Problem 50 - Chemistry The Central Science In Si Units

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

Statement (b) is correct because Xe gas, having more massive atoms than \(\text{N}_2\), results in higher density in the same volume at STP.

Step 1: Understanding the Question Requirements

First, identify the scenario: comparing the density of nitrogen gas (\(\text{N}_2\)) and xenon gas (Xe) at Standard Temperature and Pressure (STP). Density is a measure of mass per unit volume.

Step 2: Analyzing Statement (a)

Statement (a) suggests that Xe atoms pack more densely because they repel less. However, at STP, gases have the same volume due to the defined conditions. This statement incorrectly relates repulsion to density without considering correct properties.

Step 3: Analyzing Statement (b)

Statement (b) proposes that because Xe atoms have a higher mass than \(\text{N}_2\) molecules and the same number of molecules exist in a given volume at STP, Xe is denser. Density is calculated as mass per volume, so heavier mass molecules in the same volume (as with STP conditions) equals higher density.

Step 4: Analyzing Statement (c)

Statement (c) claims that Xe atoms are larger and thus occupy more space. Though interesting, size primarily affects volume but does not directly address molecular count per volume at STP.

Step 5: Analyzing Statement (d)

Statement (d) suggests slower Xe atoms exert less upward force due to their mass. While mass affects motion, this does not correlate with how gas density is defined by mass per volume in identical volumes at STP.

Step 6: Selecting the Correct Statement

According to the conditions and definitions at STP, statement (b) accurately explains the reason. Since Xe atoms are more massive, but the volume at STP remains constant, the overall mass in the same volume results in a higher density for Xe gas.

Key Concepts

Molecular Mass

Molecular mass, also known as molecular weight, is the sum of the masses of all atoms in a molecule. It is measured in atomic mass units (amu). Understanding molecular mass is essential because it directly affects various properties of a gas, such as density.
The molecular mass of a substance determines how much mass is contained in each mole of that substance. For example:

• For xenon (Xe), the atomic mass is approximately 131.29 amu.
• For nitrogen (N_2), the molecular mass is approximately 28.02 amu (since each nitrogen atom is about 14.01 amu, and there are two of them in a nitrogen molecule).

These differences in molecular mass explain why gases can have varying densities under the same conditions. The higher the molecular mass, the greater the density when comparing gases under the same volume and temperature conditions.

STP Conditions

STP stands for Standard Temperature and Pressure, which is a set of conditions used as a reference to compare different gases. The standard conditions are:

• Temperature: 0 degrees Celsius or 273.15 Kelvin.
• Pressure: 1 atmosphere (atm).

Under these conditions, one mole of an ideal gas occupies 22.4 liters of volume.
STP conditions are important because they allow scientists to have a consistent basis for comparing properties like gas density. When gases are measured at STP, they all occupy the same volume per mole, making it easier to directly compare their densities. Therefore, the differences in gas densities result primarily from differences in molecular mass, as both have the same volume under STP.

Xenon Gas

Xenon is a noble gas with the symbol Xe and an atomic number of 54. It is a heavy gas with a high atomic mass of approximately 131.29 amu.
Xenon's status as a noble gas means that it is chemically inert and does not easily form bonds with other elements. This chemical inertness does not directly affect its density but contributes to its unique place in the periodic table and its behavior in different conditions.
At STP, xenon gas is denser than many other gases due to its significant atomic mass. When comparing it with nitrogen gas at STP, xenon's higher mass compared to nitrogen results in greater density, even though both occupy the same volume.

Nitrogen Gas

Nitrogen gas, or N_2, is a diatomic molecule composed of two nitrogen atoms. It constitutes about 78% of the Earth's atmosphere and is a colorless, odorless gas.
The molecular mass of nitrogen gas is relatively low, at approximately 28.02 amu. This lower molecular mass compared to gases like xenon means that nitrogen gas is less dense, especially under STP conditions where volume per mole is fixed.
Being less dense, nitrogen gas will exert the same pressure within a given volume as a heavier gas at STP, but it will do so with a smaller mass per unit volume. This fundamental property makes nitrogen permeable and less dense compared to heavier gases.