Question

Explain why the measured properties of a mixture of gases depend only on the total number of moles of particles, not on the identity of the individual gas particles. How is this observation summarized as a law?

Short answer

The measured properties of a mixture of gases depend only on the total number of moles of particles because in an ideal gas, particles are assumed to have no interactions and occupy no volume. According to the Ideal Gas Law (\(PV = nRT\)), properties of an ideal gas do not depend on the identity of the gas particles. This observation is summarized as Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases.

Step-by-step solution

Understanding Ideal Gas

An ideal gas is defined as a theoretical gas where the particles are assumed to occupy no space and there are no interactions between them. In other words, the only contributing factor to the gas properties is the number of particles (moles) in the system.

The Ideal Gas Law

The Ideal Gas Law is an equation that relates the pressure (P), volume (V), temperature (T), and the number of moles (n) of an ideal gas. It is given by the formula: \(PV = nRT\), where R is the ideal gas constant.

Properties Depend on Total Number of Moles

According to the Ideal Gas Law, since the properties of an ideal gas are solely dependent on the pressure, volume, temperature, and number of moles, they do not depend on the identity of the individual gas particles. This means that a mixture of gases can be treated as a single gas with a total number of moles equal to the sum of the moles of the individual gases.

Law Summarizing the Observation

The observation that the properties of a mixture of gases depend only on the total number of moles of particles, not on the identity of the individual gas particles, is summarized as Dalton's Law of Partial Pressures. This law states that in a mixture of non-reacting ideal gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. The partial pressure of each individual gas is the pressure it would exert if it were alone in the container, and it is directly proportional to the number of moles of that gas. In conclusion, the measured properties of a mixture of gases depend only on the total number of moles of particles because ideal gases are assumed to have no interactions between particles and occupy no volume. This observation is summarized as Dalton's Law of Partial Pressures, which states that the total pressure exerted by a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases.