Ideal Gases: Properties and Conditions

• Gases are not hard spheres
• Gases are small relative to the size of the system volume
• Gases undergo elastic collisions and don’t stick or react
• Gases have a temperature equal to the system temperature, giving them the same kinetic energy (Ek)
• All gases have the same Ek, but because Ek = ½ mv², they have different velocities, which are inversely proportional to the square root of their mass
• When two samples of ideal gases have the same temperature, their molecules must have the same average kinetic energy
• The equation m1v1² = m2v2² applies to diffusion and effusion, represented as m1d1² = m2d2²
• Velocities in a vacuum are much greater than velocities when diffusing through gases

Conditions for Ideal Gases

• Ideal conditions for gases occur when collisions are rare and elastic
• Low pressure (P) minimizes collisions
• Large volume (V) minimizes collisions
• Small amount of substance (n) minimizes collisions
• High temperature (T) prevents sticking
• Small and nonpolar gases also don't stick

Van der Waals Equation

• The Van der Waals equation corrects for non-ideality in gases: (P + a correction factor) (V + b correction factor) = nRT
• 'a' corrects for stickiness (intermolecular attraction); large and polar gases have large 'a', while small nonpolar gases have small 'a'
• 'b' corrects for size; large molecules have large 'b', while small molecules have small 'b'
• A gas with a larger Van der Waals constant "a" indicates that its molecules have stronger intermolecular attractions for each other

Ranking Gas Ideality

• To rank gas ideality, consider size and stickiness (intermolecular forces)
• Ideal gases like He and H2 are small and non-polar
• Non-ideal gases like H2O, NH3, SF6, and CCl4, have large intermolecular forces (like H-bonding in water) or are large gases (like SF6 or CCl4)
• When given a collection of molecules, you can rank them as you would IMFs

Ranking Gases

• Non-polar: He < N2 < CO2 < CHCl3 < H2O
• Ranking is based on size, polarity, and H-bonding

Intra- vs. Intermolecular Forces

• Covalent triple bonds (C≡C) have the largest intramolecular forces
• Ionic bonds increase with increasing charge density: NaCl < CaO < Al2O3
• Dispersion forces are dominant in nonpolar molecules
• Dipole-dipole interactions are dominant in polar molecules
• Hydrogen bonds (H-bond) are stronger than dipole-dipole and dispersion forces
• Covalent single bonds (C−C) are weaker than covalent double bonds (C=C)

Applying Force Knowledge

• Dispersion forces result from the distortion of the electron cloud of an atom or molecule by the presence of nearby atoms or molecules
• Dispersion forces occur from instantaneous dipoles formed by asymmetrically distributed electrons
• Dispersion occurs in all compounds but is the dominant force in non-polar (symmetrical) molecules
• As molecules increase in size, dispersion forces can grow to allow formation of liquids and solids
• Dipole-dipole interactions occur in molecules that have permanent dipoles (polar compounds)
• Magnitude of dipole-dipole related to size of the permanent dipole ∑ ΔEN

Hydrogen Bonding and IMF

• Down the periodic table, larger compounds exhibit more dispersion forces
• Note the normal linear relationship between the size of compound and IMF increases as shell increases as well as the number of e
• NH3, H2O, and HF abruptly increase in IMF despite their small dispersion
• Attributed to ΔEN NH (0.9), OH (1.4), HF (1.9), which prompts stronger O – H … O – H attractions
• H2O's behavior is due to H-bonds
• Ranking: NH3 < HF < H2O
• HF has only one H-F bond, while OH shows up as multiple H-bonds in sugars, causing them to be very sticky

Identifying Dominant IMF

• Non-polar (CH4): dispersion
• Polar (CH3Cl): permanent dipole
• H-F, O-H, N-H (CH3OH): H-bonding
• Salt (Na+Cl-): ionic

Examples of IMF

• N≡N ⋯ O=O: Instantaneous dipole–instantaneous dipole
• H3CCl ⋯ H3CCl: dipole–dipole
• H3CCl ⋯ O=O: dipole–instantaneous dipole
• H3CCl ⋯ Na+⋯Cl-: dipole–ionic
• Na+⋯Cl- ⋯ Na+⋯Cl-: ionic–ionic
• Note that the answer is the most dominant force of each molecule or ion

Physical Properties of Liquids

• Boiling Point: Gas bubbles form from the vapor of the liquid, and escape when the vapor pressure of bubble > atm. pressure
• Surface Tension: Inward force reduces the surface area of liquid
• Capillary Action: Liquid climbs the walls of the container because of IMF
• Viscosity: Liquid's resistance to pouring due to IMF attraction to bulk solution
• ΔHvap: Energy in IMF that must be overcome for a liquid on the surface to vaporize
• Vapor Pressure: Pressure of the vapor above the surface, inversely related to IMF
• Evaporation Rate: How quickly a liquid will vaporize, increases as IMF decreases
• Surface tension describes the inward forces that must be overcome in order to expand the surface area of a liquid

Ranking Compounds by Properties and IMF

• Compounds can be ranked based on liquid or solid properties, which are ordered based on IMF
• Properties directly proportional to IMF: Dispersion, dipole, H-bond, ionic
• Boiling point, Viscosity, Surface tension, Capillary action, Adhesion, Cohesion, ΔHvap, Nonideality, Melting point
• Use the bucket method to separate multiple compounds

Compounds to Separate Based on IMF properties

• Ionic
• Hydrogen bond
• Dipole
• Dispersion