Unit 1: Atomic Structure and Properties

Moles and Molar Mass

• Definition of the Mole: A mole represents \(6.022 \times 10^{23}\) representative particles, linking the microscopic world of atoms to measurable laboratory amounts. This constant, called Avogadro’s number, applies equally to atoms, molecules, ions, or formula units depending on the substance in question. Understanding the mole concept is essential for converting between particle counts, mass, and later, gas volumes at standard conditions.
• Molar Mass and Its Importance: The molar mass is the mass of one mole of a substance in \(\text{g·mol}^{-1}\), numerically equal to the average atomic or molecular mass in atomic mass units (u). It is calculated by summing the atomic masses from the periodic table for all atoms in a given formula, including polyatomic groups and any hydrate waters. This quantity is a fundamental conversion factor in nearly all stoichiometric and quantitative analyses.
• Hydrates and Molar Mass: For compounds containing water of hydration (e.g., \(\mathrm{CuSO_4\cdot 5H_2O}\)), the molar mass must include both the anhydrous salt and the water molecules. The number of waters per formula unit affects both the mass and stoichiometric calculations in reactions involving the hydrate. Ignoring these waters leads to significant errors in yield predictions and purity analysis.
• Dimensional Analysis in Mole Calculations: Multi-step mole conversions often link mass, moles, and particles, requiring careful unit tracking. For example, converting from grams to particles involves dividing by molar mass to get moles, then multiplying by Avogadro’s number. Writing each step with units ensures clarity and prevents calculation mistakes on exams.
• Experimental Determination of Molar Mass: Molar mass can be experimentally determined by measuring mass and the amount of substance via chemical reactions or gas laws. For instance, a reaction that produces a measurable gas volume can be used with the ideal gas law to back-calculate the molar mass of the reactant. Such methods are common in lab-based AP Chemistry free-response questions.
• Connection to Stoichiometry: The mole concept is the foundation of stoichiometry, allowing the scaling of balanced equations to predict reactant and product amounts. This connection means any uncertainty in molar mass propagates into reaction yield predictions. Mastery of mole calculations ensures accuracy in later topics such as titrations and limiting reactant problems.

Mass Spectrometry of Elements

• Principle of Mass Spectrometry: Mass spectrometry separates ions according to their mass-to-charge ratio (\(m/z\)) after ionization. A sample is vaporized, ionized, accelerated through an electric field, and deflected by a magnetic field, with lighter ions deflecting more. The resulting pattern on the detector provides a direct measure of isotope masses and their relative abundances.
• Isotopes and Mass Spectra: Isotopes are atoms of the same element with identical proton counts but different neutron numbers, resulting in different masses. In a mass spectrum, each isotope appears as a distinct peak, with the x-axis showing mass and the y-axis showing relative abundance. The relative height or area of a peak corresponds to how common that isotope is in nature.
• Calculating Average Atomic Mass: The average atomic mass is found by multiplying each isotope’s mass by its fractional abundance and summing the products. For example, if chlorine has 75.78% \(\mathrm{Cl-35}\) and 24.22% \(\mathrm{Cl-37}\), the average atomic mass is \((0.7578 \times 34.969) + (0.2422 \times 36.966) \approx 35.45\ \text{u}\). This value is the same as the molar mass in grams per mole used in stoichiometric calculations.
• Interpreting Spectral Patterns: The position of each peak reveals the isotope’s mass, while the spacing between peaks reflects neutron differences. Heavier isotopes produce peaks at higher \(m/z\) values, and peak clusters can indicate polyatomic ions or molecular fragments. Recognizing such patterns is important for both elemental identification and structural analysis.
• Applications in Chemistry: Mass spectrometry is used to verify purity, identify unknown elements, and determine isotopic composition in environmental and forensic samples. In AP Chemistry, students may be asked to deduce isotope abundances from a given spectrum or confirm electron configurations using PES data. Understanding this connection between isotopes and electronic structure strengthens cross-topic reasoning.
• Common Errors in Data Interpretation: Errors often occur when abundances are not converted from percentages to decimal fractions before calculations. Another common mistake is confusing the most abundant isotope with the average atomic mass value. Careful reading of axis labels and units prevents these misunderstandings.
• Connection to Periodic Trends: The relative abundance of isotopes can slightly influence an element’s reported average atomic mass across different sources. This can impact precise molar mass calculations, especially in high-precision analytical chemistry. Being aware of natural isotopic variation ensures better accuracy in advanced chemical applications.

Elemental Composition of Pure Substances

• Percent composition expresses the mass percentage of each element in a compound and is calculated from the compound’s formula and atomic masses. Because it is based on the ratio of masses, it remains constant for a pure compound regardless of sample size. This property is often used to verify a compound’s identity or detect impurities.
• Percent composition can be calculated experimentally by analyzing a sample’s mass before and after a reaction that isolates a particular element. For example, burning a hydrocarbon and measuring the mass of CO₂ produced allows the mass of carbon in the original compound to be determined. This method links laboratory data directly to theoretical composition.
• Empirical formulas represent the simplest whole-number ratio of atoms in a compound and can be determined from percent composition data. Converting the mass or percent of each element to moles and dividing by the smallest value yields this simplest ratio. This process is fundamental in chemical analysis, especially when molecular formulas are unknown.
• The molecular formula can be derived from the empirical formula if the compound’s molar mass is known. This is done by finding the ratio of the molecular mass to the empirical formula mass and multiplying the subscripts accordingly. This distinction explains why substances like glucose and formaldehyde can share the same empirical formula but have different properties.
• Hydrates require special treatment because water molecules are part of their structure and must be included in composition calculations. Heating a hydrate until it reaches a constant mass removes the water, allowing determination of the mole ratio between water and the salt. This process illustrates how physical changes can alter composition without changing the chemical identity of the anhydrous salt.
• Knowledge of elemental composition is essential in material science, pharmaceuticals, and environmental chemistry for quality control and compliance with regulations. For instance, monitoring the percent composition of active ingredients ensures drug safety and effectiveness. In AP Chemistry, understanding composition problems builds skills for later stoichiometry and limiting reactant calculations.

Composition of Mixtures

• Mixtures consist of two or more substances physically combined in variable proportions, meaning their composition can change from sample to sample. Because mixtures do not have fixed formulas, percent composition must be determined experimentally. The lack of a fixed ratio distinguishes mixtures from pure compounds.
• Percent by mass for a component in a mixture is calculated as \(\frac{\text{mass of component}}{\text{total mass of mixture}} \times 100\%\). This measurement allows comparison of mixture composition across samples or batches. Consistency in percent composition is important for product quality in industrial and laboratory settings.
• Analytical techniques such as filtration, distillation, or spectroscopy can separate or measure components of a mixture to determine composition. For example, filtering a sand-salt mixture allows the mass of each component to be determined and the percent by mass calculated. These methods connect physical properties like solubility or boiling point to composition analysis.
• In reaction-based analysis, a specific component of a mixture is made to react in a way that produces a measurable product. For example, titrating an acid-base mixture with a standard base allows calculation of the acid content. This approach uses stoichiometry to connect measured quantities to the mixture’s composition.
• Law of conservation of mass can help determine unknown amounts in mixtures when combined with partial mass data. If one component’s mass is measured, the other’s mass can be found by subtraction from the total. This principle ensures internal consistency in mixture problems.
• Mixture composition affects macroscopic properties such as melting point, density, and conductivity. For example, increasing salt concentration in water raises density and conductivity while lowering freezing point. These changes illustrate how composition directly influences material behavior.
• Understanding mixtures is important for solution chemistry, where molarity, molality, and percent composition are used interchangeably depending on context. Mastering these calculations early helps with later units involving colligative properties and reaction kinetics in solutions. In AP Chemistry, these concepts frequently appear in both multiple-choice and free-response formats.

Atomic Structure and Electron Configuration

Subatomic Particles and Atomic Number

• Atoms are composed of protons, neutrons, and electrons, each with unique properties and locations. Protons have a positive charge and are found in the nucleus, neutrons are neutral and also located in the nucleus, and electrons are negatively charged and occupy regions outside the nucleus. The strong nuclear force holds protons and neutrons together despite the repulsion between positively charged protons.
• The atomic number \(Z\) is the number of protons in the nucleus, which defines the identity of the element. A neutral atom has the same number of electrons as protons, while ions have unequal numbers of protons and electrons. Changing the number of protons changes the element itself, whereas changing neutrons creates isotopes and changing electrons forms ions.
• The mass number \(A\) is the sum of protons and neutrons, and isotopes of an element differ in neutron number but have identical chemical properties. The relative atomic mass reported on the periodic table is the weighted average of all isotopes based on natural abundance. This value is used in molar mass calculations and connects atomic structure to measurable laboratory quantities.

Historical Models and Key Experiments

• Dalton’s Atomic Theory (1803) proposed that matter is made of indivisible atoms, atoms of the same element are identical, and compounds form from whole-number ratios of atoms. While still foundational, later discoveries revealed that atoms are divisible into subatomic particles and that isotopes exist. Dalton’s emphasis on fixed ratios still underlies modern stoichiometry.
• Thomson’s cathode ray tube experiment (1897) discovered the electron, showing it had a negative charge and a much smaller mass than atoms. This led to the “plum pudding” model, where electrons were embedded in a positively charged sphere. The model could not explain nuclear properties or scattering results.
• Rutherford’s gold foil experiment (1911) demonstrated that atoms have a small, dense, positively charged nucleus where most of the mass is concentrated. Most alpha particles passed through foil, but a few deflected at large angles, proving that the positive charge is localized. This overturned the plum pudding model and introduced the nuclear model of the atom.
• Bohr’s model (1913) introduced quantized energy levels for electrons, explaining hydrogen’s emission spectrum. While it worked for hydrogen-like atoms, it failed for multi-electron systems. The idea of quantized energy transitions persisted into the modern quantum mechanical model.

Quantum Mechanical Model and Quantum Numbers

• The quantum mechanical model uses Schrödinger’s equation to describe electrons as probability distributions (orbitals) rather than fixed paths. Orbitals have specific shapes (s, p, d, f) and orientations in space. The model accounts for electron–electron repulsion, shielding, and penetration effects that Bohr’s model could not explain.
• Four quantum numbers describe each electron: \(n\) (principal quantum number) gives energy level and size of the orbital, \(\ell\) (angular momentum quantum number) determines shape, \(m_\ell\) (magnetic quantum number) describes orientation, and \(m_s\) (spin quantum number) specifies spin direction. No two electrons in an atom can have the same set of four quantum numbers (Pauli exclusion principle).
• Orbitals in the same energy level can have different shapes, affecting how close electrons can approach the nucleus. s-orbitals penetrate closer than p or d orbitals of the same \(n\), meaning s-electrons feel a higher effective nuclear charge. This penetration influences sublevel energies and explains irregularities in electron filling order.

Electron Configuration Rules

• The Aufbau principle states that electrons fill orbitals from lowest to highest energy, following a specific order determined by orbital energies. The order generally follows the periodic table structure: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc. This filling sequence minimizes the atom’s total energy.
• Hund’s rule states that electrons occupy degenerate orbitals singly before pairing, with parallel spins, to minimize electron–electron repulsion. This leads to the most stable arrangement of electrons in a given subshell. Failure to follow Hund’s rule results in a higher-energy configuration.
• The Pauli exclusion principle states that no two electrons in the same atom can have the same set of four quantum numbers. This means each orbital can hold at most two electrons with opposite spins. This rule explains the observed electron capacity of orbitals: 2 for s, 6 for p, 10 for d, and 14 for f.
• Some transition metals and heavier elements have irregular configurations due to extra stability of half-filled or fully filled d- and f-subshells. For example, chromium is \([\mathrm{Ar}]\,4s^1\,3d^5\) and copper is \([\mathrm{Ar}]\,4s^1\,3d^{10}\). Recognizing these exceptions is essential for accurate predictions of magnetic and chemical behavior.

Photoelectron Spectroscopy (PES) Connection

• PES measures the energy needed to remove electrons from specific orbitals, providing experimental evidence for electron configurations. Peaks in a PES spectrum correspond to subshells, with their height proportional to the number of electrons in that subshell. Binding energies increase for electrons closer to the nucleus, reflecting higher effective nuclear charge.
• PES data confirms orbital ordering and reveals differences between elements in the same period or group. Shifts in peak positions across a period indicate increasing effective nuclear charge. Understanding PES allows students to connect abstract electron configurations to experimental observations.

Connection to the Periodic Table

• The periodic table is arranged to reflect recurring patterns in electron configuration, with elements in the same group having the same valence electron configuration. This explains similarities in chemical behavior within a group. For main-group elements, the group number corresponds to the number of valence electrons.
• Elements are grouped into blocks (s, p, d, f) based on their highest-energy electron’s subshell. s-block elements have valence electrons in s-orbitals, p-block in p-orbitals, and so on. This block structure helps predict electron configurations and reactivity trends.
• Effective nuclear charge, shielding, and penetration explain periodic trends in atomic radius, ionization energy, and electron affinity. Across a period, increasing \(Z_{\text{eff}}\) pulls electrons closer, decreasing atomic radius and increasing ionization energy. Down a group, additional electron shells increase radius and reduce ionization energy despite higher nuclear charge.

Configuration Rules

Aufbau Principle

• The Aufbau principle states that electrons fill atomic orbitals in order of increasing energy, beginning with the lowest energy orbital available. This minimizes the total energy of the atom and produces the most stable electron configuration. The general filling order is determined by the periodic table and follows the sequence 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, and so on.
• Orbital energy ordering can be predicted using the \(n + \ell\) rule, where \(n\) is the principal quantum number and \(\ell\) is the angular momentum quantum number. Lower \(n + \ell\) values are filled first, and for equal \(n + \ell\) values, the orbital with the lower \(n\) is filled first. This explains why the 4s orbital fills before the 3d orbital in neutral atoms.
• There are notable exceptions to the Aufbau principle, particularly among transition metals and heavier elements, where electron–electron repulsion and subshell stability cause deviations. For example, chromium is \([\mathrm{Ar}]\,4s^1\,3d^5\) instead of \([\mathrm{Ar}]\,4s^2\,3d^4\), because half-filled d-subshells are more stable. Understanding these exceptions is essential for accurately predicting chemical and magnetic properties.

Hund’s Rule

• Hund’s rule states that when electrons occupy orbitals of equal energy (degenerate orbitals), they fill each orbital singly before pairing. This minimizes electron–electron repulsion and maximizes total spin, leading to a more stable arrangement. As a result, p, d, and f subshells fill with one electron in each orbital before any orbital receives a second electron.
• This rule is based on quantum mechanical exchange energy, which stabilizes arrangements with parallel spins in separate orbitals. By avoiding pairing until necessary, atoms reduce repulsive forces between electrons. For example, nitrogen’s configuration is \(1s^2\,2s^2\,2p^3\), with one electron in each of the three 2p orbitals, all with parallel spins.
• Violating Hund’s rule in electron configuration diagrams would increase repulsion and raise the atom’s energy. Such configurations are unstable and not observed in ground-state atoms. Correct application of Hund’s rule is critical when drawing orbital box diagrams for AP Chemistry problems.

Pauli Exclusion Principle

• The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers (\(n, \ell, m_\ell, m_s\)). This means that each orbital can hold a maximum of two electrons, and they must have opposite spins (\(m_s = +\frac{1}{2}\) and \(m_s = -\frac{1}{2}\)). This principle is fundamental to the structure of the periodic table and the arrangement of electrons in atoms.
• Opposite spins in the same orbital reduce electron–electron repulsion due to the formation of a more stable paired state. This explains why orbitals are drawn with arrows pointing in opposite directions when fully occupied. The Pauli principle applies to all fermions, including electrons, protons, and neutrons, but is most frequently discussed in the context of electron configurations.
• This principle ensures that electrons are distributed among available orbitals in a way that produces unique quantum states for each electron. Without the Pauli exclusion principle, all electrons would collapse into the lowest-energy orbital, eliminating the structure of the periodic table. Its enforcement is what makes the arrangement of elements and periodic trends possible.

Connections and Applications

• The Aufbau principle, Hund’s rule, and the Pauli exclusion principle work together to determine the ground-state electron configuration of an atom. Correct application of these rules allows prediction of chemical properties, reactivity, and magnetic behavior. For example, Hund’s rule explains why oxygen has two unpaired electrons and is paramagnetic.
• Exceptions to these rules often occur when atoms can achieve greater stability by having half-filled or fully filled subshells. Recognizing and explaining these exceptions is an important skill in AP Chemistry, especially for transition metals and heavier main-group elements. These deviations are tied to the interplay of subshell energy differences, electron–electron repulsion, and exchange stabilization.
• These rules also form the basis for understanding spectroscopy, as electron configurations determine possible electronic transitions. In photoelectron spectroscopy (PES), the energies of ejected electrons correspond directly to the orbital energies dictated by these principles. This provides experimental verification for the theoretical rules governing electron arrangements.

Photoelectron Spectroscopy (PES)

Principle of PES

• PES is an experimental technique used to measure the binding energies of electrons in atoms or molecules. High-energy photons, often in the ultraviolet or X-ray range, are directed at a sample, causing electrons to be ejected via the photoelectric effect. By measuring the kinetic energy of these electrons and knowing the photon energy, the binding energy can be calculated using \( E_{\text{bind}} = h\nu - E_k \).
• Binding energy reflects how strongly an electron is held by the nucleus, with electrons in inner shells having higher binding energies than those in outer shells. This relationship means PES can directly probe the arrangement of electrons in an atom. The deeper the electron, the more photon energy is needed to remove it.
• PES works under the assumption that each ejected electron’s measured energy corresponds to a single photon–electron interaction. This allows for a direct mapping between photon input and electron output, making PES a reliable tool for determining electron configurations experimentally.

Interpreting PES Spectra

• A PES spectrum plots the number of electrons detected (y-axis) against their binding energy (x-axis), often inverted so higher binding energies appear to the left. Each peak corresponds to a subshell, and the height of a peak is proportional to the number of electrons in that subshell. For example, a 2p peak will be three times taller than a 2s peak if fully occupied.
• Peaks with higher binding energy correspond to core electrons closer to the nucleus, while lower binding energy peaks represent valence electrons. Valence peaks are smaller in binding energy but are crucial in chemical bonding and reactivity. This distinction between core and valence peaks is a key analytical feature of PES.
• The ratio of peak areas can confirm subshell occupancy. For instance, in nitrogen’s spectrum, the 2p peak should be three times the area of the 2s peak, reflecting the 3:1 electron ratio. Discrepancies in ratios can indicate unusual electronic arrangements or ionization states.

PES and Electron Configuration

• PES provides direct evidence for electron configurations by showing how many electrons occupy each subshell and how strongly they are bound. This allows for experimental confirmation of the Aufbau principle, Hund’s rule, and the Pauli exclusion principle. For example, oxygen’s PES spectrum shows 1s, 2s, and 2p peaks in the expected order of binding energy.
• Comparing PES spectra across a period shows that binding energies for all electrons increase as nuclear charge increases. This shift to higher binding energies reflects greater effective nuclear charge (\( Z_{\text{eff}} \)) and reduced atomic radius. Such comparisons reinforce the connection between electron structure and periodic trends.
• PES can also reveal differences between atoms and ions. Removing electrons changes the electron–electron repulsion and effective nuclear charge experienced by the remaining electrons, shifting binding energies higher for cations and lower for anions.

Applications and Limitations

• PES is used in chemistry, materials science, and physics to investigate surface composition, oxidation states, and chemical bonding. In AP Chemistry, it is primarily used to deduce electron configurations and validate periodic trends. By analyzing spectra, students can connect theoretical models to real experimental data.
• While PES is powerful, it has limitations: it measures electrons from the surface layer of a sample, so bulk properties may differ. Additionally, overlapping peaks from subshells close in energy can make interpretation difficult without advanced resolution. Understanding these limitations is important for drawing accurate conclusions from PES data.
• PES complements other spectroscopic techniques by focusing on electron binding energies rather than energy transitions between levels. Together, these techniques provide a more complete picture of an atom’s or molecule’s electronic structure.

Periodic Trends

Effective Nuclear Charge and Shielding

• Effective nuclear charge (\( Z_{\text{eff}} \)) is the net positive charge experienced by an electron after accounting for the shielding effect of other electrons. Core electrons block some of the attraction from the nucleus, so valence electrons feel less than the full nuclear charge. Across a period, \( Z_{\text{eff}} \) increases because protons are added while shielding stays nearly constant, pulling electrons closer to the nucleus.
• Shielding occurs when inner electrons repel outer electrons, reducing the attraction between the nucleus and the valence electrons. Down a group, more electron shells increase shielding, which counteracts the increasing nuclear charge. This explains why outer electrons in larger atoms are held less tightly despite a higher number of protons.
• Penetration describes how close an electron in a given orbital can get to the nucleus. s-electrons penetrate more than p, which penetrate more than d, leading to differences in how orbitals are stabilized by the nucleus. This explains why the 4s orbital fills before 3d in the Aufbau order and why there are exceptions in transition metals.

Atomic and Ionic Radii

• Atomic radius decreases from left to right across a period because increasing \( Z_{\text{eff}} \) pulls the electron cloud inward without adding new shells. This results in smaller atoms even though more protons and electrons are present. This shrinkage contributes to higher ionization energies and stronger electron affinities across a period.
• Atomic radius increases down a group because new electron shells are added, increasing the distance between the nucleus and the outermost electrons. Increased shielding reduces the pull from the nucleus, allowing the electron cloud to expand. This explains why alkali metals are much larger than halogens in the same period.
• Cations are smaller than their parent atoms because losing electrons reduces electron–electron repulsion and sometimes removes an entire shell. Anions are larger than their parent atoms due to increased electron–electron repulsion and a decrease in \( Z_{\text{eff}} \) per electron. These size changes directly influence lattice energies and ionic bond strength.

Ionization Energy

• Ionization energy (IE) is the energy required to remove an electron from a gaseous atom or ion. First ionization energy generally increases across a period because \( Z_{\text{eff}} \) increases, making it harder to remove an electron. Down a group, IE decreases because added shells increase distance and shielding, reducing the nuclear pull on valence electrons.
• Large jumps in ionization energy occur when an electron is removed from a stable noble gas configuration or from a core shell. For example, magnesium’s first and second IEs are relatively low, but the third is much higher because it requires removing a core electron. Recognizing these jumps helps identify an element’s group from ionization data.
• Exceptions to the general IE trend occur when removing an electron relieves electron–electron repulsion or results in a more stable subshell. For example, boron’s IE is lower than beryllium’s because removing the p-electron in boron is easier than removing a paired s-electron in beryllium. These exceptions highlight the importance of subshell stability in periodic trends.

Electron Affinity

• Electron affinity (EA) is the energy change when a neutral atom gains an electron to form a negative ion. Across a period, EA generally becomes more negative because \( Z_{\text{eff}} \) increases and the added electron is more strongly attracted to the nucleus. This trend explains why halogens have some of the most negative electron affinities.
• Down a group, EA generally becomes less negative because the added electron enters an orbital farther from the nucleus, where attraction is weaker. Increased shielding also reduces the nucleus’s ability to attract the additional electron. However, there are irregularities due to subshell filling, such as in group 2 and group 15 elements, where adding an electron creates electron–electron repulsion.

Electronegativity

• Electronegativity measures the ability of an atom in a molecule to attract shared electrons in a bond. Across a period, electronegativity increases as \( Z_{\text{eff}} \) increases and atomic radius decreases, strengthening the pull on shared electrons. Down a group, electronegativity decreases as valence electrons are farther from the nucleus and shielding increases.
• Fluorine is the most electronegative element due to its high \( Z_{\text{eff}} \) and small atomic radius, while francium is the least electronegative. Electronegativity differences between atoms can predict bond type: large differences indicate ionic bonding, while small differences suggest covalent or metallic bonding. This property is essential in understanding polarity, reactivity, and intermolecular forces.

Connections Across Trends

• Periodic trends are interconnected because they all stem from changes in \( Z_{\text{eff}} \), shielding, and distance between electrons and the nucleus. For example, as atomic radius decreases across a period, ionization energy increases and electronegativity increases. Conversely, as radius increases down a group, ionization energy and electronegativity decrease while metallic character increases.
• Understanding these relationships allows for prediction of chemical behavior without memorizing individual values. For instance, knowing that cesium has a low ionization energy and low electronegativity explains why it reacts violently with water to form an ionic compound. These patterns make the periodic table a predictive tool rather than just a reference chart.

Valence Electrons and Ionic Compounds

Valence Electrons and Their Importance

• Valence electrons are the outermost electrons of an atom, located in the highest occupied principal energy level (\(n\)) for main-group elements. These electrons are responsible for chemical bonding, as they are the most weakly held and thus the easiest to share, gain, or lose. The number of valence electrons determines an element’s group number for main-group elements and largely dictates its reactivity.
• Elements in the same group of the periodic table have the same number of valence electrons, which explains their similar chemical properties. For example, all halogens have seven valence electrons and tend to form \(-1\) anions. This pattern of reactivity is one of the key organizing principles of the periodic table.
• For transition metals, valence electrons include both the outer \(ns\) electrons and any unfilled \((n-1)d\) electrons that participate in bonding. This leads to multiple possible oxidation states and a wider range of chemical behaviors. Understanding which electrons are available for bonding is critical when predicting ion charges for these elements.

Formation of Ions

• Atoms form ions to achieve a more stable electron configuration, often resembling the nearest noble gas. Metals tend to lose valence electrons to form cations, while nonmetals tend to gain electrons to form anions. This transfer of electrons results in ions with opposite charges, which are attracted to each other through electrostatic forces.
• When metals lose electrons, the resulting cations are smaller than the original atoms because the loss of an entire electron shell reduces size and electron–electron repulsion. In contrast, anions are larger than their parent atoms because adding electrons increases repulsion and slightly decreases the effective nuclear charge per electron. These size changes affect physical properties like density, melting point, and lattice energy.
• Some elements can form multiple cations with different charges, especially transition metals. For example, iron can form \(\mathrm{Fe^{2+}}\) or \(\mathrm{Fe^{3+}}\), depending on which electrons are lost. Roman numerals in compound names indicate the charge in these cases, such as iron(II) chloride vs. iron(III) chloride.

Ionic Bonding and Structure

• Ionic bonds form when cations and anions attract each other through Coulomb’s law, \(F = k\frac{q_1q_2}{r^2}\), where \(q_1\) and \(q_2\) are the charges and \(r\) is the distance between them. The strength of the attraction increases with higher charges and smaller ionic radii. This explains why \(\mathrm{MgO}\) has a much higher melting point than \(\mathrm{NaCl}\).
• Ionic compounds do not exist as individual molecules but as extended lattices of ions arranged to maximize attraction and minimize repulsion. This arrangement results in properties like high melting points, brittleness, and the inability to conduct electricity in solid form. However, they conduct well when molten or dissolved in water, because ions are free to move.
• The ratio of ions in an ionic compound reflects the need for overall charge neutrality. For example, in \(\mathrm{CaF_2}\), each \(\mathrm{Ca^{2+}}\) is balanced by two \(\mathrm{F^-}\) ions to produce a net charge of zero. Balancing these charges is a key step in writing correct ionic formulas.

Lattice Energy

• Lattice energy is the energy released when gaseous ions form an ionic solid, and it reflects the strength of the ionic bonds. According to Coulomb’s law, lattice energy increases with higher ionic charges and smaller ionic radii. This means \(\mathrm{Al_2O_3}\) has a much greater lattice energy than \(\mathrm{NaCl}\) due to the \(3+\) and \(2-\) charges involved.
• High lattice energies correlate with high melting points, low solubility in water, and greater hardness of ionic solids. Conversely, compounds with low lattice energies tend to be more soluble and have lower melting points. These trends help predict the physical properties of ionic substances without experimental data.
• Lattice energy can be estimated using the Born–Haber cycle, which combines ionization energies, electron affinities, and enthalpies of formation. In AP Chemistry, qualitative comparisons are more common, focusing on how charge and size influence bond strength. This connects lattice energy to other periodic trends like atomic radius and ionization energy.