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Which of the following best helps explain why the pressure of a sample of CH4(g) (molar mass 16 g/mol) is closer to the pressure predicted by the ideal gas law than a sample of NH3(g) (molar mass 17 g/mol)?


ANH3 molecules are polar while CH4 molecules are not, and the greater attractions between NH3 molecules cause the molecules to collide with the walls of the container with less force.
BNH3 molecules have a greater molar mass than CH4 molecules, so the NH3 molecules collide with the walls of the container with more force.
CCH4 molecules have more hydrogen atoms than NH3 molecules, so CH4 molecules have more hydrogen bonding and greater intermolecular forces.
DCH4 molecules are larger than NH3 molecules, so the actual CH4 molecules take up a significant portion of the volume of the gas.

Verified Answer :

  • The ideal gas law assumes no intermolecular forces and negligible particle volume.
  • \(\text{NH}_3\) is a polar molecule, leading to dipole-dipole attractions, whereas \(\text{CH}_4\) is nonpolar with only weak London dispersion forces.
  • Stronger attractive forces reduce the impact force of gas molecules colliding with container walls, causing deviations from the ideal gas law.
  • Because \(\text{CH}_4\) has weaker intermolecular forces than \(\text{NH}_3\), its behavior is closer to the ideal gas law; thus, option A is correct.
  • Final Answer: \(\boxed{A}\)

Explanation

  1. Ideal Gas Law Assumptions

The ideal gas law, \(PV=nRT\), is based on two primary assumptions: gas particles have negligible volume and there are no intermolecular forces between them. Real gases deviate from these ideal assumptions, particularly at high pressures or low temperatures. To determine why \(\text{CH}_4\) (methane) behaves more ideally than \(\text{NH}_3\) (ammonia), we must examine their molecular properties.

  1. Comparing Intermolecular Forces

Methane (\(\text{CH}_4\)) is a nonpolar molecule with a tetrahedral geometry, meaning the only significant intermolecular forces present are weak London dispersion forces. Ammonia (\(\text{NH}_3\)) has a trigonal pyramidal geometry and is polar due to the lone pair of electrons on the nitrogen atom and the difference in electronegativity between nitrogen and hydrogen. This polarity allows \(\text{NH}_3\) molecules to exhibit significant dipole-dipole interactions, which are much stronger than the dispersion forces in \(\text{CH}_4\).

  1. Relating Forces to Pressure Deviations

Intermolecular attractive forces pull gas molecules toward one another, which reduces the frequency and force with which the molecules collide with the container walls. Because the actual pressure exerted by a real gas depends on these collisions, stronger attractive forces lead to a greater deviation from the pressure predicted by the ideal gas law (the ideal pressure is typically higher than the observed pressure for real gases). Since \(\text{NH}_3\) experiences stronger attractive forces than \(\text{CH}_4\), \(\text{NH}_3\) shows a larger deviation from ideal gas behavior. Conversely, \(\text{CH}_4\) has weaker forces and thus behaves more like an ideal gas.

  1. Conclusion

Based on the analysis, option A correctly identifies that \(\text{NH}_3\) molecules are polar while \(\text{CH}_4\) molecules are not, and that the stronger attractions in \(\text{NH}_3\) result in fewer or weaker collisions with the container walls, thus causing a greater deviation from ideality. Options B, C, and D contain incorrect premises or misinterpretations of molecular behavior. Therefore, option A is the best explanation.

Examples

Understanding intermolecular forces is essential for real-world engineering, such as designing pressure vessels for industrial gases. If an engineer assumes a gas behaves ideally but it actually has strong polar attractions, the calculated storage capacity or required wall thickness might be incorrect. By accounting for these forces, we can more accurately predict how gases will behave under varying conditions of temperature and pressure in systems like chemical reactors or fuel storage.

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