General Chemistry 2: Chemical and Acid-Base Equilibrium

Chemical Equilibrium and Dynamic Processes

Definition of Chemical Equilibrium: Chemical equilibrium is defined as the state reached by a reaction mixture when the rates of the forward and reverse reactions have become equal.
Reversibility: In principle, all chemical reactions are reversible ( $\rightleftharpoons$ ). Many reactions lead to an incomplete conversion of reactants into products.
Dynamic Equilibrium: Systems where both the forward and reverse processes are still actively occurring at equal rates are in a state of dynamic equilibrium.
Spontaneity: Chemical reactions always proceed spontaneously toward equilibrium.
Equilibrium Favorability: * Product-favored: If there are more products than reactants at equilibrium, the reaction is product-favored ( $\rightarrow$ ). * Reactant-favored: If there are more reactants than products at equilibrium, the reaction is reactant-favored ( $\leftarrow$ ).

The Equilibrium Constant (K)

The Equilibrium Constant Expression: This mathematical equation relates the concentrations of reactants and products for a reaction at equilibrium. The constant $K$ characterizes a reaction in equilibrium.
Concentration-based Constant ( $K_c$ ): For a general reaction at a given temperature: $aA + bB \rightleftharpoons cC + dD$ , the expression is: $\text{K}_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$ * All concentrations must be equilibrium concentrations.
Partial Pressure-based Constant ( $K_p$ ): For the same general reaction where components are gases: $\text{K}_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$
Rules for Writing Expressions: 1. Equilibrium partial pressures or concentrations of products (right side) appear in the numerator. 2. Equilibrium partial pressures or concentrations of reactants (left side) appear in the denominator. 3. Each partial pressure or concentration is raised to a power equal to its stoichiometric coefficient in the balanced equation. 4. The values of $K$ are dimensionless. 5. All values used must be equilibrium values.
Relationship between $K_p$ and $K_c$ : * The formula relating the two is: $K_p = K_c(RT)^{\Delta n_g}$ . * $\Delta n_g$ is the change in the number of moles of gas: $\Delta n_g = n_{\text{product}} - n_{\text{reactant}}$ . * $R$ is the gas law constant: $0.0821\,L \cdot atm / mol \cdot K$ . * $T$ is the temperature in Kelvin.

Equilibrium Constants in Heterogeneous and Aqueous Systems

Reactions Involving Solids: The concentrations of any solid reactants and products are not included in the equilibrium constant expression. * Example: Oxidation of yellow sulfur: $S(s) + O_2(g) \rightleftharpoons SO_2(g)$ . * Expression: $K_c = \frac{[SO_2]}{[O_2]}$ .
Reactions in Solution: For reactions in aqueous solutions, the concentration of liquid water ( $H_2O(l)$ ) is not included. * Example: Ammonia in water: $NH_3(aq) + H_2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)$ . * Expression: $K_c = \frac{[NH_4^+][OH^-]}{[NH_3]}$ .

Predicting Reaction Direction and the Reaction Quotient (Q)

Significance of the Magnitude of K: * If K > 1: The reaction is product-favored or forward-favored. Concentrations of products are greater than reactants at equilibrium. * If K < 1: The reaction is reactant-favored or backward-favored. Concentrations of reactants are greater than products at equilibrium.
Reaction Quotient (Q): Used when reactants and products are not at equilibrium. For $aA + bB \rightleftharpoons cC + dD$ : $Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}$
Predicting Direction with Q and K: * If Q < K: The system must convert reactants to products to reach equilibrium. The forward reaction is favored. * If Q > K: The system must convert products to reactants to reach equilibrium. The backward reaction is favored. * If $Q = K$ : The reaction mixture is already at equilibrium.

Le Chatelier's Principle

Core Principle: A change in any of the factors that determine equilibrium conditions causes the system to change in a manner that reduces or counteracts the effect of that change (stress).
Disturbance 1: Change in Concentration: * Add Reactant: System removes it; product concentration increases; shift forward. * Add Product: System removes it; reactant concentration increases; shift backward. * Remove Reactant: System increases it; product concentration decreases; shift backward. * Remove Product: System increases it; reactant concentration increases; shift forward.
Disturbance 2: Change in Pressure/Volume (Gaseous Systems): * Decrease Volume (Increase Pressure): Favors the side with the smaller number of gas molecules. * Increase Volume (Decrease Pressure): Favors the side with the larger number of gas molecules. * Equal Moles: If total reactant gas molecules equal product gas molecules, volume change has no effect.
Disturbance 3: Change in Temperature: * Endothermic Reaction ( $+\Delta H_{rxn}^o$ , heat is a reactant): * $T$ increases: Shift forward (forms more products). * $T$ decreases: Shift backward (forms more reactants). * Exothermic Reaction ( $-\Delta H_{rxn}^o$ , heat is a product): * $T$ increases: Shift backward (favors reactants). * $T$ decreases: Shift forward (favors products).

Acid-Base Definitions

Arrhenius Definition: * Acid: Increases $H^+$ concentration (produces $H^+$ or $H_3O^+$ ) in aqueous medium. * Base: Increases $OH^-$ concentration (produces $OH^-$ ) in aqueous medium.
Bronsted-Lowry Definition: * Acid: Proton ( $H^+$ ) donor. * Base: Proton ( $H^+$ ) acceptor. * Conjugate Acid-Base Pairs: Formed when an acid loses a proton or a base gains one (e.g., $NH_3/NH_4^+$ ).
Lewis Definition: Lewis Acid (electron pair acceptor) and Lewis Base (electron pair donor).

Acid-Base Properties of Water

Amphoterism: Water can act as either an acid or a base. * As a Base: $HBr(aq) + H_2O(l) \rightleftharpoons H_3O^+(aq) + Br^-(aq)$ . * As an Acid: $H_2O(l) + NH_3(aq) \rightleftharpoons NH_4^+(aq) + OH^-(aq)$ .

Acidity and the pH Scale

Logarithmic Scale: * $pH = -\log[H_3O^+]$ . * $pOH = -\log[OH^-]$ .
Neutrality at $25^{\circ}C$ : * $[H_3O^+] = 1.0 \times 10^{-7}\,M$ . * $pH = -\log(1.0 \times 10^{-7}) = 7.00$ .
Characterization: * Acidic: pH < 7.00. * Basic: pH > 7.00.
Relationship: $pH + pOH = 14$ (at $25^{\circ}C$ ).
Measurement Methods: * Electronic pH meter: Fast, accurate, and the preferred method. * Acid-base Indicator: Substances (like bromthymol blue or phenolphthalein) that change color over specific pH ranges. Cheap and convenient.

Quantitative Examples and Applications

Example 1: $K_c$ for Sulfur Trioxide Equilibrium: Reaction: $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$ . Conditions: $852\,K$ . Concentrations: $[SO_2] = 3.61 \times 10^{-3}\,mol/L$ , $[O_2] = 6.11 \times 10^{-4}\,mol/L$ , $[SO_3] = 1.01 \times 10^{-2}\,mol/L$ . Calculation: $K_c = \frac{[SO_3]^2}{[SO_2]^2[O_2]}$ .
Example 2: Methane Production: Reaction: $CO(g) + 3H_2(g) \rightleftharpoons CH_4(g) + H_2O(g)$ . Conditions: $1200\,K$ . Equilibrium moles in $1\,L$ : $0.30\,mol\,CO$ , $0.10\,mol\,H_2$ , $0.020\,mol\,H_2O$ , $0.40\,mol\,CH_4$ .
Example 3: Hydrofluoric Acid in Water: Reaction: $HF(aq) + H_2O(l) \rightleftharpoons F^-(aq) + H_3O^+(aq)$ . Equilibrium mass in $3.5\,L$ : $4.04\,g\,HF$ , $8.10\,g\,H_2O$ , $0.466\,g\,F^-$ , $0.159\,g\,H_3O^+$ .
Example 4: pH of Strong Base Solution: Find the pH of $0.0012\,M\,NaOH$ . Dissociation: $NaOH \rightarrow Na^+ + OH^-$ . $[OH^-] = 0.0012 \, M$ . $pOH = -\log(0.0012)$ . $pH = 14 - pOH$ .
Example 5: Diet Soda Concentration: If $pH = 4.32$ , then $[H_3O^+] = 10^{-4.32}$ .

Administrative and Assessment Tasks

Attendance: Starts at 2:10 PM.
Project: Work on branding for an alcohol brand; deadline is April 22, 2026 (Wednesday).
ALEKS Module: Module 5 Subtopic 1 is moved to today.
Assessment Questions: * Identify conjugate pairs for: $HCl + NH_3$ , $CH_3OH + HNO_3$ , $H_2SO_4 + H_2O$ . * Shift analysis for $2SO_3(g) \rightleftharpoons 2SO_2(g) + O_2(g)$ where $\Delta H^o = 2198\,kJ/mol$ . * Calculate $[H_3O^+]$ and $[OH^-]$ for $pH = 7.20$ and $pH = 4.60$ .