Three flasks are connected as shown in the figure. The...

Three flasks are connected as shown in the figure. The starting conditions are shown. (a) What is the final pressure inside the system when all the stopcocks are open? (b) What is the partial pressure of each of the three gases? Assume that the connecting tube has negligible volume. Assume no change in $T$.

Three flasks are connected as shown in the figure. The starting conditions are shown.
(a) What is the final pressure inside the system when all the stopcocks are open?
(b) What is the partial pressure of each of the three gases? Assume that the connecting tube has negligible volume. Assume no change in $T$.

Key Concepts

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure, volume, temperature, and moles of a gas. In problems where the temperature remains constant, it often simplifies to Boyle’s Law, which states that pressure and volume are inversely proportional. This law serves as the foundation for analyzing how gas properties change when systems are connected and allowed to equilibrate.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure is the sum of the partial pressures of each individual gas. Each gas exerts pressure as if it were alone in the container, and its partial pressure is proportional to its mole fraction in the mixture. This concept is essential for determining the contribution of each gas after mixing occurs.

Pressure Equilibration in Connected Systems

When multiple containers or flasks are connected by conduits, the gases will mix and reach a uniform pressure throughout the entire system. This pressure equilibrium process is governed by the redistribution of gas molecules until the pressure differences are evened out. Understanding this scenario is critical for determining the final system pressure after all connections are open.

Conservation of Moles and Mass

In a closed system where gases mix without any chemical reactions or losses, the total number of moles remains constant. This conservation principle allows one to use the initial conditions of each gas, such as their initial pressures and volumes, to calculate the final state after mixing. This concept underpins the determination of both the overall pressure and the partial pressures by considering the sum of the contributions from all gases.

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