Molecular Geometry, Gas Laws, and Intermolecular Forces

Posted on Jan 2, 2026 in Physics

Molecular Geometry and Hybridization

To determine electron domain geometry, molecular geometry, hybridization, polarity, and bond angles, you must count electron domains (bonding pairs and lone pairs) around the central atom of a Lewis structure.

  • Electron Domain Geometry: The arrangement of all electron domains. For example, four domains result in a tetrahedral geometry.
  • Molecular Geometry: The arrangement of only the atoms. For example, four domains with one lone pair result in a trigonal pyramidal geometry.
  • Hybridization: This matches the number of electron domains:
    • 2 domains = sp
    • 3 domains = sp2
    • 4 domains = sp3
    • 5 domains = sp3d
    • 6 domains = sp3d2
  • Bond Angles: Ideal angles are modified by lone pairs. For instance, a tetrahedral arrangement is 109.5°, but lone pairs reduce this angle slightly.
  • Polarity: This depends on molecular geometry and bond polarity. Symmetric molecules are typically nonpolar, while asymmetric molecules with polar bonds are polar.

Example: NH3 has four electron domains (three bonds and one lone pair). Its electron domain geometry is tetrahedral, its molecular geometry is trigonal pyramidal, its hybridization is sp3, its bond angle is approximately 107°, and it is a polar molecule.

Understanding Hybridization

Hybridization is the mixing of atomic orbitals on the central atom to form new hybrid orbitals of equal energy capable of forming sigma bonds. For example, one s orbital and three p orbitals mix to form four sp3 hybrid orbitals in methane (CH4).

VSEPR Theory Defined

VSEPR stands for Valence Shell Electron Pair Repulsion. This theory states that electron pairs around a central atom arrange themselves to minimize repulsion by staying as far apart as possible.

Sigma and Pi Bond Symmetry

  • Sigma (σ) Bonds: Formed by head-on orbital overlap along the internuclear axis. Free rotation is possible. These include all single bonds and the first bond in double or triple bonds.
  • Pi (π) Bonds: Formed by side-by-side overlap of p orbitals above and below the internuclear axis. No free rotation is possible. These include the second bond in C=C and the second and third bonds in C≡C.

Counting Bonds in Lewis Structures

  • Single Bond: 1 σ bond
  • Double Bond: 1 σ bond + 1 π bond
  • Triple Bond: 1 σ bond + 2 π bonds

Example: C2H4 (ethene) contains one C=C double bond (1σ + 1π) and four C-H single bonds (4σ), totaling 5σ and 1π bonds.

Molecular Orbital Diagrams and Bond Order

  • Filling: Place valence electrons in molecular orbitals from lowest to highest energy, following Hund’s rule.
  • Bond Order: Calculated as (bonding electrons – antibonding electrons) ÷ 2. A higher bond order indicates a stronger, shorter bond.
  • Magnetic Properties: A molecule is paramagnetic if unpaired electrons are present and diamagnetic if all electrons are paired.

Example: O2 has 12 valence electrons. In its MO diagram, there are two unpaired electrons in the π* orbitals, making it paramagnetic with a bond order of 2.

Unit Conversions for Volume and Pressure

Milliliters to Liters

To convert milliliters (mL) to liters (L), divide by 1,000:

L = mL ÷ 1,000

Alternatively, use the conversion factor: 1 L = 1,000 mL. For example, 250 mL ÷ 1,000 = 0.250 L.

Pressure Units

1 atm = 760 torr = 760 mmHg = 101,325 Pa = 101.325 kPa = 1.01325 bar = 1,013.25 mbar = 14.7 psi (pounds per square inch).

Gas Laws and Kinetic Molecular Theory

Pressure and Temperature Conversions

Convert between pressure units using the standard values above. For temperature, you must use Kelvin: K = °C + 273.15.

Core Gas Law Equations

  • Changing Conditions: Use Boyle’s Law (P1V1 = P2V2), Charles’s Law (V1/T1 = V2/T2), or the Combined Gas Law (P1V1/T1 = P2V2/T2).
  • Ideal Gas Law: PV = nRT (where R = 0.0821 L·atm/mol·K).
  • Gas Density: d = PM/RT (where M is molar mass).
  • Molar Mass from Density: M = dRT/P.
  • Stoichiometry: Use PV = nRT with balanced equations. At STP, the molar volume of an ideal gas is 22.4 L/mol.
  • Effusion and Diffusion: Graham’s Law states rate1/rate2 = √(M2/M1).

Dalton’s Law and Mole Fraction

Total pressure is the sum of partial pressures: Ptotal = P1 + P2 + P3… The mole fraction (χ) is moles of component ÷ total moles, and Pcomponent = χ × Ptotal.

Kinetic Molecular Theory Principles

  • Gas molecules move in straight lines until they collide.
  • Collisions are elastic (no net energy loss).
  • Molecular speed is proportional to the square root of temperature.
  • Lighter molecules move faster than heavier ones at the same temperature.

Intermolecular Forces and Phase Changes

States of Matter

  • Solids: Closely packed, fixed positions, strong intermolecular forces (IMFs), definite shape and volume.
  • Liquids: Close together but mobile, definite volume, take the shape of the container.
  • Gases: Far apart, weak IMFs, move freely, no definite shape or volume.

Types of Intermolecular Forces (IMFs)

  • London Dispersion Forces (LDF): Weakest forces present in all molecules; strength increases with molecular size.
  • Dipole-Dipole Forces: Occur between polar molecules.
  • Hydrogen Bonding: A strong type of dipole-dipole interaction occurring when H is bonded to N, O, or F.

Impact of IMFs on Physical Properties

  • Vapor Pressure: Stronger IMFs lead to lower vapor pressure.
  • Boiling Point: Stronger IMFs lead to higher boiling points.
  • Melting Point: Stronger IMFs lead to higher melting points.

Phase Diagrams and Heating Curves

Heating curves show temperature versus heat added. Flat regions represent phase changes where temperature remains constant as energy breaks IMFs. Phase diagrams show the state of matter at various pressures and temperatures, featuring the triple point (all three phases coexist) and the critical point.

Calculating Heat for Phase Changes

  • Temperature Change: q = mcΔT
  • Melting/Freezing: q = nΔHfus
  • Boiling/Condensing: q = nΔHvap