Comprehensive Study Guide: General Chemistry II Final Exam Topics

Solutions

Concentration and Molarity

Concentration describes the amount of solute dissolved in a given quantity of solvent or solution. Molarity (M) is the most common unit, defined as moles of solute per liter of solution.

• Formula: $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Example: To prepare 1.0 L of 0.5 M NaCl, dissolve 0.5 mol NaCl in enough water to make 1.0 L of solution.

• Particle Diagrams: Visual representations showing the relative number of solute and solvent particles in a solution.

Colligative Properties

Colligative properties depend on the number of solute particles, not their identity. Key properties include:

• Freezing Point Depression: $\Delta T_f = iK_f m$

• Boiling Point Elevation: $\Delta T_b = iK_b m$

• Vapor Pressure Lowering: Addition of solute lowers the vapor pressure of the solvent.

• Where: $i$ = van 't Hoff factor, $K_f$ and $K_b$ = constants, $m$ = molality.

• Example: Adding salt to ice lowers its freezing point, causing ice to melt at lower temperatures.

Enthalpy of Solution and Intermolecular Forces

The enthalpy of solution ($\Delta H_{soln}$) is the heat absorbed or released when a solute dissolves. Intermolecular forces (IMFs) such as hydrogen bonding, dipole-dipole, and London dispersion forces affect solubility and solution properties.

• Example: Ionic compounds dissolve in water due to ion-dipole interactions.

Kinetics

Rate of Reaction

The rate of reaction measures how quickly reactants are converted to products, typically as change in concentration over time.

• Formula: $\text{Rate} = -\frac{\Delta [A]}{\Delta t}$

• Example: If [A] decreases from 1.0 M to 0.5 M in 10 s, rate = 0.05 M/s.

Order of Reaction

The order of reaction indicates how the rate depends on reactant concentrations. Determined experimentally.

• Example: Rate law: $\text{Rate} = k[A]^m[B]^n$

Rate Constants

The rate constant (k) is a proportionality constant in the rate law, specific to a reaction at a given temperature.

• Units depend on overall reaction order.

Activation Energy and Reaction Progress Diagrams

Activation energy (E_a) is the minimum energy required for a reaction to occur. Reaction progress diagrams show energy changes during a reaction.

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

Equilibria

Equilibrium and Equilibrium Constants

Chemical equilibrium occurs when the rates of forward and reverse reactions are equal. The equilibrium constant (K) expresses the ratio of product to reactant concentrations at equilibrium.

• Expression: $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

ICE Tables

ICE (Initial, Change, Equilibrium) tables help calculate equilibrium concentrations.

• Example: For $A \rightleftharpoons B$, set up initial, change, and equilibrium rows to solve for unknowns.

Relationship Between $K_c$ and $K_p$

$K_c$ uses concentrations; $K_p$ uses partial pressures. For gases:

• $K_p = K_c(RT)^{\Delta n}$

• $\Delta n$ = change in moles of gas

Reaction Quotient (Q) and Le Chatelier’s Principle

The reaction quotient (Q) predicts the direction a reaction will proceed to reach equilibrium. Le Chatelier’s Principle states that a system at equilibrium responds to disturbances by shifting to counteract the change.

• Example: Increasing reactant concentration shifts equilibrium toward products.

Aqueous Equilibria

Acids, Bases, and Conjugates

Strong acids/bases dissociate completely; weak acids/bases only partially. Conjugate acid-base pairs differ by one proton.

• Example: $\text{NH}_3$ (base) and $\text{NH}_4^+$ (conjugate acid)

pH Calculations Using $K_a$ and $K_b$

$K_a$ and $K_b$ are equilibrium constants for acids and bases. pH is calculated as:

• $\text{pH} = -\log[H^+]$

• Use ICE tables and $K_a$/$K_b$ to solve for [H+] or [OH-].

Solubility Product ($K_{sp}$) and Molar Solubility

$K_{sp}$ describes the solubility of sparingly soluble salts. Molar solubility is the number of moles of solute that dissolve per liter.

• Example: For $\text{AgCl}$, $K_{sp} = [Ag^+][Cl^-]$

Thermodynamics

Entropy Changes

Entropy (S) measures disorder. Increases with more particles, higher temperature, or phase changes (solid → liquid → gas).

• Example: Dissolving salt in water increases entropy.

Gibbs Free Energy and Spontaneity

Gibbs free energy (G) predicts spontaneity:

• $\Delta G = \Delta H - T\Delta S$

• If $\Delta G < 0$, the process is spontaneous.

Relationship Between $\Delta G$ and $K$

• $\Delta G^\circ = -RT \ln K$

Nuclear Chemistry

Isotopes

Isotopes are atoms of the same element with different numbers of neutrons.

• Example: $^{12}C$, $^{13}C$, and $^{14}C$ are isotopes of carbon.

Types of Nuclear Changes

Includes alpha decay, beta decay, gamma emission, and nuclear fission/fusion.

• Example: $^{14}C \rightarrow ^{14}N + \beta^-$ (beta decay)

Half-Life Calculations

Half-life (t1/2) is the time for half of a radioactive sample to decay.

• $N = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}$

Oxidation-Reduction (Redox)

Balancing Redox Equations

Redox reactions involve electron transfer. Equations are balanced by separating into half-reactions and balancing mass and charge.

• Example: $\text{Zn} + \text{Cu}^{2+} \rightarrow \text{Zn}^{2+} + \text{Cu}$

Cell Voltage in Voltaic Cells

Voltaic (galvanic) cells generate electricity from spontaneous redox reactions. Cell voltage (Ecell) is calculated from standard reduction potentials.

• $E_{cell} = E_{cathode} - E_{anode}$

Nernst Equation

The Nernst equation calculates cell potential under nonstandard conditions:

• $E = E^\circ - \frac{0.0592}{n} \log Q$

Organic Compounds

Hydrocarbon Isotopes

Hydrocarbons are compounds of hydrogen and carbon. Isotopes refer to molecules with different isotopic forms of carbon or hydrogen.

• Example: Methane with $^{13}C$ instead of $^{12}C$.

Functional Groups

Functional groups are specific groups of atoms within molecules that determine chemical reactivity.

• Examples: Alcohol (-OH), carboxylic acid (-COOH), amine (-NH2), alkene (C=C), alkyne (C≡C).

• Sample Structure: The diagram provided shows a simple hydrocarbon chain, likely representing an alkane.

Additional info: This guide expands on the provided outline with definitions, formulas, and examples for each topic, ensuring a comprehensive review for a General Chemistry II final exam.