General Chemistry Exam 3 Study Guide: Atomic Structure, Periodic Trends, Bonding, and Solutions

Atomic Spectroscopy

Energy of Transitions in Hydrogen

Atomic spectroscopy involves the study of the interaction between electromagnetic radiation and atoms. In hydrogen, energy transitions occur when electrons move between quantized energy levels, emitting or absorbing photons of specific wavelengths.

• Key Point: The energy difference between levels determines the wavelength of light emitted or absorbed.

• Formula: The energy of a photon emitted during a transition is given by: $E = h\nu = \frac{hc}{\lambda}$

• Example: Calculating the wavelength of light produced when an electron transitions from n=3 to n=2 in hydrogen.

Quantum Numbers and Atomic Orbitals

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them. Each electron in an atom is defined by four quantum numbers: principal (n), angular momentum (l), magnetic (ml), and spin (ms).

• Principal Quantum Number (n): Indicates the energy level and size of the orbital.

• Angular Momentum Quantum Number (l): Defines the shape of the orbital (s, p, d, f).

• Magnetic Quantum Number (ml): Specifies the orientation of the orbital.

• Spin Quantum Number (ms): Indicates the spin direction (+1/2 or -1/2).

• Example: For n=2, l=1, ml=0, ms=+1/2, the electron is in a 2p orbital.

Atomic Orbitals

Atomic orbitals are regions in space where electrons are likely to be found. The shapes and orientations are determined by quantum numbers.

• s orbitals: Spherical shape.

• p orbitals: Dumbbell shape, oriented along x, y, or z axes.

• d orbitals: More complex shapes, often cloverleaf.

• Example: Sketching a 4d atomic orbital and its probability density function.

Coulomb's Law and Periodic Trends

Coulomb's Law

Coulomb's Law describes the electrostatic interaction between charged particles. In atoms, it helps explain trends in ionization energy and electron affinity.

• Formula: $E = \frac{kQ_1Q_2}{r}$

• Application: Explains why the ionization energy of sulfur is less than that of oxygen due to increased electron shielding and atomic radius.

Periodic Trends

Periodic trends are recurring patterns in element properties across the periodic table.

• Atomic Radius: Increases down a group, decreases across a period.

• Ionization Energy: Decreases down a group, increases across a period.

• Electron Affinity: Generally becomes more negative across a period.

• Metallic Character: Increases down a group, decreases across a period.

• Example: Sr has a larger radius than Br; Ca has a higher first ionization energy than K.

Electron Configurations and Orbital Diagrams

Electron Configurations

Electron configurations show the distribution of electrons among the orbitals of an atom.

• Aufbau Principle: Electrons fill orbitals from lowest to highest energy.

• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers.

• Example: Ni: [Ar] 4s2 3d8

Orbital Diagrams

Orbital diagrams visually represent electron configurations using boxes and arrows.

• Boxes: Represent orbitals.

• Arrows: Represent electrons and their spins.

• Example: Drawing the orbital diagram for Ni and Mn.

Lewis Structures and Molecular Geometry

Lewis Structures

Lewis structures depict the arrangement of valence electrons in molecules and ions. They are essential for predicting molecular geometry and reactivity.

• Steps: Count valence electrons, arrange atoms, distribute electrons to satisfy the octet rule.

• Formal Charge: Used to determine the most stable structure.

• Example: Drawing Lewis structures for H2O, CO2, PCl3, CH2O, N2, etc.

Molecular Geometry (VSEPR Theory)

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the shapes of molecules based on electron pair repulsion.

• Linear: 180° bond angle (e.g., CO2).

• Trigonal Planar: 120° bond angle (e.g., BF3).

• Tetrahedral: 109.5° bond angle (e.g., CH4).

• Example: Estimating bond angles and molecular geometry for given Lewis structures.

Bonding and Lattice Energy

Types of Bonds

Chemical bonds include ionic, covalent, and metallic bonds, each with distinct properties.

• Ionic Bonds: Formed by transfer of electrons between metals and nonmetals.

• Covalent Bonds: Formed by sharing electrons between nonmetals.

• Metallic Bonds: Delocalized electrons among metal atoms.

Lattice Energy

Lattice energy is the energy required to separate one mole of an ionic solid into gaseous ions. It is a measure of the strength of ionic bonds.

• Formula: $\Delta H_{lattice} = k \frac{Q_1Q_2}{r}$

• Born-Haber Cycle: Used to calculate lattice energy using enthalpy changes for formation, ionization, electron affinity, and sublimation.

• Example: Calculating lattice energy for KCl using tabulated enthalpy values.

Colligative Properties and Solutions

Colligative Properties

Colligative properties depend on the number of solute particles in a solution, not their identity. These include boiling point elevation, freezing point depression, and osmotic pressure.

• Boiling Point Elevation: $\Delta T_b = iK_bm$

• Freezing Point Depression: $\Delta T_f = iK_fm$

• Osmotic Pressure: $\Pi = iMRT$

• Example: Calculating the boiling point elevation when NaCl is added to water.

Solution Concentration

Concentration measures the amount of solute in a given amount of solvent or solution.

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Molality (m): $m = \frac{\text{moles of solute}}{\text{kg of solvent}}$

• Example: Calculating molarity and molality for a solution of NaCl.

Tables

Born-Haber Cycle Data Table

The following table is used to calculate lattice energy and enthalpy of formation using Hess's Law and the Born-Haber cycle.

Process	Energy (kJ/mol)
First Ionization Energy for K	419
Dissociation Energy for Cl2	242
Electron Affinity for Cl	-349
Enthalpy of Formation of KCl	-437

Additional info: The Born-Haber cycle combines these values to solve for the lattice energy of KCl.

Process	Energy (kJ/mol)
First Ionization Energy for Ca	590
Second Ionization Energy for Ca	1145
Dissociation Energy for Cl2	242
Electron Affinity for Cl	-349
Enthalpy of Formation of CaCl2	-795

Additional info: Use Hess's Law to combine these values and calculate the heat of formation for CaCl2.

Summary

This study guide covers key topics for General Chemistry Exam 3, including atomic structure, periodic trends, electron configurations, molecular geometry, bonding, lattice energy, and colligative properties. Practice problems and tables are provided to reinforce understanding and application of these concepts.