Problem 50 - Chemistry: The Central Science

Question

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

Step-by-Step Solution

Answer

The best explanation for why nitrogen gas at STP is less dense than Xe gas at STP is (b), which states that Xe atoms have a higher mass than \(\mathrm{N}_{2}\) molecules. Since both gases at STP have the same number of molecules per unit volume, the Xe gas must be denser due to its higher mass.

Step 1: Evaluate Statement (a)

In statement (a), it is mentioned that Xe is a noble gas, so there is less tendency for Xe atoms to repel one another. However, this statement does not discuss the density concept, so it cannot be the best explanation.

Step 2: Evaluate Statement (b)

In statement (b), it is mentioned that Xe atoms have a higher mass than \(\mathrm{N}_{2}\) molecules. Both gases at STP have the same number of molecules per unit volume, so the Xe gas must be denser due to its higher mass. This statement discusses the concept of density considering mass, so this could be the best explanation.

Step 3: Evaluate Statement (c)

In statement (c), it is mentioned that Xe atoms are larger than \(\mathrm{N}_{2}\) molecules and thus take up a larger fraction of the space occupied by the gas. However, this statement does not discuss the density directly and only considers the size, so it cannot be the best explanation.

Step 4: Evaluate Statement (d)

In statement (d), it is mentioned that Xe atoms are much more massive than the \(\mathrm{N}_{2}\) molecules and they move more slowly, exerting less upward force. However, this statement primarily discusses the motion of the particles and not the density concept, making it an unlikely explanation.

Step 5: Choose the best explanation

From the evaluation of the statements, statement (b) directly discusses the concept of density and considers the higher mass of Xe atoms, making it the statement that best explains why nitrogen gas at STP is less dense than Xe gas at STP. Therefore, the answer is (b).

Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental principle in chemistry and physics that describes the behavior of an ideal gas. It is mathematically expressed as \[ PV = nRT \]where:

• \(P\) is the pressure of the gas
• \(V\) is the volume of the gas
• \(n\) is the number of moles of gas
• \(R\) is the universal gas constant
• \(T\) is the temperature in Kelvin

This law can be used to determine the density of a gas under specific conditions. Density is mass per unit volume (\( \text{density} = \frac{\text{mass}}{\text{volume}} \) $), and can be related to the ideal gas law. By manipulating the equation, you can connect molecular mass to density, providing insights into why one gas might be denser than another under the same conditions.

Molecular Mass

Molecular mass, also known as molecular weight, is the sum of the masses of all atoms in a molecule. It is typically measured in atomic mass units (amu) or grams per mole. The molecular mass of a compound influences many of its physical properties, including density.

When considering gases like xenon (Xe) and nitrogen (\(\text{N}_2\), it's important to compare their molecular masses to understand why one is denser than the other at STP. Xenon has a substantially higher atomic mass (approximately 131.29 amu) compared to nitrogen, which has a molecular mass of about 28 amu for \(\text{N}_2\). This difference in mass directly affects density, as density is directly proportional to mass. In essence, the greater the mass of the gas, the denser it will be.

STP Conditions

STP stands for Standard Temperature and Pressure. These conditions are frequently used in scientific measurements to enable fair comparisons between different gases. STP is defined as a temperature of 273.15 Kelvin (0 degrees Celsius) and a pressure of 1 atmosphere (atm).

Under STP conditions, gases exhibit predictable behaviors that can often be described by the ideal gas law. Because STP is a standard condition used across experiments, the volume occupied by one mole of an ideal gas is 22.4 liters. At STP, it becomes easier to compare the densities of different gases, because they all occupy the same volume per mole. Thus, denser gases have greater molecular mass as seen in the comparison between nitrogen gas and xenon gas.

Noble Gases

Noble gases are a group of chemical elements with similar properties. They are all odorless, colorless, monatomic gases with very low chemical reactivity under standard conditions. The noble gases include helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).

Among these, xenon is particularly heavy, contributing to its high density compared to other gases like nitrogen. Whilst the chemical inertness of noble gases doesn't directly affect density, their atomic masses do. Xenon, being a noble gas with a large atomic number, inherently has a higher molecular mass. This constitutes one reason why xenon gas is denser than nitrogen gas when evaluated at STP.