Three flasks are connected as shown in the figure on p. 473...

Three flasks are connected as shown in the figure on p. $473 .$ The starting conditions, with the stopcocks closed, are shown. Assume $T$ does not change. (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.

Three flasks are connected as shown in the figure on p. $473 .$ The starting conditions, with the stopcocks closed, are shown. Assume $T$ does not change.
(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.

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Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is the foundational relationship connecting pressure, volume, temperature, and the number of moles of gas. In problems where temperature is constant (isothermal conditions), this law determines how the pressure changes when gas from multiple containers is combined into a single, larger volume, by summing the number of moles from each container and using the total volume.

Conservation of Moles

When separate gas containers are connected without the addition or loss of gas, the total number of moles remains constant throughout the process. This conservation principle is critical for determining the final state of the system, as it allows one to sum the contributions of gas from different compartments before applying the ideal gas law to find the final pressure.

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 contributes a pressure that is proportional to its mole fraction in the mixture, and this concept is essential for determining the partial pressures of the gases once they have mixed and reached equilibrium.

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