Consider three identical-sized cylinders, all at the same...

Consider three identical-sized cylinders, all at the same temperature. Cylinder A contains 2 moles of nitrogen $\left(\mathrm{N}_{2}\right)$ gas. Cylinder $\mathrm{B}$ contains 1 mole of nitrogen gas and 1 mole of methane $\left(\mathrm{CH}_{4}\right)$ gas. Cylinder $\mathrm{C}$ contains $2 \mathrm{moles}$ of methane gas. Which cylinder has the higher pressure?

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Key Concepts

Ideal Gas Law

This is the relationship PV = nRT that describes the behavior of an ideal gas, where pressure (P) is directly proportional to the number of moles (n) of gas if the volume (V) and temperature (T) remain constant. In problems like this, it is crucial to recognize that the total number of gas moles determines the pressure, independent of the type of gas present when other factors are held constant.

Mole Concept

The mole is a measure of the amount of substance. In the context of the ideal gas law, the number of moles in a given container is the key determinant of the pressure exerted by the gas, as more moles mean more particles colliding with the container walls, hence higher pressure. This concept illustrates that two different gases with the same number of moles will exert the same pressure in identical conditions.

Dalton's Law of Partial Pressures

This law states that in a mixture of non-reacting ideal gases, the total pressure is equal to the sum of the partial pressures of the individual gases. Each gas in a mixture contributes to the total pressure proportionally to its mole fraction, meaning that in a mixture with a fixed total number of moles, the overall pressure is the sum of the pressures each gas would exert if it alone occupied the entire volume.

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