Question

Which of the following statements best explains why nitrogen gas at STP is less dense than Xe gas at STP? \begin{equation}\begin{array}{l}{\text { (a) Because Xe is a noble gas, there is less tendency for the Xe }} \\ {\text { atoms to repel one another, so they pack more densely in }} \\ {\text { the gaseous state. }} \\ {\text { (b) Xe atoms have a higher mass than } \mathrm{N}_{2} \text { molecules. Because }} \\ {\text { both gases at STP have the same number of molecules per }} \\ {\text { unit volume, the Xe gas must be denser. }}\\\\{\text { (c) The Xe atoms are larger than } \mathrm{N}_{2} \text { molecules and thus take }} \\ {\text { up a larger fraction of the space occupied by the gas. }} \\\ {\text { (d) Because the Xe atoms are much more massive than the }} \\\ {\mathrm{N}_{2} \text { molecules, they move more slowly and thus exert }} \\\ {\text { less upward force on the gas container and make the gas }} \\ {\text { appear denser. }}\end{array}\end{equation}

Short answer

The best explanation for why nitrogen gas at STP is less dense than Xe gas at STP is statement (b): Xe atoms have a higher mass than N₂ molecules, and since both gases at STP have the same number of molecules per unit volume, Xe gas must be denser.

Step-by-step solution

Understanding the gas density

Density is defined as mass per unit volume. In the context of gases, this would imply that a gas with a higher molecular mass would have a higher density, given that the number of molecules per unit volume of that gas is the same as that of another gas. Gases at STP have the same number of molecules per unit volume due to Avogadro's law, which states that equal volumes of all gases at the same temperature and pressure contain the same number of molecules.

Analyzing statement (a)

Statement (a) states that Xe atoms have less tendency to repel each other, so they pack more densely in the gaseous state due to being a noble gas. This statement doesn't take into account the molecular mass and volume of the gases, which are directly related to the density.

Analyzing statement (b)

Statement (b) says that Xe atoms have a higher mass than N₂ molecules, and because both gases at STP have the same number of molecules per unit volume, Xe gas must be denser. This statement accurately reflects the concept of density and how it relates to molecular mass and the number of molecules per unit volume of a gas at STP.

Analyzing statement (c)

Statement (c) suggests that the larger size of Xe atoms compared to N₂ molecules is the reason for the density difference. However, the statement doesn't consider the actual mass of the molecules, which is the main factor contributing to the density.

Analyzing statement (d)

Statement (d) mentions that Xe atoms are more massive than N₂ molecules, and thus they move more slowly. This would affect the upward force on the gas container but doesn't necessarily explain the density difference between the two gases. The focus should be on the molecular mass and the number of molecules per unit volume at STP.

Conclusion

Based on the analysis of the given statements, statement (b) best explains why nitrogen gas at STP is less dense than Xe gas at STP. This is because Xe atoms have a higher mass than N₂ molecules, and since both gases at STP have the same number of molecules per unit volume, Xe gas must be denser.

Key concepts

Avogadro's law

Avogadro's law is a cornerstone principle in the realm of chemistry, specifically in understanding gases. It tells us that at the same temperature and pressure, equal volumes of different gases contain the same number of molecules.

Think of it as a universal gas agreement; no matter what type of gas you have, if the conditions are the same and you measure the same volume, you'll count the same number of gas particles. This has incredible implications for calculating things like molar volume and comparing gas densities, as illustrated in our exercise. By recognizing the equal number of particles in the same volume at STP (standard temperature and pressure), the problem becomes simpler. You only need to weigh the types of particles – the heavier they are, the denser the gas.

Molecular mass

Molecular mass (often called molecular weight) is essentially the combined weight of all the atoms in a molecule, measured in atomic mass units (amu). It gives us a way to compare the 'heaviness' of different molecules.

To illustrate, imagine molecular mass as the total baggage weight a molecule carries. This figure is key to computing the density of a gas, since a gas composed of 'heavier' molecules (higher molecular mass) will be denser than one with 'lighter' molecules, assuming the number of molecules in a given volume is the same – a situation Avogadro's law guarantees at STP. So, when we say nitrogen gas (N₂) is less dense than xenon gas (Xe) at STP, it's like saying a suitcase full of feathers (nitrogen) is lighter than one filled with rocks (xenon), given they're of the same size and packed equally tight.

STP conditions

STP conditions, short for Standard Temperature and Pressure, are a set of predefined reference conditions used in chemistry to ensure consistency when discussing the properties of gases. Standard temperature is defined as 0 degrees Celsius (273.15 Kelvin), and standard pressure is 1 atmosphere (atm).

In the realm of gases, STP is like the 'home base', where every comparison starts. It's crucial because gas properties can vary widely with changes in temperature and pressure. By always referring to STP, chemists can compare apples to apples, or in our case, N₂ to Xe molecules. The problem from our exercise relies on these conditions to claim an equal number of gas molecules in the same volume, allowing us to focus solely on molecular mass to determine gas density.

Gas molecule behavior

The behavior of gas molecules is influenced by the kinetic molecular theory, which states that gas particles are in constant, random motion and that they collide with each other and the walls of their container. These collisions result in pressure, a measure of the force that the gas exerts.

Distinct factors like intermolecular forces and molecular mass can influence how these molecules act. For example, heavier gas molecules (such as Xe) move more sluggishly than lighter ones (like N₂) due to their greater mass. Meanwhile, at STP, this behavior doesn't directly impact density. The density is more a question of how much these 'liberally' moving particles weigh altogether in a given space—think of it as a lively dance of particles, where each brings a varying amount of mass that adds up to the total 'weight' of the gas we feel.