Chapter 15 – Chemical Equilibrium

15.1 The Concept of Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products over time.

• Equilibrium Definition: A dynamic state where the forward and reverse reaction rates are equal.

• Reaction Rates: At equilibrium, both forward and reverse reactions continue to occur, but at equal rates.

• Concentration Stability: The concentrations of reactants and products remain constant, not necessarily equal.

• Example: In the reaction , equilibrium is reached when the rate of ammonia formation equals its decomposition.

15.2 The Equilibrium Constant

The equilibrium constant quantifies the ratio of product and reactant concentrations at equilibrium for a given reaction.

• Kc: The equilibrium constant in terms of concentration. Units depend on the reaction.

• Writing Kc: For ,

• Kp: The equilibrium constant in terms of partial pressures. , where is the change in moles of gas.

• Conversion: Use to convert between Kc and Kp.

• Example: For , .

15.3 Using Equilibrium Constants

The magnitude of the equilibrium constant indicates the extent to which a reaction favors products or reactants.

• Large Kc: Reaction favors products ("leans right").

• Small Kc: Reaction favors reactants ("leans left").

• Hess’s Law: Equilibrium constants can be manipulated mathematically when reactions are reversed or multiplied.

• Reversing Reaction: becomes .

• Multiplying Reaction: is raised to the power of the coefficient.

• Combining Reactions: Multiply individual values to get the net $K_c$.

15.4 Heterogeneous Equilibria

Heterogeneous equilibrium involves reactants and products in different phases. Only concentrations of gases and aqueous species are included in equilibrium expressions.

• Rule: Exclude pure solids and pure liquids from equilibrium constant expressions.

• Example: For , .

15.5 Calculating Equilibrium Constants

Equilibrium constants can be calculated using equilibrium concentrations or by setting up ICE tables when concentrations are not given.

• Direct Calculation: Plug equilibrium concentrations into the expression.

• ICE Tables: Used to determine equilibrium concentrations when only initial values are given.

• Example: For , use ICE table to solve for equilibrium concentrations.

15.6 Some Applications of Equilibrium Constants

The reaction quotient (Q) predicts the direction in which a reaction will proceed to reach equilibrium.

• Reaction Quotient (Q): Calculated like , but with current concentrations.

• Comparison: If , reaction shifts right; if , reaction shifts left.

15.7 Le Chatelier’s Principle

Le Chatelier’s Principle states that a system at equilibrium will adjust to counteract changes in concentration, pressure, volume, or temperature.

• Concentration: Adding reactant shifts equilibrium right; adding product shifts left.

• Pressure/Volume: Increasing pressure favors side with fewer moles of gas; decreasing pressure favors more moles.

• Temperature: Raising temperature favors endothermic direction; lowering favors exothermic.

• Catalyst: Speeds up attainment of equilibrium but does not shift equilibrium position.

• Sign of : Indicates whether reaction is endothermic () or exothermic ().

Chapter 16 – Acid-Base Equilibria

16.1 Classification of Acids and Bases

Acids and bases are classified by their behavior in water and their ability to donate or accept protons or electron pairs.

• Arrhenius: Acids produce in water; bases produce .

• Brønsted–Lowry: Acids donate protons (); bases accept protons.

• Lewis: Acids accept electron pairs; bases donate electron pairs.

• Amphiprotic: Water can act as both an acid and a base.

16.2 Conjugate Acid-Base Pairs

Conjugate pairs consist of two species that differ by a single proton.

• Conjugate Acid: Formed when a base gains a proton.

• Conjugate Base: Formed when an acid loses a proton.

• Strength Relationship: Strong acids have weak conjugate bases, and vice versa.

• Ka and Kb: Larger Ka or Kb means stronger acid or base.

16.3 The Autoionization of Water

Water autoionizes to form and ions, establishing an equilibrium.

• Equation:

• Equilibrium Expression:

• Calculations: Use to find or .

16.4 The pH Scale

The pH scale measures the acidity or basicity of a solution.

• pH:

• pOH:

• Neutral: pH = 7; Acidic: pH < 7; Basic: pH > 7

• Interconversion:

16.5 Strong Acids and Bases

Strong acids and bases dissociate completely in water.

• Strong Acids: 7 common strong acids (memorize names and formulas).

• Strong Bases: 8 common strong bases (memorize names and formulas).

• Ion-Dissociation: Complete dissociation; use stoichiometry to calculate pH/pOH.

• Example:

16.6 Weak Acids

Weak acids only partially dissociate in water, establishing an equilibrium.

• Ka Expression:

• Strength: Smaller Ka means weaker acid.

• Calculations: Use ICE tables and quadratic equation for pH or Ka.

• Mathematical "Cheat": For very weak acids,

16.7 Weak Bases

Weak bases partially accept protons in water, establishing an equilibrium.

• Kb Expression:

• Strength: Smaller Kb means weaker base.

• Calculations: Similar to weak acids, but may require extra steps to find pH.

• Example: Ammonia () is a common weak base.

16.8 The Relationship Between Ka and Kb

Ka and Kb for conjugate acid-base pairs are related through the ionization constant of water.

• Equation:

• pKa + pKb = pKw = 14$

Chapter 17 – Aqueous Equilibria: Buffers, Titrations, and Solubility

17.1 The Common-Ion Effect

The common-ion effect occurs when a solution contains two substances that produce the same ion, affecting equilibrium and solubility.

• Effect: Addition of a common ion suppresses ionization of a weak acid/base.

• Calculations: Use ICE tables to determine pH in presence of a common ion.

17.2 Buffers

Buffers are solutions that resist changes in pH when small amounts of acid or base are added.

• Components: Weak acid and its conjugate base, or weak base and its conjugate acid.

• Purpose: Maintain stable pH.

• Henderson-Hasselbalch Equation:

• Example: Mixture of HF and NaF forms a buffer.

17.3 Acid-Base Titrations

Titrations involve adding a solution of known concentration to another solution to determine its concentration.

• Strong Acid/Strong Base: Equivalence point at pH = 7.

• Strong/Weak Systems: Equivalence point pH depends on relative strengths.

• Equivalence Point: Moles of acid = moles of base.

• Endpoint: Indicator changes color; may not coincide with equivalence point.

• Calculations: Use stoichiometry, ICE tables, and pH equations.

17.4 Solubility Equilibria

Solubility equilibria describe the dissolution of salts in water and are quantified by the solubility product constant (Ksp).

• Ksp Expression: For ,

• Calculations: Find Ksp from ion concentrations or vice versa.

• Molar Solubility: Amount of salt that dissolves per liter.

• Mass Solubility: Amount of salt that dissolves per liter in grams.

17.5 Factors that Affect Solubility

Solubility can be affected by the presence of a common ion, acidity, or formation of complex ions.

• Common Ion: Decreases solubility of salts.

• Acidic Solution: Increases solubility of salts containing basic anions.

• Complex Ion Formation: Increases solubility of certain salts.

Appendix: Periodic Table of the Elements

The periodic table is a fundamental reference for chemical properties, atomic numbers, and atomic masses of elements. It is essential for understanding chemical reactions, stoichiometry, and equilibrium calculations.