General Chemistry Practice Exam Study Guide: Atomic Structure, Periodicity, Bonding, and Chemical Reactions

Atomic Structure and Electromagnetic Radiation

Electromagnetic Spectrum and Energy Calculations

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which differ in wavelength and frequency. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength.

• Key Equation: $E = h\nu$ where $E$ is energy, $h$ is Planck's constant, and $\nu$ is frequency.

• Wavelength and Frequency Relationship: $c = \lambda \nu$ where $c$ is the speed of light, $\lambda$ is wavelength, and $\nu$ is frequency.

• Photoelectric Effect: Electrons are ejected from a metal surface when light of sufficient frequency (threshold frequency) is incident.

• Threshold Frequency Table:

Metal	Threshold Frequency (Hz)
Cu	4.751 x 1014
Na	5.205 x 1014
Ag	6.627 x 1014
Fe	6.937 x 1014
Al	7.757 x 1014
Au	8.205 x 1014
Pb	8.625 x 1014
Zn	1.006 x 1015
Mg	1.122 x 1015
Ca	1.183 x 1015
K	1.382 x 1015

Example: Calculate the energy of a photon with frequency $1.5 \times 10^{15}$ Hz.

Solution: $E = (6.626 \times 10^{-34} \text{ J s}) \times (1.5 \times 10^{15} \text{ Hz}) = 9.94 \times 10^{-19} \text{ J}$

Quantum Numbers and Atomic Orbitals

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them:

• Principal quantum number ($n$): Indicates the energy level.

• Angular momentum quantum number ($l$): Indicates the shape of the orbital (s, p, d, f).

• Magnetic quantum number ($m_l$): Indicates the orientation of the orbital.

• Spin quantum number ($m_s$): Indicates the spin direction (+1/2 or -1/2).

Example: For $n=4$, $l=2$, $m_l=-2$, $m_s=+1/2$, the electron is in a 4d orbital.

Atomic Orbitals and Shapes

• s orbital: Spherical shape.

• p orbital: Dumbbell shape, three orientations.

• d orbital: Cloverleaf shape, five orientations.

Example: The $d_{x^2-y^2}$ orbital is a fourth-shell d orbital.

Electron Configurations and Periodicity

Electron Configurations

Electron configurations describe the arrangement of electrons in an atom. The Aufbau principle, Pauli exclusion principle, and Hund's rule govern electron filling.

• Aufbau Principle: Electrons fill the lowest energy orbitals first.

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

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

Example: Ground state electron configuration of Iodine (I): $[Kr] 4d^{10} 5s^2 5p^5$

Periodic Trends

• Atomic Radius: Decreases across a period, increases down a group.

• Ionization Energy: Increases across a period, decreases down a group.

• Electronegativity: Increases across a period, decreases down a group.

• Zeff (Effective Nuclear Charge): Increases across a period.

Example: Arrange Na, Ca, B, Cl, K in order of decreasing first ionization energy: Cl > B > Na > Ca > K

Chemical Bonding and Molecular Structure

Lewis Structures and Resonance

Lewis structures represent the arrangement of electrons in molecules. Resonance structures occur when more than one valid Lewis structure can be drawn.

• Octet Rule: Atoms tend to have eight electrons in their valence shell.

• Resonance: Delocalization of electrons among multiple structures.

Example: The most acceptable Lewis structure for N2O is one with a triple bond between N atoms and a single bond to O.

Bond Energy and Bond Length

• Bond Energy: Energy required to break a bond.

• Bond Length: Distance between nuclei of bonded atoms; shorter bonds are stronger.

Example: The C-H bond in CH3CH2CH2CH2Cl is most easily broken due to inductive effects.

Chemical Reactions and Stoichiometry

Types of Chemical Reactions

• Precipitation Reactions: Formation of an insoluble product.

• Redox Reactions: Transfer of electrons between species.

• Acid-Base Reactions: Transfer of protons (H+).

Example: Net ionic equation for Ca(OH)2 and Na3PO4:

$3Ca^{2+} (aq) + 2PO_4^{3-} (aq) \rightarrow Ca_3(PO_4)_2 (s)$

Stoichiometry and Solution Calculations

• Molarity ($M$): Moles of solute per liter of solution.

• Mass Calculations: Use molar mass and volume to determine required mass.

Example: To make 250 mL of 0.133 M KNO3 solution, use:

$\text{mass} = M \times V \times \text{molar mass}$

Thermochemistry and Lattice Energy

Born-Haber Cycle

The Born-Haber cycle is used to calculate lattice energy of ionic compounds using enthalpy changes for each step.

• Lattice Energy ($U$): Energy released when gaseous ions form an ionic solid.

Example: For the formation of Al2S3 from Al and S, sum the enthalpy changes for each step to find the lattice energy.

Additional info:

• Some questions involve advanced applications of periodic trends, quantum numbers, and molecular structure, which are foundational for understanding chemical reactivity and properties.

• Tables and diagrams have been interpreted and expanded for clarity.