1. Concentration Units: Molarity, Molality & Mole Fraction
Key concentration metrics: (1) Molarity (M): M = (moles of solute) / (Volume of solution in Liters) = (w2 / M2) × (1000 / V_mL). Dependent on temperature because liquid volume expands with heating. (2) Molality (m): m = (moles of solute) / (Mass of solvent in kilograms) = (w2 / M2) × (1000 / w1_grams). INDEPENDENT of temperature because mass does not change with temperature (preferred in colligative calculations). (3) Mole Fraction (x): x_A = n_A / (n_A + n_B), where sum of mole fractions x_A + x_B = 1. Dimensionless and temperature independent. (4) Parts Per Million (ppm): ppm = (mass of solute / total mass of solution) × 10^6.
2. Raoult's Law & Colligative Properties
Colligative properties depend solely on the number of solute particles relative to solvent molecules: (1) Raoult's Law for volatile liquids: P_total = P°_A x_A + P°_B x_B. (2) Relative Lowering of Vapour Pressure: (P° - P) / P° = i · x2 = i · (n2 / n1) for dilute solutions. (3) Elevation in Boiling Point: ΔTb = Tb - Tb° = i · Kb · m, where Kb is molal boiling point elevation constant (ebullioscopic constant). (4) Depression in Freezing Point: ΔTf = Tf° - Tf = i · Kf · m, where Kf is molal freezing point depression constant (cryoscopic constant). (5) Osmotic Pressure: π = i · C R T = i (n2 / V) R T. Van 't Hoff Factor (i): i = normal molar mass / observed molar mass = actual number of particles / number of formula units. For dissociation (degree α, n ions): i = 1 + (n - 1)α. For association: i = 1 + (1/n - 1)α.
3. Electrochemistry: Conductivity & Kohlrausch's Law
Resistance and Conductance: Resistance R = ρ(l / A); Conductance G = 1/R. Conductivity (Specific Conductance, κ): κ = (1/R) · (l / A) = G · G*, where G* = l/A is the cell constant (cm^-1 or m^-1). Molar Conductivity: Λm = (1000 · κ) / Molarity (in S·cm^2·mol^-1) or κ / (1000 · M) (in S·m^2·mol^-1). Kohlrausch's Law of Independent Migration of Ions: Limiting molar conductivity of an electrolyte is the sum of limiting ionic conductivities of its constituent ions: Λ°m (AxBy) = x λ°m (A^y+) + y λ°m (B^x-). Degree of dissociation for weak electrolyte: α = Λm / Λ°m. Dissociation constant: Ka = (C α^2) / (1 - α).
4. Nernst Equation & Gibbs Free Energy
For a redox electrode reaction M^n+ + n e- -> M: E(M^n+/M) = E°(M^n+/M) - (RT / nF) ln(1 / [M^n+]). For a complete galvanic cell at standard 298 K (25 °C): E_cell = E°_cell - (0.0591 / n) log10 Q_c, where n is number of moles of electrons transferred and Q_c is reaction quotient ([products]^coeff / [reactants]^coeff). Standard Cell EMF: E°_cell = E°_cathode (reduction) - E°_anode (reduction). At equilibrium (Q_c = Kc, E_cell = 0): E°_cell = (0.0591 / n) log10 Kc. Relation to standard Gibbs Free Energy: ΔrG° = -n F E°_cell = -2.303 R T log10 Kc. For a spontaneous reaction under standard conditions: E°_cell > 0 and ΔrG° < 0.
5. Chemical Kinetics: Integrated Rate Laws & Half-Life
Reaction rate expressions: Rate = -(1/a) d[A]/dt = k [A]^x [B]^y. Overall order = x + y. (1) Zero Order Reactions: Rate = k; Integrated equation: [A] = [A]0 - kt; Half-life: t_1/2 = [A]0 / (2k) (directly proportional to initial concentration); Unit of k: mol·L^-1·s^-1. (2) First Order Reactions: Rate = k[A]; Integrated equation: k = (2.303 / t) log10([A]0 / [A]); Half-life: t_1/2 = ln(2) / k = 0.693 / k (COMPLETELY INDEPENDENT of initial concentration); Unit of k: s^-1. High-frequency time relationships for 1st order: t_75% = 2 × t_50%; t_87.5% = 3 × t_50%; t_99% = 2 × t_90%; t_99.9% ≈ 10 × t_50%.
6. Temperature Dependence: Arrhenius Equation
Arrhenius Equation describes temperature sensitivity of reaction rates: k = A e^(-Ea / RT), where A is the pre-exponential frequency factor and Ea is the activation energy. In logarithmic form: ln k = ln A - Ea / (R T), or log10 k = log10 A - Ea / (2.303 R T). A plot of log10 k vs 1/T yields a straight line with slope = -Ea / (2.303 R) and y-intercept = log10 A. Two-temperature relation: log10(k2 / k1) = [Ea / (2.303 R)] · [(T2 - T1) / (T1 T2)]. For most reactions near room temperature, the rate constant approximately doubles for every 10 °C rise in temperature (temperature coefficient ≈ 2 to 3).