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?

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

The kinetic molecular theory of ideal gases is based on the following postulates: 1. Gases consist of a large number of identical particles (molecules or atoms) that are in constant, random motion. 2. The size of the particles is negligibly small compared to the distance between them. 3. The particles do not influence each other with any forces, except when colliding with each other or with the walls of their container. These collisions are perfectly elastic, meaning that there is no net energy loss during the collision. 4. The average kinetic energy of the particles is directly proportional to the temperature of the gas, which implies that all gases have the same average kinetic energy at a given temperature.

Dalton's law of partial pressures supports the following postulates of the kinetic molecular theory: 1. Postulate 1 (Constant, random motion of particles): Dalton's law assumes that the individual gas particles do not interact with each other, except during collisions. This implies that each gas behaves independently, supporting the notion of random motion. 2. Postulate 2 (Negligibly small size of particles): Since Dalton's law states that the total pressure of the gas mixture is the sum of the individual gas pressures, it considers each gas independently, implying that their individual sizes have no impact on the pressure. 3. Postulate 3 (No forces between particles, except during collisions): Dalton's law assumes that the particles don't exert any forces on each other and interact only during collisions. The lack of interaction plays a role in the addition of the partial pressures of each gas to calculate the total pressure of the gas mixture. In summary, Dalton's law of partial pressures supports some postulates of the kinetic molecular theory by assuming each gas in a mixture behaves independently, with no forces between particles, allowing the calculation of the total pressure of the gas mixture from the sum of the partial pressures.