Physical Chemistry

First Law of Thermodynamics

Energy Conservation: ΔU = Q + W

Energy cannot be created or destroyed, only converted from one form to another.

• Internal Energy (U): Total energy of a system
• Heat (Q): Energy transferred due to temperature difference
• Work (W): Energy transferred through mechanical means

Second Law of Thermodynamics

Entropy of an isolated system always increases: ΔS ≥ 0

Processes occur spontaneously when entropy increases.

Enthalpy (H)

H = U + PV

Heat content at constant pressure. Used to measure heat changes in reactions.

Gibbs Free Energy (G)

G = H - TS

Predicts spontaneity: ΔG < 0 means spontaneous reaction.

Key Concepts

• Exothermic: Releases heat (ΔH < 0)
• Endothermic: Absorbs heat (ΔH > 0)
• Entropy: Measure of disorder or randomness
• Equilibrium: Dynamic balance between forward and reverse reactions

Reaction Rate

Rate = -d[A]/dt = k[A]^m[B]^n

Describes how fast reactants are consumed or products are formed.

Rate Law

Relationship between reaction rate and concentrations:

• Zero Order: Rate = k (constant rate)
• First Order: Rate = k[A]
• Second Order: Rate = k[A]² or k[A][B]

Factors Affecting Reaction Rate

• Temperature: Higher temperature increases rate (Arrhenius equation)
• Concentration: Higher concentration increases collision frequency
• Catalyst: Lowers activation energy
• Surface Area: More surface area = faster reaction

Arrhenius Equation

k = A·e^(-Ea/RT)

Relates rate constant (k) to temperature (T) and activation energy (Ea).

Catalysis

Catalysts speed up reactions by providing alternative reaction pathways with lower activation energy. They are not consumed in the reaction.

Wave-Particle Duality

Matter exhibits both wave and particle properties. This is fundamental to understanding atomic structure.

Schrödinger Equation

Ĥψ = Eψ

Describes the quantum state of a system. Solutions give energy levels and electron probability distributions.

Atomic Orbitals

• s orbital: Spherical, holds 2 electrons
• p orbital: Dumbbell-shaped, 3 orientations, holds 6 electrons
• d orbital: Complex shapes, 5 orientations, holds 10 electrons
• f orbital: Very complex, 7 orientations, holds 14 electrons

Quantum Numbers

• n (principal): Energy level (1, 2, 3...)
• l (angular): Shape of orbital (0 to n-1)
• ml (magnetic): Orientation (-l to +l)
• ms (spin): Electron spin (+½ or -½)

Molecular Orbital Theory

Electrons are delocalized over entire molecules, forming bonding and antibonding orbitals.

Redox Reactions

Transfer of electrons between species:

• Oxidation: Loss of electrons
• Reduction: Gain of electrons

Electrochemical Cells

• Galvanic (Voltaic) Cell: Spontaneous reaction generates electricity
• Electrolytic Cell: External voltage drives non-spontaneous reaction

Nernst Equation

E = E° - (RT/nF)ln(Q)

Calculates cell potential under non-standard conditions.

Standard Reduction Potential (E°)

Measure of tendency to gain electrons. More positive = stronger oxidizing agent.

Batteries and Fuel Cells

Practical applications converting chemical energy to electrical energy.

Electromagnetic Spectrum

Different regions provide information about different molecular properties:

• UV-Vis: Electronic transitions
• IR: Vibrational transitions (functional groups)
• NMR: Nuclear spin transitions (molecular structure)
• MS: Mass-to-charge ratios (molecular weight)

IR Spectroscopy

Identifies functional groups by characteristic vibrational frequencies.

• C-H stretch: ~3000 cm⁻¹
• C=O stretch: ~1700 cm⁻¹
• O-H stretch: ~3300 cm⁻¹

NMR Spectroscopy

Reveals molecular structure through nuclear magnetic resonance. Chemical shifts indicate local environment.

Applications

Used in drug discovery, environmental monitoring, food safety, and forensic analysis.