General Chemistry Exam 3 Study Guide: Thermochemistry, Quantum Mechanics, and Periodic Properties

Thermochemistry

Energy, Work, and Heat

Thermochemistry studies the energy changes that occur during chemical reactions and changes of state. It focuses on the transfer of energy as heat and work between a system and its surroundings.

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

• Surroundings: Everything outside the system.

• Internal Energy (U): The total energy contained within a system.

• First Law of Thermodynamics: Energy cannot be created or destroyed, only transferred or transformed.

Key Equations:

• $\Delta U = q + w$ (Change in internal energy equals heat plus work)

• $q = m \cdot C_s \cdot \Delta T$ (Heat transfer, where $m$ is mass, $C_s$ is specific heat, $\Delta T$ is temperature change)

• $w = -P \Delta V$ (Work done by the system at constant pressure)

Example: If a system absorbs 50 J of heat and does 20 J of work on the surroundings, $\Delta U = 50\,J + (-20\,J) = 30\,J$.

Enthalpy and Calorimetry

Enthalpy ($H$) is a measure of the total energy of a thermodynamic system, including internal energy and the energy required to displace its environment.

• Enthalpy Change ($\Delta H$): The heat exchanged at constant pressure.

• Calorimetry: Experimental technique to measure heat changes in chemical reactions.

Key Equations:

• $\Delta H = \Delta U + P\Delta V$

• $q_{cal} = C_{cal} \cdot \Delta T$ (Heat absorbed by calorimeter)

Example: Mixing chemicals in a calorimeter and measuring temperature change to determine reaction enthalpy.

Standard Enthalpy of Formation and Hess's Law

The standard enthalpy of formation ($\Delta H_f^\circ$) is the enthalpy change when one mole of a compound is formed from its elements in their standard states.

• Hess's Law: The total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.

Key Equation:

• $\Delta H_{rxn}^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})$

Example: Calculating $\Delta H_{rxn}$ using tabulated $\Delta H_f^\circ$ values.

The Quantum-Mechanical Model of the Atom

Electromagnetic Radiation and Atomic Spectra

Atoms absorb and emit energy in the form of electromagnetic radiation, which includes visible light, ultraviolet, and infrared.

• Wavelength ($\lambda$): Distance between successive peaks of a wave.

• Frequency ($\nu$): Number of wave cycles per second.

• Speed of Light ($c$): $c = 3.00 \times 10^8$ m/s

Key Equations:

• $c = \lambda \nu$

• $E = h \nu$ (Energy of a photon, $h = 6.626 \times 10^{-34}$ J·s)

Example: Calculating the frequency of red light with $\lambda = 700$ nm: $\nu = \frac{c}{\lambda}$.

Atomic Orbitals and Quantum Numbers

Electrons in atoms occupy orbitals defined by quantum numbers, which describe their energy, shape, and orientation.

• Principal Quantum Number ($n$): Energy level (shell)

• Angular Momentum Quantum Number ($l$): Subshell (shape: s, p, d, f)

• Magnetic Quantum Number ($m_l$): Orientation of orbital

• Spin Quantum Number ($m_s$): Electron spin (+1/2 or -1/2)

Example: For a 4p electron: $n=4$, $l=1$, $m_l=-1,0,1$, $m_s=\pm1/2$.

Electron Configuration and the Periodic Table

Electron configurations describe the arrangement of electrons in an atom. The periodic table reflects these configurations, with elements grouped by similar valence electron arrangements.

• Aufbau Principle: Electrons fill lowest energy orbitals first.

• 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: Carbon: $1s^2 2s^2 2p^2$

Periodic Properties of the Elements

Trends in the Periodic Table

Periodic properties such as atomic radius, ionization energy, and electron affinity vary predictably across the periodic table due to changes in nuclear charge and electron configuration.

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

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

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

• Effective Nuclear Charge ($Z_{eff}$): The net positive charge experienced by valence electrons.

Example: Sodium (Na) has a larger atomic radius than chlorine (Cl) in the same period.

Useful Equations and Constants

• Avogadro's Number: $6.022 \times 10^{23}$ particles = 1 mol

• Planck's Constant: $h = 6.626 \times 10^{-34}$ J·s

• Speed of Light: $c = 3.00 \times 10^8$ m/s

Periodic Table Reference

The periodic table organizes elements by increasing atomic number and groups elements with similar chemical properties. It is essential for determining electron configurations, valence electrons, and periodic trends.

Sample Table: Quantum Numbers for Orbitals

Orbital Type	n	l	ml	ms
1s	1	0	0	+1/2, -1/2
2p	2	1	-1, 0, +1	+1/2, -1/2
3d	3	2	-2, -1, 0, +1, +2	+1/2, -1/2

Sample Table: Periodic Trends

Property	Across a Period	Down a Group
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Becomes more negative	Becomes less negative

Practice and Application

Practice problems and multiple-choice questions are essential for mastering these concepts. They test your understanding of thermochemistry, quantum mechanics, and periodic trends, and help you apply equations and principles to real chemical scenarios.

Additional info: These notes expand on the exam practice questions and review topics provided in the file, covering chapters 7 (Thermochemistry), 8 (Quantum-Mechanical Model of the Atom), and 9 (Periodic Properties of the Elements) as specified. Equations and tables are inferred and expanded for clarity and completeness.