2. The ideal gas law best describes the properties of which of the following gases at 0°C and 1 atm? — States of Matter Chemistry Question

STEPS:

1. Understand the characteristics of an ideal gas: According to the Kinetic Molecular Theory (KMT), an ideal gas is defined by two key assumptions:
* The gas particles themselves have negligible (virtually zero) molecular volume compared to the total volume of the container.
* There are no intermolecular attractive or repulsive forces between the gas particles.
2. Identify when real gases deviate from ideal behavior: Real gases deviate most from ideal behavior under conditions of high pressure (where particles are forced close together and their individual molecular volumes become significant) and low temperature (where particles move slowly enough that attractive intermolecular forces can pull them together). Conversely, real gases behave most ideally when their intermolecular forces (IMFs) are extremely weak and their molecular size is small.
3. Analyze the intermolecular forces (IMFs) of each gas at standard conditions ($0^\circ\text{C}$ and $1\text{ atm}$):
* $\text{PH}_3$ (Phosphine): Has a trigonal pyramidal molecular geometry with a lone pair on the central phosphorus atom. This asymmetry makes $\text{PH}_3$ a polar molecule, which experiences both London dispersion forces and dipole-dipole attractions.
* $\text{HBr}$ (Hydrogen bromide): A diatomic molecule with a polar covalent bond due to the electronegativity difference between hydrogen and bromine. It is a polar molecule and experiences both London dispersion forces and dipole-dipole attractions.
* $\text{SO}_2$ (Sulfur dioxide): Has a bent molecular geometry due to the lone pair on the central sulfur atom. This makes $\text{SO}_2$ a highly polar molecule with strong dipole-dipole attractions and London dispersion forces.
* $\text{N}_2$ (Nitrogen gas): A homonuclear diatomic molecule ($\text{N}\equiv\text{N}$) with completely equal sharing of electrons. It is entirely nonpolar and experiences only very weak London dispersion forces.
4. Compare and select the gas with the weakest interactions: Because $\text{N}_2$ is completely nonpolar and has a small molecular volume, it has the weakest intermolecular attractions among the choices.
5. Conclude: At $0^\circ\text{C}$ and $1\text{ atm}$, $\text{N}_2$ experiences the least attraction between its molecules and its volume behaves most like a point mass. Thus, it deviates the least from KMT assumptions and is best described by the ideal gas law, confirming Option D is the correct answer.

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WHY_OTHERS_WRONG:

• Option A is incorrect: $\text{PH}_3$ is a polar molecule due to its asymmetric pyramidal structure. The dipole-dipole attractions between phosphine molecules are stronger than the weak dispersion forces in $\text{N}_2$, leading to a greater deviation from ideal behavior.
• Option B is incorrect: $\text{HBr}$ is polar and has a larger, more highly polarizable electron cloud due to the heavy bromine atom. This increases both dipole-dipole forces and London dispersion forces, causing $\text{HBr}$ to deviate more from ideal gas behavior than $\text{N}_2$.
• Option C is incorrect: $\text{SO}_2$ is a highly polar, bent molecule. The combination of strong dipole-dipole forces and significant London dispersion forces (due to its larger size) makes its intermolecular attractions the strongest in this group. Consequently, $\text{SO}_2$ deviates the most from ideal behavior of all the choices.