A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon. a. Which of the two gases exerts the greater partial pressure? b. The molecules or atoms of which gas will have the greater average velocity? c. The molecules of which gas will have the greater average kinetic energy? d. If a small hole were opened in the flask, which gas would effuse more quickly?

In the realm of gases, the term 'partial pressure' denotes the pressure exerted by a single gas within a mixture of gases. Dalton's Law of Partial Pressures simplifies understanding how this pressure behaves. It states that the total pressure in a system is equivalent to the sum of all individual gas pressures—each measured as if the other gases were absent.

For instance, in a scenario where equal moles of nitrogen and xenon are present in a closed container, each gas contributes equally to the total pressure if the volume and temperature remain constant. It's like sharing the responsibility of blowing up a balloon equally; no one gas works harder than the other. Therefore, neither gas exerts a greater partial pressure than the other; they are the same because the amount of each gas (in moles) is equal.

Graham's law of effusion is a fascinating aspect of gas behavior. It encapsulates how the molar mass of a gas influences its rate of effusion – the process by which gas molecules escape through a tiny hole.

The law provides a clear inverse relationship: lighter gases effuse faster than heavier ones. Think of it as a race between balloons of different sizes through a narrow corridor; the smaller balloon zips through much more quickly. In essence, the gas with the lower molar mass will have the greater average velocity, leading to a swifter effusion rate. Hence, nitrogen, which is lighter than xenon, will effuse more quickly in accordance with Graham's law.

The average kinetic energy of gas particles is a measure of the energy due to their random motion. It's a bit like measuring the collective hustle and bustle of a busy marketplace, where each vendor represents a gas particle.

For an ideal gas, the average kinetic energy depends solely on the temperature and can be calculated using the equation \(\frac{3}{2}kT\), with \(k\) representing the Boltzmann constant. Regardless of the type of gas or its molar mass, as long as they're at the same temperature, they all share identical average kinetic energy. This is why, in our example involving nitrogen and xenon at room temperature, both gases have the same average kinetic energy.

The molar mass of a gas is intrinsically linked to its effusion rate. This connection is beautifully illustrated by Graham's law of effusion, which pinpoints molar mass as the deciding factor in the effusion process.

The rule is unequivocal: a gas with a lower molar mass effuses more rapidly than one with a higher molar mass. It's akin to two messages sent via different modes of transportation - the lighter one, perhaps an email, arrives almost instantaneously, while the heavier one, like a parcel, takes longer. Nitrogen, having a lower molar mass than xenon, will thus find its way out of a punctured container more swiftly, mirroring how lighter objects tend to move faster.