General Chemistry II Final Exam Review – Key Concepts and Problem Types

Provided Equations and Constants

Essential Equations for General Chemistry

This section lists fundamental equations and constants commonly used in General Chemistry, including thermodynamics, kinetics, equilibrium, and electrochemistry.

• Clausius-Clapeyron Equation: $\ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$

• Gibbs Free Energy: $\Delta G = \Delta H - T\Delta S$

• Arrhenius Equation: $k = Ae^{-E_a/RT}$

• Equilibrium Constant: $K = \frac{[products]}{[reactants]}$ (for balanced reaction)

• Henderson-Hasselbalch Equation: $\mathrm{pH} = \mathrm{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Nernst Equation: $E_{cell} = E^\circ_{cell} - \frac{0.0592}{n}\log Q$

• First Law of Thermodynamics: $\Delta E = q + w$

• Rate Law (General): $\text{Rate} = k[A]^m[B]^n$

• Zero, First, Second Order Integrated Rate Laws:

  • Zero: $[A]_t = [A]_0 - kt$

  • First: $\ln[A]_t = \ln[A]_0 - kt$

  • Second: $\frac{1}{[A]_t} = \frac{1}{[A]_0} + kt$

Additional info: These equations are foundational for solving quantitative chemistry problems involving gases, solutions, kinetics, equilibrium, and thermodynamics.

Intermolecular Forces

Types and Identification of Intermolecular Forces

• Dispersion (London) Forces: Present in all molecules, especially nonpolar ones (e.g., CH4).

• Dipole-Dipole Forces: Occur between polar molecules (e.g., HCl, NH3).

• Hydrogen Bonding: Strong dipole-dipole interaction when H is bonded to N, O, or F (e.g., H2O, NH3).

• Ion-Ion Forces: Occur between ionic compounds (e.g., NaNO3).

Substance	Strongest Force
CH4	Dispersion
Cl2	Dispersion
KBr	Ion-Ion
NH3	Hydrogen Bonding
H2O	Hydrogen Bonding
HCl	Dipole-Dipole
NaNO3	Ion-Ion

Example: H2O exhibits hydrogen bonding, making it have higher boiling point than similar-sized molecules.

Phase Transitions

Understanding Phase Diagrams and Transitions

• Phase Diagram: Graphical representation of pressure (P) vs. temperature (T) showing regions of solid, liquid, and gas.

• Phase Transition: Change from one state of matter to another (e.g., melting, boiling, sublimation).

• Key Points: Moving from one region to another (e.g., A to C) corresponds to a specific phase change.

Example: Moving from solid to gas directly is called sublimation.

Colligative Properties

Boiling Point Elevation and Freezing Point Depression

• Colligative Properties: Depend on the number of solute particles, not their identity.

• Boiling Point Elevation: $\Delta T_b = i K_b m$

• Freezing Point Depression: $\Delta T_f = i K_f m$

• Van't Hoff Factor (i): Number of particles the solute dissociates into.

Example: 1.0 m NaCl (i = 2) will have a higher boiling point than 0.5 m KCl (i = 2), but the lowest boiling point will be the solution with the fewest particles.

Kinetics – Rate Laws

Writing Rate Laws for Elementary Reactions

• Elementary Reaction: Rate law can be written directly from the stoichiometry.

• General Form: For $aA + bB \rightarrow$ products, $\text{Rate} = k[A]^a[B]^b$

Example: For $2A + B \rightarrow C$, $\text{Rate} = k[A]^2[B]$

Kinetics – Mechanisms

Reaction Mechanisms and Rate-Determining Step

• Mechanism: Sequence of elementary steps that make up the overall reaction.

• Rate-Determining Step: The slowest step controls the overall rate law.

• Writing Rate Law: Express in terms of initial reactants; intermediates must be substituted out using pre-equilibrium or steady-state approximation.

Example: For a mechanism with a slow step involving CHCl3 and Cl, the rate law is $\text{Rate} = k[\text{CHCl}_3][\text{Cl}]$.

Kinetics – Reaction Barriers

Energy Profiles and Activation Energy

• Activation Energy ($E_a$): Minimum energy required for a reaction to proceed.

• Reaction Coordinate Diagram: Shows energy changes during a reaction; catalyzed reactions have lower $E_a$.

• Exothermic vs. Endothermic: Exothermic reactions release energy; endothermic absorb energy.

Example: The solid curve in an energy diagram is typically the uncatalyzed reaction; the dashed curve is the catalyzed reaction.

Equilibrium Constant Expressions

Writing $K_c$ and $K_p$ Expressions

• Equilibrium Constant ($K$): Ratio of product concentrations to reactant concentrations, each raised to the power of their coefficients.

• General Form: For $aA + bB \rightleftharpoons cC + dD$, $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Example: For $2CH_3Cl + Cl_2 \rightleftharpoons 2CH_2Cl_2 + H_2$, $K_c = \frac{[CH_2Cl_2]^2[H_2]}{[CH_3Cl]^2[Cl_2]}$

Le Chatelier's Principle

Predicting Shifts in Equilibrium

• Le Chatelier's Principle: If a system at equilibrium is disturbed, it will shift to counteract the disturbance.

• Factors Affecting Equilibrium: Concentration, pressure/volume, temperature, and catalysts.

• Endothermic vs. Exothermic: Increasing temperature favors endothermic direction; decreasing favors exothermic.

Example: Adding more reactant shifts equilibrium to the right (toward products).

Bronsted-Lowry Acids and Bases

Identifying Conjugate Acid-Base Pairs

• Bronsted-Lowry Acid: Proton (H+) donor.

• Bronsted-Lowry Base: Proton acceptor.

• Conjugate Base: Species formed when an acid loses a proton.

Species	Conjugate Base
H2S	HS-
CH4	CH3-
H3O+	H2O
CH3COOH	CH3COO-

Titration Curves

Acid-Base Titration and Equivalence Point

• Titration Curve: Plot of pH vs. volume of titrant added.

• Equivalence Point: Point where moles of acid equal moles of base.

• Weak Acid/Strong Base: Curve shows buffer region, sharp rise at equivalence.

Example: Titration of acetic acid with NaOH shows a buffer region before equivalence point.

Balancing Redox Reactions

Steps for Balancing Redox Equations

• Assign oxidation numbers to all elements.

• Write half-reactions for oxidation and reduction.

• Balance atoms and charges (add H2O, H+, OH- as needed).

• Combine half-reactions and balance electrons.

Example: $Br_2 + HCl \rightarrow BrCl + H_2O$ (balance using half-reactions).

Heat and Phase Transitions

Calculating Energy for Heating and Phase Changes

• q = mcΔT: Energy to change temperature within a phase.

• q = nΔH: Energy for phase change (fusion, vaporization).

• Sum energy for each step (heating, melting, vaporizing, etc.).

Example: To heat ice from -10°C to 90°C, calculate energy for warming ice, melting, warming water, vaporizing, etc.

Freezing/Melting Point Changes

Calculating Molality and Boiling Point Elevation

• Freezing Point Depression: $\Delta T_f = i K_f m$

• Boiling Point Elevation: $\Delta T_b = i K_b m$

• Molality (m): Moles of solute per kg of solvent.

Example: If a solution freezes at -1.2°C, use $K_f$ to find molality.

Determining Rate Laws

Using Experimental Data to Find Rate Law and Rate Constant

• Compare initial rates as concentrations change to determine reaction order with respect to each reactant.

• Plug values into rate law to solve for rate constant $k$.

Initial [A] (M)	Initial [B] (M)	Initial Rate (M/s)
0.10	0.10	0.71
0.20	0.10	1.40
0.20	0.05	0.35

Example: Doubling [A] doubles the rate, so first order in A; halving [B] halves the rate, so first order in B.

Arrhenius Equation

Temperature Dependence of Reaction Rates

• Arrhenius Equation: $k = Ae^{-E_a/RT}$

• Linear Form: $\ln k = -\frac{E_a}{R}\frac{1}{T} + \ln A$

• Activation Energy ($E_a$): Determined from slope of $\ln k$ vs. $1/T$ plot.

Example: Slope of $-2.00 \times 10^4$ K gives $E_a = 2.00 \times 10^4 \times R$.

Equilibrium Problems

Calculating Equilibrium Concentrations

• Set up ICE table (Initial, Change, Equilibrium).

• Use $K_c$ to solve for unknown concentrations at equilibrium.

Example: For $K_c = 3.1 \times 10^{-13}$, very little product forms; equilibrium lies far to the left.

Acid/Base pH Problems

Calculating pH of Weak Acid Solutions

• Set up equilibrium expression for weak acid dissociation.

• Use $K_a$ to solve for [H+], then $\mathrm{pH} = -\log[H^+]$.

Example: For 0.1 M HF, $K_a = 6.8 \times 10^{-4}$, solve for [H+].

Henderson-Hasselbalch Equation

Buffer Solutions and pH Calculation

• Buffer: Solution of weak acid and its conjugate base resists pH changes.

• Equation: $\mathrm{pH} = \mathrm{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

• Adding strong base converts some acid to conjugate base; recalculate concentrations and pH.

Example: Mixing CH3COOH and NaCH3COO forms an acetic acid/acetate buffer.

Solubility Products

Calculating Molar Solubility Using $K_{sp}$

• Solubility Product ($K_{sp}$): $K_{sp} = [Ag^+][Cl^-]$ for AgCl.

• In presence of common ion (e.g., NaCl), solubility decreases due to common ion effect.

Example: Calculate $s$ for AgCl in pure water and in 0.05 M NaCl.

ΔH, ΔS, and ΔG

Thermodynamic Quantities and Their Calculation

• ΔH (Enthalpy): Heat change at constant pressure.

• ΔS (Entropy): Measure of disorder.

• ΔG (Gibbs Free Energy): Determines spontaneity: $\Delta G = \Delta H - T\Delta S$

• Use standard values to calculate for reactions.

Example: For $2CO + O_2 \rightarrow 2CO_2$, use tabulated values to find $\Delta S^\circ$.

Nernst Equation

Electrochemical Cells and Cell Potentials

• Nernst Equation: $E_{cell} = E^\circ_{cell} - \frac{0.0592}{n}\log Q$

• Q: Reaction quotient; $n$ is number of electrons transferred.

• Use concentrations and standard potentials to calculate $E_{cell}$.

Example: For a cell with Cu and Sn electrodes, calculate $E_{cell}$ at nonstandard conditions.

Harder Nernst Equation Applications

Calculating Equilibrium Constants from Cell Potentials

• At equilibrium, $E_{cell} = 0$ and $Q = K$.

• Use $E^\circ_{cell}$ to solve for $K$:

$E^\circ_{cell} = \frac{0.0592}{n} \log K$

Example: For $AgCl_{(s)} + Cl^- \rightarrow AgCl_2^-$, use standard reduction potentials to find $K$.