General Chemistry Study Guide: Chemical Equilibrium, Acids & Bases, and Aqueous Ionic Equilibria

Chapter 16: Chemical Equilibrium

Key Terms

• Reversible reactions: Chemical reactions that can proceed in both the forward and reverse directions.

• Dynamic equilibrium: The state in which the rate of the forward reaction equals the rate of the reverse reaction, so the concentrations of reactants and products remain constant over time.

• Equilibrium constant (K): A numerical value that expresses the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their coefficients in the balanced equation.

• Law of mass action: States that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants, each raised to a power equal to its coefficient in the balanced equation.

• Reaction quotient (Qc): The ratio of product concentrations to reactant concentrations at any point in time, not necessarily at equilibrium.

• X is small approximation: An assumption used to simplify equilibrium calculations when the change in concentration (x) is much smaller than the initial concentration.

• Le Châtelier's principle: If a system at equilibrium is disturbed, the system will shift in a direction that minimizes the disturbance.

Concepts

• Equilibrium constant expression: Expresses the relationship between the concentrations of products and reactants at equilibrium.

• Interpretation of K:

  • If $K > 1$, products are favored at equilibrium.

  • If $K < 1$, reactants are favored at equilibrium.

• Dynamic equilibrium: At equilibrium, the rates of the forward and reverse reactions are equal, but the concentrations of reactants and products do not change.

• Law of mass action: The equilibrium constant expression is derived from this law.

• Relationship between Kc and Kp: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the change in moles of gas.

• Reaction quotient (Q): Used to determine the direction a reaction will proceed to reach equilibrium.

  • If $Q < K$, the reaction proceeds forward (toward products).

  • If $Q > K$, the reaction proceeds in reverse (toward reactants).

  • If $Q = K$, the system is at equilibrium.

• Le Châtelier's principle: Predicts how a system at equilibrium responds to changes in concentration, pressure, or temperature.

Equations and Relationships

• General equilibrium constant expression: $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ for the reaction $aA + bB \rightleftharpoons cC + dD$

• Relationship between Kc and Kp: $K_p = K_c(RT)^{\Delta n}$

• Reaction quotient: $Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (same form as $K_c$, but for non-equilibrium concentrations)

Learning Outcomes Checklist

Outcome
Write equilibrium constant expressions for chemical equations.
Predict how changes in the chemical equation affect the equilibrium constant.
Write equilibrium constants in terms of partial pressures or concentrations.
Write equilibrium constants for chemical equations that contain solids and pure liquids.
Calculate equilibrium constants from experimental concentration measurements.
Predict the direction of a reaction by comparing the reaction quotient to the equilibrium constant.
Calculate unknown equilibrium concentrations from known equilibrium constants and initial concentrations or pressures.
Calculate unknown equilibrium concentrations from known equilibrium constants and initial concentrations or pressures in cases with a relatively small equilibrium constant.
Predict the effect of a concentration change on equilibrium.
Predict the effect of a volume or pressure change on equilibrium.
Predict the effect of a temperature change on equilibrium.

Acids and Bases

Key Terms

• Carboxylic acid: Organic acids containing a carboxyl group (-COOH).

• Arrhenius acid/base: Acids produce H+ in water; bases produce OH- in water.

• Brønsted-Lowry acid/base: Acids donate protons (H+); bases accept protons.

• Amphoteric: Substances that can act as both acids and bases.

• Conjugate acid-base pair: Two species that differ by one proton.

• Strong/weak acid or base: Strong acids/bases dissociate completely; weak acids/bases only partially dissociate.

• Monoprotic/polyprotic acid: Acids that can donate one or more than one proton per molecule.

• Autoionization: The process by which water self-ionizes to form H3O+ and OH-.

• Ion product constant for water (Kw): $K_w = [H_3O^+][OH^-]$

• pH: $pH = -\log[H^+]$

• Percent ionization: The fraction of acid molecules that ionize, expressed as a percentage.

• Base ionization constant (Kb): Equilibrium constant for the ionization of a base.

• Lewis acid/base: Lewis acids accept electron pairs; Lewis bases donate electron pairs.

Concepts

• Acid and base definitions: Arrhenius, Brønsted-Lowry, and Lewis definitions provide different perspectives on acid-base behavior.

• Conjugate acid-base pairs: Every acid has a conjugate base, and every base has a conjugate acid.

• Acid and base strength: Strong acids/bases dissociate completely; weak acids/bases do not.

• Relationship between acid strength and conjugate base strength: The stronger the acid, the weaker its conjugate base.

• pH and pOH: $pH + pOH = 14$ at 25°C.

• Polyprotic acids: Acids that can donate more than one proton, with each ionization step having its own Ka.

• Autoionization of water: $K_w = 1.0 \times 10^{-14}$ at 25°C.

Equations and Relationships

• Acid ionization constant: $K_a = \frac{[H_3O^+][A^-]}{[HA]}$

• Ion product constant for water: $K_w = [H_3O^+][OH^-]$

• pH and pOH: $pH = -\log[H^+]$ $pOH = -\log[OH^-]$ $pH + pOH = 14$

• Relationship between Ka, Kb, and Kw: $K_a \times K_b = K_w$

Learning Outcomes Checklist

Outcome
Analyze acids and bases by definition and their corresponding properties.
Perform calculations involving Ka and Kb.
Quantify the acidity of a solution using the pH scale.
Perform percent ionization calculations for acids.
Perform pH calculations for mixtures of acids.
Classify an anion in solution as a weak base or neutral.
Classify a cation in solution as acidic, basic, or neutral.
Calculate the concentration of ions in weak diprotic acid solutions.
Predict acidity based on molecular structure.
Analyze acids and bases in terms of the Lewis model definition.

Aqueous Ionic Equilibria: Buffers, Titrations, and Solubility

Key Terms

• Buffer: A solution that resists changes in pH when small amounts of acid or base are added.

• Common ion effect: The shift in equilibrium caused by the addition of a compound having an ion in common with the dissolved substance.

• Henderson-Hasselbalch equation: Relates pH, pKa, and the ratio of conjugate base to acid.

• Buffer capacity: The amount of acid or base a buffer can neutralize before the pH changes significantly.

• Acid-base titration: A technique to determine the concentration of an acid or base by reacting it with a base or acid of known concentration.

• Indicator: A substance that changes color at a specific pH range, used to signal the end point of a titration.

• Equivalence point: The point in a titration where the amount of titrant added is stoichiometrically equivalent to the amount of analyte in solution.

• Solubility product constant (Ksp): The equilibrium constant for the dissolution of a sparingly soluble ionic compound.

• Molar solubility: The number of moles of solute that dissolve per liter of solution to reach saturation.

• Selective precipitation: The process of adding a reagent to a solution to precipitate one ion while leaving others in solution.

• Complex ion: An ion formed from a metal ion and one or more ligands.

• Ligand: A molecule or ion that binds to a central metal ion to form a complex ion.

• Formation constant (Kf): The equilibrium constant for the formation of a complex ion from a metal ion and ligands.

Concepts

• Buffer solutions: Contain a weak acid and its conjugate base or a weak base and its conjugate acid; resist changes in pH.

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

• Buffer capacity: Greatest when concentrations of acid and conjugate base are high and approximately equal.

• Titration curves: Graphs of pH versus volume of titrant added; used to determine equivalence points and pKa values.

• Indicators: Chosen based on their pH transition range relative to the expected equivalence point.

• Solubility product (Ksp): Describes the equilibrium between a solid and its ions in solution.

• Common ion effect: The solubility of a salt decreases in the presence of a common ion.

• Complex ion formation: Can increase the solubility of certain salts by removing ions from solution.

Equations and Relationships

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

• Solubility product constant: $K_{sp} = [A^+]^m[B^-]^n$ for $A_mB_n(s) \rightleftharpoons mA^+ + nB^-$

• Formation constant: $K_f = \frac{[\text{complex ion}]}{[\text{metal ion}][\text{ligand}]^n}$

• Relationship between Q and Ksp:

  • If $Q < K_{sp}$, no precipitation occurs.

  • If $Q > K_{sp}$, precipitation occurs.

  • If $Q = K_{sp}$, the solution is saturated.

Learning Outcomes Checklist

Outcome
Perform pH calculations for buffer solutions containing a common ion.
Perform pH calculations for buffer solutions using the Henderson-Hasselbalch equation.
Perform pH calculations for buffer solutions after the addition of a small amount of strong acid or strong base.
Perform pH calculations for buffer solutions containing a weak base and its conjugate acid before and after the addition of an acid or base.
Describe the preparation of an effective buffer solution.
Perform calculations for the titration of a strong acid with a strong base.
Perform calculations for the titration of a weak acid with a strong base.
Identify specific points along the titration curve for a diprotic acid with a strong base.
Predict properties of indicators in solutions.
Perform Ksp calculations for ionic compounds in pure water.
Perform Ksp calculations involving the common ion effect.
Determine the effect of pH on solubility.
Predict precipitation reactions by comparing Q to Ksp.
Perform calculations involving selective precipitation.
Perform calculations involving complex ion equilibria.

Additional info: These notes are structured to provide a comprehensive overview of key equilibrium, acid-base, and solubility concepts in General Chemistry, suitable for exam preparation and self-study.