General Chemistry: Thermodynamics, Atomic Structure, and Periodic Trends Study Guide

Thermodynamics

Heat, Work, and the First Law of Thermodynamics

Thermodynamics studies the flow of energy as heat (q) and work (w) in chemical systems. The First Law of Thermodynamics states that the internal energy change of a system (ΔU) is the sum of heat and work exchanged with the surroundings:

• ΔU = q + w

• Endothermic process: Heat is absorbed by the system (q > 0).

• Exothermic process: Heat is released by the system (q < 0).

Example: If heat flows into a system (arrow pointing toward the box), the process is endothermic.

Enthalpy and Hess's Law

Enthalpy (ΔH) is the heat change at constant pressure. Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps:

• ΔH_{reaction} = ΣΔH_{steps}

To determine ΔH for a reaction, manipulate and sum given equations so that their sum matches the target reaction.

Example: Calculating ΔH for Ag2O(s) + 2 HCl(aq) → 2 AgCl(s) + H2(g) + O2(g) using provided thermochemical equations.

Phase Changes and Calorimetry

Heat of vaporization (ΔHvap) is the energy required to convert a liquid to a gas at its boiling point. Calorimetry measures heat changes in physical and chemical processes.

• q = m × ΔHvap / Molar mass

Example: To evaporate 15.4 g of ethanol (C2H5OH) at its boiling point, calculate the moles and multiply by ΔHvap.

Specific Heat and Thermal Equilibrium

Specific heat capacity (c) is the amount of heat required to raise the temperature of 1 g of a substance by 1°C. When two substances at different temperatures are mixed, heat lost by the hotter substance equals heat gained by the cooler one:

• qlost + qgained = 0

• q = m × c × ΔT

Example: Given masses, initial and final temperatures, and one specific heat, solve for the unknown specific heat.

Energy, Power, and Unit Conversions

Power is the rate of energy transfer (1 watt = 1 joule/second). To find total energy over time:

• Energy (J) = Power (W) × Time (s)

• 1 kcal = 4184 J

Example: Calculate energy emitted by a lamp in kcal over 12 hours.

Relationship Between ΔH and ΔU

ΔH (enthalpy change) and ΔU (internal energy change) are related by:

• $ΔH = ΔU + Δn_gRT$

• Δng = change in moles of gas

ΔH > ΔU when the number of moles of gas increases (Δng > 0).

Energy Types: Kinetic and Potential

Kinetic vs. Potential Energy

• Kinetic energy: Energy due to motion of an object ($KE = \frac{1}{2}mv^2$)

• Potential energy: Energy due to position or arrangement (e.g., gravitational, chemical bonds)

High heat content does not always mean high temperature; temperature is a measure of average kinetic energy, while heat is total energy transfer.

Atomic Structure and Electron Configuration

Electron Configuration

Describes the arrangement of electrons in an atom. Follows the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Example: For Z = 108, the ground-state configuration is [Rn]7s25f146d6.

Valence Electrons

Valence electrons are those in the outermost shell, important for chemical bonding.

• Example: Vanadium (V): [Ar]4s23d3, 5 valence electrons.

Unpaired Electrons

Unpaired electrons are those not paired in an orbital, affecting magnetism and reactivity.

Element	Number of Unpaired Electrons
S	2
Co	3
Ca	0
Cl	1

Quantum Numbers and Subshells

Each electron is described by four quantum numbers. The spin quantum number (ms) can be +1/2 or -1/2. Subshells (s, p, d, f) have different capacities for electrons with the same spin.

• s: 1 orbital, 2 electrons

• p: 3 orbitals, 6 electrons

• d: 5 orbitals, 10 electrons

• f: 7 orbitals, 14 electrons

Each orbital can hold 2 electrons with opposite spins.

Radial Probability Distribution

Shows the probability of finding an electron at a certain distance from the nucleus. 1s orbitals have the highest electron density close to the nucleus, followed by 2s and 3s.

Periodic Trends and Properties

Isoelectronic Ions and Ionic Radii

Isoelectronic ions have the same number of electrons. For such ions, ionic radius decreases as nuclear charge increases.

Ion	Nuclear Charge (Z)	Relative Radius
Cl-	17	Largest
Br-	35	Intermediate
F-	9	Smallest

Metals, Nonmetals, and Metalloids

Classification is based on position in the periodic table and properties. Gallium (Ga) is a metal because it is below aluminum (a metal) in the periodic table.

Atomic Spectra and Quantum Experiments

Atomic Emission and Characteristic Wavelengths

Each element emits light at characteristic wavelengths when excited. The frequency and wavelength are related by $c = \lambda \nu$.

Element	Characteristic Wavelength (nm)
Cd	228.802
Cu	324.754
Fe	259.652
Hg	253.652

Quantum Mechanical Experiments

• Electron Diffraction: Demonstrates wave-like behavior of electrons.

• Heisenberg Uncertainty Principle: It is impossible to know both the position and momentum of an electron precisely at the same time.

• Photoelectric Effect: Electrons are ejected from a metal when it absorbs light of sufficient energy.

• Atomic Emission Spectra: Electrons occupy quantized energy levels; transitions between levels emit or absorb photons of specific energies.

Born-Haber Cycle and Lattice Energy

Born-Haber Cycle

The Born-Haber cycle is a thermochemical cycle used to analyze the steps in the formation of an ionic compound from its elements. It includes sublimation, ionization, bond dissociation, electron affinity, and lattice energy.

• $ΔH_f^\circ =$ sum of all steps (sublimation, ionization, etc.)

Example: Calculating $ΔH_f^\circ$ for CuCl2(s) using provided data and comparing stability with CuCl(s).

Shielding and Penetration

Slater's Rules and Shielding

Shielding describes how inner electrons reduce the effective nuclear charge felt by outer electrons. Penetration refers to how close an electron can get to the nucleus. s > p > d > f in terms of penetration.

• Adjustments to Slater's rules may be needed to account for differences in penetration between 3s, 3p, and 3d orbitals.

Summary Table: Key Formulas and Concepts

Concept	Formula
First Law of Thermodynamics	$ΔU = q + w$
Enthalpy Change	$ΔH = ΔU + Δn_gRT$
Heat (q)	$q = m c ΔT$
Energy (Joules)	$E = P \times t$
Frequency-Wavelength	$c = \lambda \nu$
Kinetic Energy	$KE = \frac{1}{2}mv^2$