mathematically, it is expressed as: \[ P_{total} = P_1 + P_2 + P_3 + ... + P_n \] where \(P_{total}\) is the total pressure, and \(P_i\) represents the partial pressure of the individual gases in the mixture.

Kinetic Molecular Theory - Gas Particles are in Constant, Random Motion

According to the kinetic molecular theory, gas particles are always moving in random directions with a wide range of velocities. These particles are assumed to be in constant motion and collide with the walls of the container, exerting pressure. When multiple gases are mixed, they behave as one gas with gas particles from each gas species moving randomly and exerting pressure on the container walls.

Kinetic Molecular Theory - Gas Particles Don't Interact With Each Other

Another fundamental postulate of the kinetic molecular theory is that gas particles do not interact with each other. They neither attract nor repel each other. This means that the pressure each gas exerts is independent of the presence of other gas particles. Dalton's law supports this idea by showing that the total pressure exerted by a gas mixture is the sum of individual pressures, without any consideration of interactions between the gases.

Pressure Exerted Depends Only on Partial Pressure

Dalton's law states that the pressure exerted by each gas in a mixture depends only on its partial pressure, which is proportional to both its concentration and temperature. This is in line with the postulates of the kinetic molecular theory, which states that the pressure a gas exerts is proportional to its concentration and its temperature. Applying Dalton's law of partial pressures to ideal gas mixtures supports the idea that the total pressure exerted by the gases results solely from the addition of the partial pressures of each individual gas. No interactions between the gases need to be considered. In conclusion, Dalton's law of partial pressures supports the assertions of the kinetic molecular theory that gas particles are in constant, random motion and do not interact with each other. Additionally, the pressure exerted by a gas in a mixture depends only on its partial pressure.