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 gas 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.

Short answer

The best explanation for why nitrogen gas at STP is less dense than Xe gas at STP is statement (b), because Xe atoms have a higher mass than ${\mathrm{N}}_2$ molecules, and both gases have the same number of molecules per unit volume (according to Avogadro's Law), resulting in a denser Xe gas.

Step-by-step solution

Examine statement (a)

Statement (a) suggests that Xe is denser because it is a noble gas, and there is less tendency for the Xe atoms to repel one another, resulting in a denser packing of atoms in the gas state. However, both nitrogen and Xe are gases at STP, and gas particles tend to have considerable space between them, regardless of their nature. This statement does not explain the difference between their density properly. #Step 2: Examine statement (b)#

Examine statement (b)

Statement (b) claims 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 (Avogadro's Law), the Xe gas must be denser. This statement is accurate, as the density of a gas depends on the mass and volume, where $density=\frac{mass}{volume}$. Higher mass particles in the same volume will indeed result in a higher density. #Step 3: Examine statement (c)#

Examine statement (c)

Statement (c) proposes that Xe atoms are larger than ${\mathrm{N}}_2$ molecules and thus occupy a larger fraction of the space, making the gas denser. However, gas particle sizes do not play a significant role in the density of a gas. The statement does not explain the density difference accurately. #Step 4: Examine statement (d)#

Examine statement (d)

Statement (d) implies that Xe atoms are more massive than ${\mathrm{N}}_2$ molecules, causing them to move more slowly and exert less upward force on the gas container, making the gas appear denser. While it is true that Xe atoms are more massive, the effect of their motion on the gas container is not the primary factor affecting density. This statement does not explain the density difference correctly. #Step 5: Choose the best explanation#

Choose the best explanation

Based on the analyses in steps 1-4, statement (b) is the best explanation for why nitrogen gas at STP is less dense than Xe gas at STP. The higher mass of Xe atoms combined with both gases having the same number of molecules per unit volume (according to Avogadro's Law) results in a denser Xe gas.