In a certain lab experiment a small vessel of volume V holds...

In a certain lab experiment a small vessel of volume $V$ holds an ideal gas at 300 K and 5 atm. The small vessel is connected to a large reservoir of volume 6 V that contains the same kind of gas at a pressure of 1 atm and a temperature of 600 K . A stopcock in the tube connecting the two containers keeps the gases separate. The temperature of each container is held constant. When the stopcock is opened, what will be the final pressure in each container?

Key Concepts

Equilibrium in Connected Gas Compartments

When two or more separated gas compartments are connected, the system will evolve toward a common equilibrium pressure. By applying the ideal gas law to each compartment and using the conservation of the total number of moles, one can determine the final uniform pressure that results from the mixing of gases under different initial conditions.

Ideal Gas Law

The ideal gas law, expressed as pV = nRT, is fundamental for relating pressure, volume, temperature, and the number of moles in a gas. This principle allows one to analyze how gas quantities change when certain parameters (like temperature or volume) are held constant, which is critical for solving problems involving equilibrium in gas systems.

Isothermal Process

An isothermal process is one where the temperature remains constant throughout any changes occurring in the system. In such cases, the ideal gas law shows that the product of pressure and volume must remain constant if the number of moles does not change, simplifying the analysis of how pressure adjusts when gases mix between different volumes.

Conservation of Mass/Moles

In a system where gases are allowed to mix or redistribute, the total number of moles of gas remains constant. This conservation law is essential for establishing relationships between the initial and final states of the system, particularly when determining the equilibrium conditions after the gases are connected.

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