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

Chapter 7: Thermochemistry

Introduction to Thermochemistry

Thermochemistry is the study of energy and heat changes that occur during chemical reactions and changes of state. It focuses on how energy is transferred between a system and its surroundings.

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

• Surroundings: Everything outside the system.

• Energy: The capacity to do work or produce heat.

Key Equations and Definitions

• First Law of Thermodynamics: Energy cannot be created or destroyed, only transferred. $\Delta E = q + w$ Where $\Delta E$ is the change in internal energy, $q$ is heat, and $w$ is work.

• Heat Capacity (C): The amount of heat required to raise the temperature of a substance by 1°C. $q = m \times C_s \times \Delta T$ Where $m$ is mass, $C_s$ is specific heat capacity, and $\Delta T$ is temperature change.

• Work Done by a Gas: $w = -P_{ext} \Delta V$ Where $P_{ext}$ is external pressure and $\Delta V$ is change in volume.

• Enthalpy (H): The heat content of a system at constant pressure. $\Delta H = \Delta E + P \Delta V$ At constant pressure, $\Delta H$ equals the heat exchanged.

• Standard Enthalpy of Reaction ($\Delta H_{rxn}$): $\Delta H_{rxn} = \sum n_p \Delta H_f^\circ (\text{products}) - \sum n_r \Delta H_f^\circ (\text{reactants})$ Where $n_p$ and $n_r$ are stoichiometric coefficients.

Calorimetry

Calorimetry is the measurement of heat flow. Two main types are constant-pressure (coffee-cup) and constant-volume (bomb) calorimetry.

• Constant-Pressure Calorimetry: Measures $q_p$, the heat at constant pressure.

• Constant-Volume Calorimetry: Measures $q_v$, the heat at constant volume.

Endothermic vs. Exothermic Reactions

• Endothermic: Absorbs heat ($\Delta H > 0$).

• Exothermic: Releases heat ($\Delta H < 0$).

Example: Calculating Heat Change

• Calculate $\Delta E$ for a system that gives off 23.0 kJ of heat and changes from 10.0 L to 17.0 L at 1.50 atm: $\Delta E = q + w$ $w = -P \Delta V = -1.50 \text{ atm} \times (17.0 - 10.0) \text{ L}$

Chapter 8: The Quantum-Mechanical Model of the Atom

Introduction to Quantum Mechanics

Quantum mechanics describes the behavior of electrons in atoms, focusing on their energy, position, and movement as both particles and waves.

• Electromagnetic Radiation: Energy transmitted through space as waves.

• Wavelength ($\lambda$): Distance between two consecutive 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

• Relationship between wavelength and frequency: $c = \lambda \nu$

• Energy of a photon: $E_{\text{photon}} = h \nu = \dfrac{hc}{\lambda}$ Where $h = 6.626 \times 10^{-34}$ J·s (Planck's constant).

• de Broglie Wavelength: $\lambda = \dfrac{h}{mv}$ Where $m$ is mass and $v$ is velocity.

• Energy change for electron transitions: $E_{\text{photon}} = -2.18 \times 10^{-18} \left( \dfrac{1}{n_{\text{final}}^2} - \dfrac{1}{n_{\text{initial}}^2} \right)$

Quantum Numbers

• Principal Quantum Number ($n$): Indicates energy level (shell).

• Angular Momentum Quantum Number ($l$): Indicates subshell (shape of orbital).

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

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

Electron Configuration and Orbitals

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

• 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: Calculating Wavelength and Frequency

• Calculate the frequency of red light ($\lambda = 710$ nm): $\nu = \dfrac{c}{\lambda}$

• Calculate the wavelength of an electron ($m = 9.11 \times 10^{-31}$ kg, $v = 3.22 \times 10^6$ m/s): $\lambda = \dfrac{h}{mv}$

Chapter 9: Periodic Properties of the Elements

Introduction to Periodic Properties

The periodic table organizes elements by increasing atomic number and recurring chemical properties. Periodic trends arise from electron configurations and effective nuclear charge.

• Groups: Vertical columns; elements have similar properties.

• Periods: Horizontal rows; properties change progressively.

Electron Configuration

• Writing Electron Configurations: Use the Aufbau principle and periodic table.

• Core Electrons: Inner electrons not involved in bonding.

• Valence Electrons: Outermost electrons involved in chemical reactions.

• Example: Ground state configuration for Sr: [Kr]5s2

Periodic Trends

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

• Ionization Energy: Energy required to remove an electron; increases across a period, decreases down a group.

• Electron Affinity: Energy change when an atom gains an electron.

Quantum Numbers and Electron Arrangement

• Each electron in an atom is described by a set of four quantum numbers ($n$, $l$, $m_l$, $m_s$).

• Example: For the last electron in O ([He]2s22p4), possible quantum numbers: $n=2$, $l=1$, $m_l=0$, $m_s=+1/2$.

Periodic Table Reference

The periodic table is essential for determining electron configurations, identifying element groups, and predicting chemical behavior.

Element	Electron Configuration	Valence Electrons	Group	Period
Oxygen (O)	1s22s22p4	6	16 (6A)	2
Strontium (Sr)	[Kr]5s2	2	2 (2A)	5
Carbon (C)	1s22s22p2	4	14 (4A)	2
Lead (Pb)	[Xe]4f145d106s26p2	4 (6p electrons)	14 (4A)	6

Additional info:

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

• Standard states for thermodynamic calculations: 1 atm for gases, 1 M for solutions, pure substances for solids/liquids.

• Periodic table image included for reference to element properties and electron configurations.