Exam 2 Review: Chemical Equilibrium, Acids and Bases, Buffers, Solubility, and Complex Ions

Chemical Equilibrium

Equilibrium Constant

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The equilibrium constant quantifies the ratio of product to reactant concentrations at equilibrium.

• Kc: Based on concentrations (mol/L). For the reaction CO2(g) + C(s) → 2 CO(g): $K_c = \frac{[CO]^2}{[CO_2]}$ Pure solids and liquids are omitted from the expression.

• Kp: Based on partial pressures (atm). $K_p = \frac{P_{CO}^2}{P_{CO_2}}$

• Conversion between Kc and Kp: $K_p = K_c (RT)^{\Delta n_{gas}}$ Where $\Delta n_{gas}$ is the change in moles of gas.

• Dependence: K depends on temperature and the way the equation is written.

Manipulating Equilibrium Constants

Equilibrium constants change based on how the chemical equation is manipulated.

• Reversing a reaction: $K \rightarrow K^{-1}$

• Multiplying by a constant n: $K \rightarrow K^n$

• Adding reactions: Multiply their K values: $K_{total} = K_1 \times K_2$

Reaction Direction and the Reaction Quotient (Q)

The reaction quotient Q is calculated like K but uses current concentrations.

• Q < K: Reaction proceeds to the right (toward products).

• Q = K: System is at equilibrium.

• Q > K: Reaction proceeds to the left (toward reactants).

• Common Pitfalls: Large or small K does not necessarily indicate reaction direction, product/reactant dominance, or reaction rate.

Le Châtelier’s Principle

Le Châtelier’s Principle predicts how a system at equilibrium responds to disturbances.

• Concentration changes: Increasing a component favors the opposite side; decreasing favors the same side.

• Volume/Pressure changes: - Increasing volume (decreasing pressure) favors the side with more gas molecules ($\Delta n_{gas} > 0$). - Decreasing volume (increasing pressure) favors the side with fewer gas molecules ($\Delta n_{gas} < 0$).

• Temperature changes: - Increasing temperature favors the endothermic direction. - Decreasing temperature favors the exothermic direction.

• Note: Adding/removing solids or liquids does not affect equilibrium.

Acids and Bases

Definitions

Acids and bases are defined by their ability to donate or accept protons or electron pairs.

• Brønsted–Lowry: - Acid: Proton donor (gives H+) - Base: Proton acceptor (receives H+) - Example: $[Al(H_2O)_6]^{3+} + NH_3 \rightleftharpoons [Al(H_2O)_5(OH)]^{2+} + NH_4^+$

• Lewis: - Acid: Electron-pair acceptor (empty valence orbitals) - Base: Electron-pair donor (lone pairs) - Examples: Lewis acids (BH3, BF3, AlF3, metal ions); Lewis bases (H2O, NH3, CN–, CO)

• Complex formation: Lewis acid–base complexes, e.g., $H_3B-NH_3$, $Fe(CO)_6$, $[Ag(NH_3)_2]^+$

pH Calculations

pH quantifies the acidity or basicity of a solution.

• pH definition: $pH = -\log[H^+]$

• pOH definition: $pOH = -\log[OH^-] = 14.00 - pH$

• Weak acid (small-x approximation): $[H^+] = \sqrt{K_a \times [HA]}$ Valid if $\frac{[H^+]}{[HA]} < 5\%$

• Weak base (small-x approximation): $[OH^-] = \sqrt{K_b \times [B]}$ Valid if $\frac{[OH^-]}{[B]} < 5\%$

pH Comparison

Comparing pH values helps determine relative acid/base strengths.

• Acids: pH < 7; stronger acids have lower pH.

• Bases: pH > 7; stronger bases have higher pH.

• Strength determination: - Higher $K_a$/$K_b$ means stronger acid/base. - Lower $pK_a$/$pK_b$ means stronger acid/base. - Stronger acids have weaker conjugate bases; stronger bases have weaker conjugate acids.

Buffer System

Buffer Solutions

Buffer solutions resist changes in pH upon addition of small amounts of acid or base. They consist of a weak acid and its conjugate base, or a weak base and its conjugate acid.

• Examples: - Acetic acid and sodium acetate (HAc + NaAc) - Ammonia and ammonium chloride (NH3 + NH4Cl)

• Henderson-Hasselbalch equation: $pH = pK_a + \log \frac{[A^-]}{[HA]}$

• Effective buffer range: $0.1 \leq \frac{[A^-]}{[HA]} \leq 10$ Buffer range: $pK_a \pm 1$

• Note: If only $pK_b$ is known, calculate $pK_a$: $pK_b = 14.00 - pK_a$

Solubility Equilibrium and Complex Ions

Solubility Equilibrium

Solubility equilibrium describes the dissolution of sparingly soluble salts in water.

• General form: $MaXb(s) \rightleftharpoons a M^{b+}(aq) + b X^{a-}(aq)$

• Common ions: - Metal ions: Ag+, Mg2+, Ca2+, Pb2+ - Anions: F–, Cl–, Br–, I–, SO42–, CO32–

• Ksp expression: Write based on the equilibrium equation.

Molar Solubility (S)

Molar solubility is the number of moles of solute that dissolve per liter of solution.

• 1:1-type salts (e.g., AgCl, PbSO4, CaCO3): $K_{sp} = S^2 \Rightarrow S = \sqrt{K_{sp}}$

• 1:2-type or 2:1-type salts (e.g., Ag2CO3, PbCl2, CaF2): $K_{sp} = 4S^3 \Rightarrow S = \sqrt[3]{\frac{K_{sp}}{4}}$

• Mass solubility: $S_{mass} (g/L) = S (mol/L) \times \text{Molar mass} (g/mol)$

• Expected calculations: Find S or $S_{mass}$ from $K_{sp}$, or vice versa.

Complex Ion Formation

Complex ions form when metal ions react with ligands in solution, increasing solubility.

• General form: $M^{a+}(aq) + n L(aq) \rightleftharpoons [ML_n]^{a+}(aq)$

• Formation constant (Kf): $K_f = \frac{[ML_n]^{a+}}{[M^{a+}][L]^n}$

• Common metal ions: Ag+, Cu+, Al3+

• Common ligands: H2O, NH3, CN–, S2O32–

• Common complex ions: [Ag(NH3)2]+, [Ag(CN)2]–, [Al(H2O)6]3+, [Cu(S2O3)2]3–

• Expected questions: Deduce charge or stoichiometry, write equilibrium equation and $K_f$ expression.

Dissolving Precipitate in Ligand-Containing Solutions

Some precipitates dissolve in the presence of ligands due to complex ion formation.

• Example: Dissolving AgBr(s) in NaCN solution: AgBr(s) $\rightleftharpoons$ Ag+(aq) + Br–(aq) ($K_{sp}$) Ag+(aq) + 2 CN–(aq) $\rightleftharpoons$ [Ag(CN)2]–(aq) ($K_f$) Net: AgBr(s) + 2 CN–(aq) $\rightleftharpoons$ [Ag(CN)2]–(aq) + Br–(aq) $K = K_{sp} \times K_f$

• Expected questions: Write equilibrium equation, calculate equilibrium constant, (bonus) calculate solubility.

Summary Table: Equilibrium Constants

Type	Expression	Units
Kc	$\frac{[products]}{[reactants]}$	mol/L
Kp	$\frac{(P_{products})}{(P_{reactants})}$	atm
Ksp	Solubility product	varies
Kf	Formation constant	varies