VSEPR Theory, Molecular Polarity, Valence Bond Theory, and Gas Laws: Study Notes for General Chemistry

Chapter 9: Molecular Geometry and Bonding Theories

VSEPR Theory and Molecular Geometries

The Valence Shell Electron Pair Repulsion (VSEPR) theory is used to predict the shapes of molecules based on the repulsion between electron pairs around a central atom. The geometry depends on the number of electron domains (bonding pairs and lone pairs) around the central atom.

• Electron Domains: Regions of electron density (bonds or lone pairs) around a central atom.

• Electron-Pair Geometry: Arrangement of all electron domains (bonding and non-bonding).

• Molecular Geometry: Arrangement of only the atoms (ignoring lone pairs).

Common geometries and their bond angles:

Number of Electron Dense Areas	Electron-Pair Geometry	No Lone Pairs	1 Lone Pair	2 Lone Pairs	3 Lone Pairs	4 Lone Pairs
2	Linear	Linear
3	Trigonal planar	Trigonal planar	Bent
4	Tetrahedral	Tetrahedral	Trigonal pyramidal	Bent
5	Trigonal bipyramidal	Trigonal bipyramidal	Seesaw	T-shaped	Linear
6	Octahedral	Octahedral	Square pyramidal	Square planar	T-shaped	Linear

Example: For AB6 (octahedral), all bond angles are 90°. Lone pairs can be placed in any position due to symmetry.

Examples of Octahedral Derivatives

• BrF5: Square pyramidal geometry (AB5E)

• XeF4: Square planar geometry (AB4E2)

Predicting Geometry and Bond Angles

To predict the electron domain geometry, molecular geometry, and bond angles, use the VSEPR model and consider the number of electron domains and lone pairs.

• Bond Angles: Typical values are 180° (linear), 120° (trigonal planar), 109.5° (tetrahedral), and less than these if lone pairs are present.

• Example: For acetic acid (CH3COOH), VSEPR can be used to predict the geometry around each atom.

Molecular Polarity and Dipole Moments

Molecular polarity depends on both the difference in electronegativity between atoms and the geometry of the molecule.

• Polar Bonds: A bond is polar if the electronegativity difference is greater than 0.5.

• Dipole Moment: A measure of charge separation in a molecule; it is a vector quantity.

• Geometry and Symmetry: Symmetric molecules (e.g., CO2) are nonpolar even if they have polar bonds, because the dipoles cancel out. Asymmetric molecules (e.g., H2O) are polar.

General Rules:

• No lone pairs on the central atom and all surrounding atoms are the same → nonpolar (e.g., BF3).

• Presence of lone pairs or different surrounding atoms → polar (e.g., NH3).

Valence Bond Theory and Hybridization

Valence Bond Theory explains covalent bonding through the overlap of atomic orbitals. Hybridization describes the mixing of atomic orbitals to form new hybrid orbitals suitable for bonding.

• sp3 Hybridization: Tetrahedral geometry (e.g., CH4, NH3, H2O)

• sp2 Hybridization: Trigonal planar geometry (e.g., BF3)

• sp Hybridization: Linear geometry (e.g., BeCl2)

How to Predict Hybridization:

1. Draw the Lewis structure.

2. Count the number of lone pairs and atoms bonded to the central atom (electron domains).

# of Lone Pairs + # of Bonded Atoms	Hybridization	Examples
2	sp	BeCl2
3	sp2	BF3
4	sp3	CH4, NH3, H2O

Expanded Octets: For central atoms in period 3 and beyond, d orbitals are available for hybridization (e.g., PBr5, XeF4).

Bond Classification: Sigma and Pi Bonds

Covalent bonds are classified as sigma (σ) or pi (π) bonds based on the type of orbital overlap.

• Sigma (σ) Bonds: Formed by end-to-end overlap of orbitals; all single bonds are sigma bonds.

• Pi (π) Bonds: Formed by side-to-side overlap; present in double and triple bonds in addition to a sigma bond.

Example: Ethene (C2H4) has a double bond between carbons: one sigma and one pi bond.

Counting Sigma and Pi Bonds

• Single bond: 1 sigma

• Double bond: 1 sigma + 1 pi

• Triple bond: 1 sigma + 2 pi

Chapter 10: Gases

Properties and Importance of Gases

Gases play vital roles in medicine, engineering, and environmental science. Their physical properties are distinct from solids and liquids.

• Shape: Not defined; gases expand to fill their container.

• Volume: Particle size is negligible compared to container volume.

• Motion: Particles move randomly and rapidly.

• Compressibility: Gases are highly compressible due to large spaces between particles.

• Flow: Gases can flow but cannot be poured like liquids.

Types of Substances That Exist as Gases

• Noble Gases: He, Ne, Ar, Kr, Xe, Rn (monatomic)

• Homonuclear Diatomic Gases: H2, N2, O2, F2, Cl2

• Molecular Compounds: H2S, CO, NH3 (low molar mass, non-metals)

• Metals and Ionic Compounds: Do not exist as gases under normal conditions.

Pressure: Definition and Measurement

Pressure is the force exerted by gas particles colliding with the walls of their container. It is a key measurable property of gases.

• Units of Pressure:

  • 1 atm = 760 mmHg = 760 torr = 101.325 kPa = 14.7 psi

• Measurement:

  • Barometer: Measures atmospheric pressure.

  • Manometer: Measures pressure of a gas sample.

Gas Laws

Boyle's Law

Describes the inverse relationship between pressure and volume for a fixed amount of gas at constant temperature.

• Mathematical Expression: $P \propto \frac{1}{V}$

• Equation: $P_1V_1 = P_2V_2$

• Graph: Hyperbolic curve (not linear)

Charles's Law

Describes the direct relationship between volume and absolute temperature for a fixed amount of gas at constant pressure.

• Mathematical Expression: $V \propto T$

• Equation: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Temperature in Kelvin: $K = ^\circ C + 273.15$

Gay-Lussac's Law

Describes the direct relationship between pressure and temperature for a fixed amount of gas at constant volume.

• Equation: $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Avogadro's Law

Describes the direct relationship between volume and number of moles of gas at constant temperature and pressure.

• Equation: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Standard Molar Volume: At STP (1 atm, 0°C), 1 mole of any gas occupies 22.41 L.

Ideal Gas Law

Combines all the above relationships into a single equation of state for ideal gases.

• Equation: $PV = nRT$

• R (Gas Constant): $R = 0.08206 \; \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol}$

• Variables: P = pressure (atm), V = volume (L), n = moles, T = temperature (K)

Combined Gas Law

Used when conditions change for a fixed amount of gas.

• Equation: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

Density and Molar Mass of Gases

The ideal gas law can be rearranged to relate density and molar mass:

• Equation: $PM = dRT$

• Density (d): Usually in g/L

Dalton's Law of Partial Pressures

In a mixture of gases, each gas exerts a pressure independently of the others. The total pressure is the sum of the partial pressures.

• Equation: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Mole Fraction: $X_i = \frac{n_i}{n_{\text{total}}}$

• Partial Pressure: $P_i = X_i \cdot P_{\text{total}}$

Gas Phase Stoichiometry

Stoichiometry can be applied to reactions involving gases using the ideal gas law to relate moles, volume, and pressure.

• Use balanced chemical equations.

• Convert between volume, moles, and mass as needed.

Kinetic Molecular Theory

The kinetic molecular theory explains the behavior of gases at the molecular level.

• Gases consist of particles in constant, random motion.

• The volume of gas particles is negligible compared to the container.

• No attractive or repulsive forces between particles.

• The average kinetic energy is proportional to absolute temperature.

• Different gases at the same temperature have the same kinetic energy, but not necessarily the same velocity.

Equation for Kinetic Energy:

• $KE_{avg} = \frac{1}{2} m v^2$

Maxwell-Boltzmann Distribution: Describes the distribution of speeds among gas particles.

Additional info:

• Some context and examples were expanded for completeness, such as the explanation of hybridization and the use of gas laws in stoichiometry.

• Tables were recreated and summarized for clarity.