Question

Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: \(\mathrm{Ne}, \mathrm{N}_{2},\) or \(\mathrm{CH}_{4}\) ? Explain.

Short answer

Neon ( Ne ) behaves most ideally due to its weak intermolecular forces.

Step-by-step solution

Identify the characteristics of ideal gases

Ideal gases are theoretical gases composed of many randomly moving particles that interact only through elastic collisions, meaning they do not attract or repel each other. The behavior of real gases approximates ideal gas behavior under conditions of low pressure and high temperature.

Analyze intermolecular forces

Under the same conditions, the ideality of gases depends on the nature and strength of the intermolecular forces. Noble gases, like neon ( Ne e), have weak dispersion forces only, whereas N_2 and CH_4 have stronger intermolecular forces due to their larger molecular size and potential for additional interactions.

Comparison of molecular masses and sizes

Compare the molecular masses and sizes: N_2 has a molar mass of 28 g/mol and CH_4 has a molar mass of 16 g/mol, while Ne has a molar mass of 20 g/mol. Despite this, Ne is smaller and more spherical, leading to weaker intermolecular forces, closer to the ideal gas model.

Determine the gas most likely to behave ideally

Considering the above characteristics, Ne is most likely to behave as an ideal gas compared to N_2 and CH_4 . This is because Ne has the weakest intermolecular forces due to its small molecular size and only having dispersion forces, matching the assumptions of ideal gas behavior more closely.

Key concepts

Intermolecular Forces

Intermolecular forces are the attractions or repulsions between molecules, which affect how gases behave. The force's strength depends on the type of molecules and how they interact. These forces include:

• Dispersion Forces: These are the weakest type and occur in all molecules due to temporary shifts in electron density. Even non-polar molecules such as noble gases have these forces.
• Dipole-Dipole Interactions: These occur in polar molecules where there is a permanent dipole moment.
• Hydrogen Bonds: A special type of dipole-dipole interaction involving molecules where hydrogen is bonded to highly electronegative elements like fluorine, oxygen, or nitrogen.

Because noble gases like neon (\( \mathrm{Ne} \)) have only dispersion forces and no permanent dipoles or significant hydrogen bonding capability, they are more likely to behave ideally. The simplicity and minimal interaction of these forces allow the gas molecules to move freely, resembling the ideal gas model.

Noble Gases

Noble gases are a group of chemical elements with similar properties found in group 18 of the periodic table. These gases include helium (\( \mathrm{He} \)), neon (\( \mathrm{Ne} \)), argon (\( \mathrm{Ar} \)), krypton (\( \mathrm{Kr} \)), xenon (\( \mathrm{Xe} \)), and radon (\( \mathrm{Rn} \)). These elements are characterized by:

• Full Valence Shells: Noble gases have complete electron shells, making them chemically inert.
• Poor Reactivity: Their full valence shells give them little tendency to gain or lose electrons, making noble gases stable and unreactive.
• Single Molecule Size: Each noble gas molecule is just a single atom, minimizing their size and maximizing their efficiency as ideal gas analogs.

Neon (\( \mathrm{Ne} \)) is an excellent example of an ideal gas due to these characteristics. Its weak intermolecular forces and single-atom structure contribute to its close adherence to the ideal gas laws more so than larger, polyatomic molecules.

Elastic Collisions

The term "elastic collisions" describes an important characteristic of ideal gases, where gas molecules encounter each other and the walls of their container without losing energy. Understanding elastic collisions involves:

• Energy Conservation: During these collisions, the total kinetic energy of the system remains constant.
• No Loss of Speed: Post-collision, the involved gas particles maintain their speed, ensuring constant motion throughout.
• Random Movement: Ideal gas particles move randomly, ensuring even distribution of speed and direction over time.

In a system behaving ideally, particles have continuous, perfectly elastic collisions ensuring that no energy is lost in the form of sound, heat, etc. Neon (\( \mathrm{Ne} \)), with its minimal intermolecular forces, demonstrates this behavior effectively, as its interactions do not cause the particles to slow or bond, providing a clear example of ideal gas behavior.