General Chemistry Exam Review: Thermodynamics, Quantum Theory, and Periodic Trends

Thermodynamics

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. This principle is foundational for understanding chemical reactions and energy changes.

• Equation: $\Delta U = q + w$

• q: Heat transferred to or from the system

• w: Work done on or by the system

• Energy Conservation: The total energy of the universe remains constant.

• Spontaneity: A spontaneous process cannot be predicted from $\Delta U$ alone.

Heat vs. Temperature

• Heat: Energy transferred between objects due to a temperature difference. Heat is a process, not a property contained within a substance.

• Temperature: A measure of the average kinetic energy of the particles in a substance.

• Key Point: Substances do not "contain heat"; heat refers to energy in transit.

System vs. Surroundings

• System: The part of the universe under study (e.g., the chemicals in a reaction vessel).

• Surroundings: Everything outside the system.

Sign Conventions

Process	Sign
Heat enters system	q > 0
Heat leaves system	q < 0
Work done ON system	w > 0
Work done BY system	w < 0

State Functions

• Depend only on the initial and final states of a system, not on the path taken.

• Examples: Internal energy (U), Enthalpy (H), Gibbs free energy (G), Entropy (S)

Entropy & Spontaneity

Spontaneous Processes

A spontaneous process occurs without continuous outside intervention. Note that spontaneity does not imply speed.

• Example: Ice melting at room temperature is spontaneous, but may occur slowly.

Second Law of Thermodynamics

• All spontaneous processes increase the entropy of the universe.

• Equation: $\Delta S_{\text{univ}} > 0$

• This is the true criterion for spontaneity.

Predicting Entropy Changes

• Entropy increases when:

  • Substance changes from solid → liquid → gas

  • Temperature increases

  • Number of particles increases (e.g., decomposition reactions)

  • Mixing occurs (e.g., dissolving salt in water)

Phase Change Entropy Equation

• Equation: $\Delta S = \frac{\Delta H}{T}$

• Used for calculating entropy changes during phase transitions (melting, boiling, etc.).

Gibbs Free Energy

Definition and Equation

Gibbs free energy ($\Delta G$) is a thermodynamic function used to predict the spontaneity of a process using system properties only.

• Equation: $\Delta G = \Delta H - T\Delta S$

Interpretation of $\Delta G$

$\Delta G$	Meaning
Negative	Spontaneous
Positive	Nonspontaneous
Zero	Equilibrium

• The relationship is derived from the entropy of the universe.

Temperature and Spontaneity

$\Delta H$	$\Delta S$	Spontaneity
-	+	Always spontaneous
+	-	Never spontaneous
-	-	Spontaneous at low T only
+	+	Spontaneous at high T only

• Temperature affects the $T\Delta S$ term, influencing spontaneity.

Quantum Theory

Nature of Light

• Light exhibits both wave-like and particle-like properties (wave-particle duality).

• This duality is essential for explaining atomic structure and electron behavior.

Key Equations

• Speed of light: $c = \lambda \nu$

• Photon energy: $E = h\nu = \frac{hc}{\lambda}$

• Frequency ($\nu$) is inversely related to wavelength ($\lambda$).

Emission Spectra

• Electrons emit photons when they transition between quantized energy levels.

• The energy difference between levels determines the energy (and color) of the photon emitted.

Atomic Orbitals and Quantum Numbers

• Orbitals are regions of space (probability clouds) where electrons are likely to be found.

• Quantum numbers describe the properties of these orbitals:

Symbol	Meaning
n	Principal quantum number (energy level)
l	Angular momentum quantum number (orbital shape)
m_l	Magnetic quantum number (orientation)
m_s	Spin quantum number (electron spin)

• Orbital shapes:

  • s: Spherical

  • p: Two lobes (dumbbell-shaped)

  • d: Clover-shaped

Nodes

• Total nodes: $n-1$

• Radial nodes: $n-l-1$

• Angular nodes: $l$

Electron Configuration Rules

1. Aufbau Principle: Fill lowest energy orbitals first.

2. Pauli Exclusion Principle: Maximum of 2 electrons per orbital, with opposite spins.

3. Hund's Rule: Fill degenerate orbitals singly before pairing electrons.

Periodic Trends

Effective Nuclear Charge

• Effective nuclear charge (Zeff) is the net positive charge experienced by valence electrons.

• It drives periodic trends by influencing atomic size and ionization energy.

Atomic Radius

• Increases down a group (more electron shells).

• Decreases across a period (increased Zeff pulls electrons closer).

Ion Size

• Cations are smaller than their parent atoms (loss of electrons reduces repulsion).

• Anions are larger than their parent atoms (gain of electrons increases repulsion).

Ionization Energy

• Energy required to remove an electron from a gaseous atom.

• Increases across a period (stronger attraction to nucleus).

• Decreases down a group (electrons are farther from nucleus).

Electron Affinity

• Energy released when an electron is added to a neutral atom.

• Varies across the periodic table; use your course's specific definition if required.

Most Tested Skills & Study Tips

• Identify processes with the largest entropy change.

• Determine when a reaction is spontaneous at high or low temperature using $\Delta H$ and $\Delta S$.

• Write correct electron configurations and apply quantum number rules.

• Compare photon energies, wavelengths, and frequencies.

• Rank ion sizes and predict periodic trends.

• Memorize the $\Delta G$ table for temperature dependence of spontaneity.

• Review entropy trends and periodic trends conceptually.

• Practice, do not memorize derivations.