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4.1 Systematic Descriptive Chemistry of Main Group Elements (s- and p-Blocks)
PRC Chemist Licensure Examination Exam
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1 Chapter 1: Exam Overview, Chemistry Law (RA 10657), and Laboratory Safety
1.1 PRC Chemist Licensure Examination: Format, Schedule, Grading, and Passing Standards 1.2 Republic Act 10657 (Chemistry Profession Act) and Professional Ethics 1.3 Chemical Laboratory Safety, GHS Classification, Hazardous Waste Management, and Quality Assurance
2 Chapter 2: Inorganic Chemistry: Atomic Structure, Periodicity, and Chemical Bonding
2.1 Atoms, Ions, Compounds, Inorganic Nomenclature, and Stoichiometry 2.2 Quantum Numbers, Electronic Configurations, and Periodic Trends 2.3 Chemical Bonding Models: Lewis Structures, VSEPR Theory, and Molecular Polarity 2.4 Molecular Orbital Theory and Magnetochemistry of Diatomic Molecules
3 Chapter 3: Inorganic Chemistry: Coordination Compounds and Transition Metals
3.1 Coordination Chemistry: Nomenclature, Formulas, and Isomerism 3.2 Crystal Field Theory, Ligand Field Theory, d-Orbital Splitting, and Reaction Mechanisms 3.3 Electronic Absorption Spectra, Tanabe-Sugano Diagrams, and Magnetic Properties
4 Chapter 4: Inorganic Chemistry: Main Group, Reactivity, Solid State, Nuclear, and Applied Topics
4.1 Systematic Descriptive Chemistry of Main Group Elements (s- and p-Blocks) 4.2 Reactivity of Inorganic Compounds: Acid-Base Concepts, HSAB, and Redox Diagrams 4.3 Solid-State Chemistry: Crystal Systems, Unit Cells, and Band Theory 4.4 Bioinorganic Chemistry: Metalloproteins, Oxygen Carriers, and Metal Ion Toxicity 4.5 Organometallic Chemistry: 18-Electron Rule, Carbonyl Complexes, and Catalysis 4.6 Nuclear Chemistry: Stability, Decay, Transmutation, and Radioanalytical Methods 4.7 Industrial, Environmental, and Atmospheric Inorganic Chemistry and Advanced Materials
5 Chapter 5: Analytical Chemistry: Measurements, Statistics, Classical Wet Analysis, and Chemical Equilibria
5.1 Analytical Measurements: Apparatus, Units, Concentration, Sampling, and Sample Preparation 5.2 Analytical Data Evaluation: Errors, Uncertainty, Statistics, and Calibration 5.3 Gravimetric Analysis and Precipitation Equilibria ($K_{sp}$) 5.4 Neutralization Titrimetry, Polyprotic Systems, Buffers, and Alpha Fractions 5.5 Complexometric (EDTA), Redox, and Precipitation (Argentometric) Titrimetry
6 Chapter 6: Analytical Chemistry: Electroanalytical Methods and Separations
6.1 Potentiometry, Ion-Selective Electrodes, and Voltammetric Techniques 6.2 Analytical Separations: Solvent Extraction, SPE, Ion Exchange, Precipitation, Masking, and Electrodeposition 6.3 Fundamentals of Chromatography: Theoretical Plates, Resolution, and van Deemter Equation 6.4 Gas Chromatography (GC): Columns, Stationary Phases, Detectors, and Applications 6.5 High-Performance Liquid Chromatography (HPLC): Normal vs. Reversed Phase and Method Development
7 Chapter 7: Analytical Chemistry: Spectroscopic, Mass Spectrometric, and Other Instrumental Methods
7.1 Molecular UV-Vis Spectroscopy and Quantitative Beer-Lambert Law 7.2 Infrared (FTIR) and Raman Spectroscopy: Vibrational Modes and Instrumentation 7.3 Atomic Spectroscopy: Atomic Absorption (AAS) and Inductively Coupled Plasma (ICP-OES/MS) 7.4 Mass Spectrometry: Ionization Sources, Mass Analyzers, and Fragmentation Analysis 7.5 Other Instrumental Methods (XRF, Flame Emission, CE, SFC, Thermal Analysis, Electronics) and Method Selection
8 Chapter 8: Physical Chemistry: Gases, Thermodynamics, and Thermochemistry
8.1 Ideal and Real Gases and the Kinetic Molecular Theory 8.2 First Law of Thermodynamics: Heat, Work, Internal Energy, and Enthalpy 8.3 Second and Third Laws of Thermodynamics: Entropy, Carnot Engine, and Absolute Entropies 8.4 Gibbs and Helmholtz Free Energy, Spontaneity, and Fundamental Equations 8.5 Chemical Potential, Partial Molar Quantities, Fugacity, and Activity
9 Chapter 9: Physical Chemistry: Equilibrium, Phase Equilibria, Solutions, and Electrochemistry
9.1 Chemical Equilibrium: Equilibrium Constants, Le Chatelier's Principle, and the van 't Hoff Equation 9.2 Phase Rule, Phase Diagrams of One- and Two-Component Systems, and Clausius-Clapeyron Equation 9.3 Solutions: Raoult's and Henry's Laws, Colligative Properties, and Electrolytes 9.4 Electrochemistry: Galvanic Cells, Standard Potentials, and the Nernst Equation 9.5 Electrolyte Conductance, Ionic Mobility, Transport Numbers, and Concentration Cells
10 Chapter 10: Physical Chemistry: Kinetics, Surface Chemistry, and Quantum Mechanics
10.1 Reaction Rates, Rate Laws, and Integrated Rate Equations 10.2 Temperature Dependence of Rates: Arrhenius Equation, Collision Theory, and Transition State Theory 10.3 Reaction Mechanisms: Steady-State Approximation, Chain Reactions, and Catalysis 10.4 Surface Chemistry, Adsorption Isotherms, Colloids, and Macromolecular Solutions 10.5 Postulates of Quantum Mechanics, Operators, Particle in a Box, and Harmonic Oscillator 10.6 Atomic Spectra, the Hydrogen Atom, Many-Electron Atoms, and Term Symbols
11 Chapter 11: Organic Chemistry: Structure, Stereochemistry, and Hydrocarbons
11.1 Systematic IUPAC Nomenclature and Conformational Analysis of Alkanes and Cycloalkanes 11.2 Stereochemistry: Chirality, Enantiomers, Diastereomers, (R)/(S) Configuration, and Optical Activity 11.3 Alkenes and Alkynes: Addition Reactions, Markovnikov Rule, and Stereospecificity 11.4 Aromaticity: Hückel's Rule, Electrophilic Aromatic Substitution, and Directing Effects
12 Chapter 12: Organic Chemistry: Functional Groups, Mechanisms, Synthesis, and Structure Elucidation
12.1 Nucleophilic Aliphatic Substitution ($S_N1$, $S_N2$) and Elimination ($E_1$, $E_2$) Mechanisms 12.2 Alcohols, Phenols, Ethers, and Epoxides: Structure, Synthesis, and Reactivity 12.3 Carbonyl Compounds I: Aldehydes and Ketones, Nucleophilic Addition, and Oxidation/Reduction 12.4 Carbonyl Compounds II: Carboxylic Acids and Derivatives, Enolate Chemistry, and Condensations 12.5 Amines: Basicity, Synthesis, Reactions, and Arenediazonium Chemistry 12.6 Structure Elucidation: NMR Spectroscopy, Combined Spectral Problems, and Qualitative Organic Tests 12.7 Organic Synthesis Strategy, Protecting Groups, Rearrangements, and Pericyclic Reactions
13 Chapter 13: Biochemistry: Cells, Biomolecules, Enzymes, and Membranes
13.1 Cells, Organelles, Water, and Biological Acid-Base Buffers 13.2 Amino Acids, Peptides, and Hierarchical Protein Structure 13.3 Protein Purification and Biochemical Analysis of Proteins, Carbohydrates, and Lipids 13.4 Enzyme Nomenclature and Classification, Cofactors, Coenzymes, and Vitamin Precursors 13.5 Enzyme Kinetics: Michaelis-Menten Model, Lineweaver-Burk Analysis, and Enzyme Inhibition 13.6 Carbohydrates, Lipids, Biological Membranes, and Membrane Transport
14 Chapter 14: Biochemistry: Metabolism, Bioenergetics, Photosynthesis, and Molecular Genetics
14.1 Carbohydrate Catabolism and Anabolism: Glycolysis, Gluconeogenesis, Glycogen, and Pentose Phosphate Pathway 14.2 Citric Acid Cycle, Mitochondrial Electron Transport, Oxidative Phosphorylation, and $\beta$-Oxidation 14.3 Photosynthesis: Light Reactions, Photophosphorylation, and the Calvin Cycle 14.4 Lipolysis and Lipid Biosynthesis: Fatty Acids, Triacylglycerols, and Cholesterol 14.5 Nitrogen Metabolism: Nitrogen Fixation, Amino Acid Metabolism, and the Urea Cycle 14.6 Nucleic Acids, DNA Replication, Transcription, Translation, and Recombinant DNA Techniques 14.7 Regulation of Gene Expression, Mutation and Mutagens, DNA Repair, Carcinogenesis, and cDNA Cloning
4.1 Systematic Descriptive Chemistry of Main Group Elements (s- and p-Blocks)
Key Takeaways Explain This Topic AI
Diagonal relationships (Li-Mg, Be-Al, B-Si) stem from comparable charge densities (polarizing power) and similar electronegativities, giving rise to anomalous chemical behaviors distinct from heavier group congeners.
Alkaline earth metal solubility trends reflect competing lattice energy and hydration energy: Group 2 hydroxides become more soluble down the group (Mg(OH)2 < Ba(OH)2) because lattice energy plummets faster than hydration energy, whereas sulfates become less soluble (MgSO4 > BaSO4) because the large sulfate anion stabilizes lattice energy while cation hydration energy diminishes.
Group 13 electron deficiency is exemplified by diborane (B2H6), which features two 3-center 2-electron (3c-2e) bridging B-H-B bonds; boron trihalide Lewis acidity increases in the counterintuitive order BF3 < BCl3 < BBr3 < BI3 due to progressively inefficient pπ-pπ back-bonding from larger halogen p-orbitals into the empty boron 2p orbital.
Industrial p-block processes include the Haber-Bosch ammonia synthesis (Fe3O4/K2O/Al2O3 catalyst at 450 °C, 200 atm), Ostwald nitric acid oxidation (Pt/Rh gauze), and the Contact process for sulfuric acid (V2O5 catalyst oxidizing SO2 to SO3, followed by absorption into H2SO4 to yield oleum H2S2O7).
Noble gas and halogen chemistry is defined by xenon fluorides (XeF2 linear, XeF4 square planar, XeF6 fluxional distorted octahedral) and interhalogens (XX'n) governed by VSEPR geometries and polar covalent bonds.
Last updated: October 2026
4.1 Systematic Descriptive Chemistry of Main Group Elements (s- and p-Blocks)
Quick Answer: Main group descriptive chemistry explores periodic trends, oxidation states, and bonding motifs across the s s s - and p p p -blocks. Key phenomena tested on the PRC Chemist Licensure Examination include diagonal relationships ( L i – M g Li\text{--}Mg L i – M g , B e – A l Be\text{--}Al B e – A l , B – S i B\text{--}Si B – S i ) arising from comparable polarizing power and electronegativity; solubility inversions in Group 2 hydroxides (increasing solubility down the group) versus sulfates (decreasing solubility down the group); electron-deficient multicenter bonding in boranes ( 3 c – 2 e 3c\text{--}2e 3 c – 2 e bonds in B 2 H 6 B_2H_6 B 2 H 6 ); anomalous boron halide Lewis acidity ( B F 3 < B C l 3 < B B r 3 BF_3 < BCl_3 < BBr_3 B F 3 < BC l 3 < BB r 3 ); silicate network classifications based on [ S i O 4 ] 4 − [SiO_4]^{4-} [ S i O 4 ] 4 − sharing; and the synthesis and VSEPR geometries of xenon fluorides and interhalogens .
Alkali and Alkaline Earth Metals: Redox, Hydrides, and Diagonal Relationships
Group 1 (alkali metals, n s 1 ns^1 n s 1 ) and Group 2 (alkaline earth metals, n s 2 ns^2 n s 2 ) are electropositive, low-electronegativity elements that act as powerful reducing agents in aqueous and non-aqueous media. Their standard reduction potentials ( E ∘ E^\circ E ∘ ) reflect the interplay between sublimation enthalpy, ionization energy, and hydration enthalpy:
M + ( a q ) + e − → M ( s ) M^+(aq) + e^- \rightarrow M(s) M + ( a q ) + e − → M ( s )
Remarkably, lithium exhibits the most negative standard reduction potential among the alkali metals ( E ∘ = − 3.04 V E^\circ = -3.04\text{ V} E ∘ = − 3.04 V for L i + / L i Li^+/Li L i + / L i , compared to − 2.71 V -2.71\text{ V} − 2.71 V for N a + / N a Na^+/Na N a + / N a and − 2.93 V -2.93\text{ V} − 2.93 V for K + / K K^+/K K + / K ). Although lithium has the highest first ionization energy ( 520 kJ/mol 520\text{ kJ/mol} 520 kJ/mol ) in Group 1, its tiny ionic radius ( r = 0.76 A ˚ r = 0.76\text{ \AA} r = 0.76 A ˚ ) yields an immense hydration enthalpy ( Δ H hyd = − 519 kJ/mol \Delta H_\text{hyd} = -519\text{ kJ/mol} Δ H hyd = − 519 kJ/mol ), driving the overall free energy of aqueous reduction to be exceptionally favorable.
Flame Photometry and Electronic Emission
Characteristic flame colors arise from thermal excitation of valence electrons to higher atomic orbitals, followed by radiative de-excitation releasing visible photons:
- Element Flame Color Primary Emission Wavelengths Analytical Utility
- L i Li L i Carmine / Crimson Red 670.8 nm 670.8\text{ nm} 670.8 nm Quantitative atomic emission
N a Na N a Intense Yellow 589.0 nm , 589.6 nm 589.0\text{ nm}, 589.6\text{ nm} 589.0 nm , 589.6 nm ( D D D -lines) Ubiquitous interference in AAS/AES
K K K Lilac / Violet 766.5 nm , 769.9 nm 766.5\text{ nm}, 769.9\text{ nm} 766.5 nm , 769.9 nm Viewed through cobalt blue glass to filter N a Na N a
C a Ca C a Brick Red 622 nm , 554 nm 622\text{ nm}, 554\text{ nm} 622 nm , 554 nm (molecular bands) Diagnostic in wet qualitative analysis
S r Sr S r Crimson / Scarlet 460.7 nm , 606 nm 460.7\text{ nm}, 606\text{ nm} 460.7 nm , 606 nm Pyrotechnic red tracer formulations
B a Ba B a Apple / Pale Green 524.2 nm , 513.7 nm 524.2\text{ nm}, 513.7\text{ nm} 524.2 nm , 513.7 nm Diagnostic precipitation confirmation
Oxidation Products: Oxides, Peroxides, and Superoxides
When burned in excess dry atmospheric dioxygen ( O 2 O_2 O 2 ), alkali metals form distinctly different oxygen-containing salts governed by cation-anion lattice radius matching:
Normal Oxides ( O 2 − O^{2-} O 2 − ): Lithium forms primarily lithium oxide ( L i 2 O Li_2O L i 2 O ). The small L i + Li^+ L i + cation ( 0.76 A ˚ 0.76\text{ \AA} 0.76 A ˚ ) stabilizes the small, highly charged oxide dianion ( O 2 − O^{2-} O 2 − , radius 1.40 A ˚ 1.40\text{ \AA} 1.40 A ˚ ) via high crystal lattice energy.
Peroxides ( O 2 2 − O_2^{2-} O 2 2 − ): Sodium reacts to yield sodium peroxide ( N a 2 O 2 Na_2O_2 N a 2 O 2 ), containing the discrete peroxide dianion with a formal oxygen-oxygen single bond ( [ – O – O – ] 2 − [\text{--}O\text{--}O\text{--}]^{2-} [ – O – O – ] 2 − , bond order 1.0, diamagnetic).
Superoxides ( O 2 − O_2^- O 2 − ): Potassium, rubidium, and cesium react to form superoxides ( K O 2 , R b O 2 , C s O 2 KO_2, RbO_2, CsO_2 K O 2 , R b O 2 , C s O 2 ). The large cations ( K + = 1.38 A ˚ , C s + = 1.67 A ˚ K^+ = 1.38\text{ \AA}, Cs^+ = 1.67\text{ \AA} K + = 1.38 A ˚ , C s + = 1.67 A ˚ ) stabilize the large, singly charged superoxide radical anion ( [ O 2 ] − [O_2]^- [ O 2 ] − , bond order 1.5, paramagnetic with one unpaired electron in a π ∗ \pi^* π ∗ antibonding orbital). Potassium superoxide is utilized in scuba rebreathers and submarine life-support systems because it absorbs carbon dioxide while releasing breathable oxygen:
4 K O 2 ( s ) + 2 C O 2 ( g ) → 2 K 2 C O 3 ( s ) + 3 O 2 ( g ) 4\,KO_2(s) + 2\,CO_2(g) \rightarrow 2\,K_2CO_3(s) + 3\,O_2(g) 4 K O 2 ( s ) + 2 C O 2 ( g ) → 2 K 2 C O 3 ( s ) + 3 O 2 ( g )
Diagonal Relationships: L i – M g Li\text{--}Mg L i – M g and B e – A l Be\text{--}Al B e – A l
A diagonal relationship exists between period 2 elements and the period 3 elements located one group to their right. Across a period, ionic radius decreases and nuclear charge increases; down a group, ionic radius increases. Moving diagonally down and to the right gives ions of comparable polarizing power (charge density) and atoms of similar Pauling electronegativity:
L i Li L i and M g Mg M g Pair (Pauling electronegativities 0.98 and 1.31):
Both react directly with atmospheric nitrogen ( N 2 N_2 N 2 ) upon heating to form ionic nitrides: 6 L i + N 2 → 2 L i 3 N 6\,Li + N_2 \rightarrow 2\,Li_3N 6 L i + N 2 → 2 L i 3 N and 3 M g + N 2 → M g 3 N 2 3\,Mg + N_2 \rightarrow Mg_3N_2 3 M g + N 2 → M g 3 N 2 . Other alkali metals do not form nitrides under ambient heating.
Thermal decomposition of carbonates: L i 2 C O 3 Li_2CO_3 L i 2 C O 3 decomposes on strong heating to L i 2 O Li_2O L i 2 O and C O 2 CO_2 C O 2 , just as M g C O 3 MgCO_3 M g C O 3 decomposes readily at ∼ 540 ∘ C \sim 540\,^\circ\text{C} ∼ 540 ∘ C to M g O MgO M g O and C O 2 CO_2 C O 2 . By contrast, N a 2 C O 3 Na_2CO_3 N a 2 C O 3 and K 2 C O 3 K_2CO_3 K 2 C O 3 do not thermally decompose below 1000 ∘ C 1000\,^\circ\text{C} 1000 ∘ C .
Solubility anomalies: Fluorides, carbonates, and phosphates of both L i Li L i and M g Mg M g are sparingly soluble in water ( L i F , L i 2 C O 3 , M g F 2 , M g C O 3 LiF, Li_2CO_3, MgF_2, MgCO_3 L i F , L i 2 C O 3 , M g F 2 , M g C O 3 have low K s p K_{sp} K s p ), whereas corresponding salts of N a Na N a and K K K are highly soluble.
Organometallic behavior: Organolithium reagents ( R L i RLi R L i ) and Grignard reagents ( R M g X RMgX RM g X ) are both covalent, ether-soluble carbanion equivalents used extensively in carbon-carbon bond construction.
B e Be B e and A l Al A l Pair:
Both form amphoteric oxides and hydroxides: B e O BeO B e O and B e ( O H ) 2 Be(OH)_2 B e ( O H ) 2 dissolve in acid to form [ B e ( H 2 O ) 4 ] 2 + [Be(H_2O)_4]^{2+} [ B e ( H 2 O ) 4 ] 2 + and in concentrated base to yield tetrahydroxidoberyllate, [ B e ( O H ) 4 ] 2 − [Be(OH)_4]^{2-} [ B e ( O H ) 4 ] 2 − . Similarly, A l 2 O 3 Al_2O_3 A l 2 O 3 and A l ( O H ) 3 Al(OH)_3 A l ( O H ) 3 dissolve in strong base to yield aluminate, [ A l ( O H ) 4 ] − [Al(OH)_4]^- [ A l ( O H ) 4 ] − .
Both chlorides ( B e C l 2 BeCl_2 B e C l 2 and A l C l 3 AlCl_3 A lC l 3 ) are covalent Lewis acids. In the vapor phase, aluminum chloride forms a dative-bonded chlorine-bridged dimer, A l 2 C l 6 Al_2Cl_6 A l 2 C l 6 , while solid beryllium chloride forms a continuous edge-sharing polymeric chain, [ B e C l 2 ] n [BeCl_2]_n [ B e C l 2 ] n , with coordinate C l → B e Cl \rightarrow Be Cl → B e dative interactions.
Both metals passivate upon exposure to concentrated nitric acid ( H N O 3 HNO_3 H N O 3 ) due to the spontaneous generation of a dense, impermeable surface oxide film.
Group 2 Solubility Trends: Lattice Energy vs. Hydration Enthalpy
A classic question concerns the opposite solubility trends observed for alkaline earth metal hydroxides versus sulfates down Group 2 ( M g → C a → S r → B a Mg \rightarrow Ca \rightarrow Sr \rightarrow Ba M g → C a → S r → B a ):
Δ G diss ∘ = Δ H diss ∘ − T Δ S diss ∘ ≈ Δ H diss ∘ = Δ H hyd ∘ − Δ H lattice ∘ \Delta G_\text{diss}^\circ = \Delta H_\text{diss}^\circ - T\Delta S_\text{diss}^\circ \approx \Delta H_\text{diss}^\circ = \Delta H_\text{hyd}^\circ - \Delta H_\text{lattice}^\circ Δ G diss ∘ = Δ H diss ∘ − T Δ S diss ∘ ≈ Δ H diss ∘ = Δ H hyd ∘ − Δ H lattice ∘
Salt Family Solubility Trend Down Group 2 Thermodynamic Origin Analytical & Industrial Significance
Hydroxides ( M ( O H ) 2 M(OH)_2 M ( O H ) 2 ) Increases: M g ( O H ) 2 < C a ( O H ) 2 < S r ( O H ) 2 < B a ( O H ) 2 Mg(OH)_2 < Ca(OH)_2 < Sr(OH)_2 < Ba(OH)_2 M g ( O H ) 2 < C a ( O H ) 2 < S r ( O H ) 2 < B a ( O H ) 2 Lattice energy decreases faster than hydration energy M g ( O H ) 2 Mg(OH)_2 M g ( O H ) 2 (milk of magnesia, K s p ≈ 5.6 × 10 − 12 K_{sp} \approx 5.6 \times 10^{-12} K s p ≈ 5.6 × 1 0 − 12 ) is an insoluble antacid; B a ( O H ) 2 Ba(OH)_2 B a ( O H ) 2 is a soluble strong base
Sulfates ( M S O 4 MSO_4 MS O 4 ) Decreases: M g S O 4 > C a S O 4 > S r S O 4 > B a S O 4 MgSO_4 > CaSO_4 > SrSO_4 > BaSO_4 M g S O 4 > C a S O 4 > S r S O 4 > B a S O 4 Hydration energy decreases faster than lattice energy M g S O 4 MgSO_4 M g S O 4 (Epsom salt) is highly soluble; B a S O 4 BaSO_4 B a S O 4 ( K s p ≈ 1.1 × 10 − 10 K_{sp} \approx 1.1 \times 10^{-10} K s p ≈ 1.1 × 1 0 − 10 ) is insoluble, serving as an inert radiopaque gastrointestinal contrast agent
The Thermodynamic Rationale
Small Anion Regime ( O H − OH^- O H − ): The hydroxide ion is small ( r = 1.33 A ˚ r = 1.33\text{ \AA} r = 1.33 A ˚ ). In M ( O H ) 2 M(OH)_2 M ( O H ) 2 , the cation-anion interionic distance r 0 = r + + r − r_0 = r_+ + r_- r 0 = r + + r − changes substantially from M g 2 + Mg^{2+} M g 2 + ( r = 0.72 A ˚ r = 0.72\text{ \AA} r = 0.72 A ˚ , r 0 = 2.05 A ˚ r_0 = 2.05\text{ \AA} r 0 = 2.05 A ˚ ) to B a 2 + Ba^{2+} B a 2 + ( r = 1.35 A ˚ r = 1.35\text{ \AA} r = 1.35 A ˚ , r 0 = 2.68 A ˚ r_0 = 2.68\text{ \AA} r 0 = 2.68 A ˚ ). Because lattice energy scales inversely with interionic distance ( U ∝ 1 / r 0 U \propto 1/r_0 U ∝ 1/ r 0 ), the lattice energy drops precipitously down the group. This sharp drop in lattice energy outpaces the decrease in cation hydration enthalpy, rendering dissolution more exergonic ( Δ G diss ∘ \Delta G_\text{diss}^\circ Δ G diss ∘ becomes more negative) and solubility increases down the group.
Large Anion Regime ( S O 4 2 − SO_4^{2-} S O 4 2 − ): The sulfate anion is bulky ( r = 2.30 A ˚ r = 2.30\text{ \AA} r = 2.30 A ˚ ). The interionic distance r 0 r_0 r 0 increases only marginally from M g S O 4 MgSO_4 M g S O 4 ( 0.72 + 2.30 = 3.02 A ˚ 0.72 + 2.30 = 3.02\text{ \AA} 0.72 + 2.30 = 3.02 A ˚ ) to B a S O 4 BaSO_4 B a S O 4 ( 1.35 + 2.30 = 3.65 A ˚ 1.35 + 2.30 = 3.65\text{ \AA} 1.35 + 2.30 = 3.65 A ˚ ). Consequently, the lattice energy remains nearly constant down the group. However, the hydration enthalpy of the divalent cation plunges dramatically ( Δ H hyd \Delta H_\text{hyd} Δ H hyd of M g 2 + = − 1921 kJ/mol Mg^{2+} = -1921\text{ kJ/mol} M g 2 + = − 1921 kJ/mol vs. B a 2 + = − 1305 kJ/mol Ba^{2+} = -1305\text{ kJ/mol} B a 2 + = − 1305 kJ/mol ) due to the larger radius. Thus, the lattice energy cannot compensate for the lost hydration stabilization, making dissolution increasingly endergonic, and solubility decreases sharply down the group.
Group 13: Boron Hydrides, Wade's Rules, and Halide Lewis Acidity
Boron ( [ H e ] 2 s 2 2 p 1 [He]2s^2 2p^1 [ He ] 2 s 2 2 p 1 ) has four valence orbitals but only three valence electrons, resulting in pervasive electron deficiency in its monomeric trivalent compounds ( B X 3 BX_3 B X 3 ).
Multicenter Bonding in Diborane ( B 2 H 6 B_2H_6 B 2 H 6 )
Monomeric borane ( B H 3 BH_3 B H 3 ) contains only 6 valence electrons and spontaneously dimerizes to diborane ( B 2 H 6 B_2H_6 B 2 H 6 ). In diborane, each boron atom adopts approximately s p 3 sp^3 s p 3 hybridization:
Four terminal B – H B\text{--}H B – H bonds represent conventional two-center two-electron ( 2 c – 2 e 2c\text{--}2e 2 c – 2 e ) covalent bonds with normal bond lengths ( 1.19 A ˚ 1.19\text{ \AA} 1.19 A ˚ ).
Two bridging B – H – B B\text{--}H\text{--}B B – H – B bonds represent three-center two-electron ( 3 c – 2 e 3c\text{--}2e 3 c – 2 e ) "banana" bonds ( 1.33 A ˚ 1.33\text{ \AA} 1.33 A ˚ ). In each bridge, an s p 3 sp^3 s p 3 hybrid orbital from each boron atom overlaps with the spherical 1 s 1s 1 s orbital of a bridging hydrogen atom, generating three molecular orbitals: one bonding, one non-bonding, and one antibonding. The single pair of electrons populates the delocalized bonding orbital, holding all three nuclei together.
Polyhedral Borane Clusters and Wade's Rules (PSEPT)
Polyhedral Skeletal Electron Pair Theory (PSEPT, formulated by Kenneth Wade) predicts cluster geometries of higher boranes and carboranes based on the number of skeletal electron pairs (SEPs):
Total Valence Electrons = 3 ( number of B ) + 1 ( number of H ) + charge \text{Total Valence Electrons} = 3(\text{number of } B) + 1(\text{number of } H) + \text{charge} Total Valence Electrons = 3 ( number of B ) + 1 ( number of H ) + charge
SEPs = Total Valence Electrons − 2 n 2 , where n = number of vertices ( B atoms) \text{SEPs} = \frac{\text{Total Valence Electrons} - 2n}{2}, \quad \text{where } n = \text{number of vertices ($B$ atoms)} SEPs = 2 Total Valence Electrons − 2 n , where n = number of vertices ( B atoms)
Cluster Classification Formula Stems Skeletal Electron Pairs (SEPs) Structural Architecture
Closo- [ B n H n ] 2 − [B_n H_n]^{2-} [ B n H n ] 2 − n + 1 n + 1 n + 1 Closed, complete deltahedral cage with n n n vertices (e.g., [ B 12 H 12 ] 2 − [B_{12}H_{12}]^{2-} [ B 12 H 12 ] 2 − , icosahedral)
Nido- B n H n + 4 B_n H_{n+4} B n H n + 4 n + 2 n + 2 n + 2 "Nest-like" cage derived from an ( n + 1 ) (n+1) ( n + 1 ) -vertex deltahedron missing one vertex (e.g., B 5 H 9 B_5H_9 B 5 H 9 )
Arachno- B n H n + 6 B_n H_{n+6} B n H n + 6 n + 3 n + 3 n + 3 "Spiderweb-like" cage derived from an ( n + 2 ) (n+2) ( n + 2 ) -vertex deltahedron missing two vertices (e.g., B 4 H 10 B_4H_{10} B 4 H 10 )
Hypho- B n H n + 8 B_n H_{n+8} B n H n + 8 n + 4 n + 4 n + 4 Open cage derived from an ( n + 3 ) (n+3) ( n + 3 ) -vertex deltahedron missing three vertices
The Anomaly of Boron Trihalide Lewis Acidity
Electronegativity considerations predict that the electron density at boron should be lowest in B F 3 BF_3 B F 3 and highest in B I 3 BI_3 B I 3 , leading to the naive expectation that B F 3 BF_3 B F 3 is the strongest Lewis acid. However, experimental equilibrium constants for adduct formation with pyridine or ethers prove the exact opposite order:
B F 3 < B C l 3 < B B r 3 < B I 3 ( increasing Lewis acidity ) BF_3 < BCl_3 < BBr_3 < BI_3 \quad (\text{increasing Lewis acidity}) B F 3 < BC l 3 < BB r 3 < B I 3 ( increasing Lewis acidity )
Theoretical Origin ( p π – p π p\pi\text{--}p\pi p π – p π Back-Bonding): In planar B X 3 BX_3 B X 3 , boron has an unhybridized, vacant 2 p z 2p_z 2 p z orbital perpendicular to the molecular plane. Halogen atoms possess filled p p p orbitals of corresponding symmetry:
In B F 3 BF_3 B F 3 , the fluorine 2 p z 2p_z 2 p z orbitals match the size and energy of boron's 2 p z 2p_z 2 p z orbital, permitting maximum overlap and strong p π – p π p\pi\text{--}p\pi p π – p π π \pi π -back-bonding. This delocalizes halogen lone pairs into the boron center, stabilizing the monomer and partially satisfying its octet.
In B C l 3 , B B r 3 BCl_3, BBr_3 BC l 3 , BB r 3 , and B I 3 BI_3 B I 3 , the halogen valence p p p orbitals ( 3 p , 4 p , 5 p 3p, 4p, 5p 3 p , 4 p , 5 p ) are increasingly diffuse, poorly matched in energy and radial extension to boron's compact 2 p 2p 2 p orbital. Overlap drops drastically, weakening π \pi π -back-bonding.
When a Lewis base coordinates to B X 3 BX_3 B X 3 , the boron center rehybridizes from planar s p 2 sp^2 s p 2 to tetrahedral s p 3 sp^3 s p 3 , completely destroying the p π – p π p\pi\text{--}p\pi p π – p π system. The energetic penalty (loss of π \pi π -resonance energy) is largest for B F 3 BF_3 B F 3 and lowest for B B r 3 / B I 3 BBr_3/BI_3 BB r 3 / B I 3 , making B B r 3 BBr_3 BB r 3 and B I 3 BI_3 B I 3 vastly superior electron-pair acceptors.
- Group 14 and 15: Silicates, Industrial Processes, and Allotropes
- Structural Classification of Silicates
The fundamental building block of all mineral silicates is the tetrahedral orthosilicate unit, [ S i O 4 ] 4 − [SiO_4]^{4-} [ S i O 4 ] 4 − , with a central s p 3 sp^3 s p 3 -hybridized silicon atom bonded to four oxygen vertices. Silicates are classified by the number of shared bridging oxygen atoms per tetrahedron:
Silicate Class Basic Anion Unit Shared Oxygens / Tetrahedron Representative Mineral Examples
Nesosilicates (Orthosilicates) [ S i O 4 ] 4 − [SiO_4]^{4-} [ S i O 4 ] 4 − 0 Olivine ( M g 2 S i O 4 Mg_2SiO_4 M g 2 S i O 4 ), Zircon ( Z r S i O 4 ZrSiO_4 Z r S i O 4 ), Garnet
Sorosilicates (Pyrosilicates) [ S i 2 O 7 ] 6 − [Si_2O_7]^{6-} [ S i 2 O 7 ] 6 − 1 Thortveitite ( S c 2 S i 2 O 7 Sc_2Si_2O_7 S c 2 S i 2 O 7 ), Hemimorphite
Inosilicates (Single Chain) [ S i O 3 ] n 2 n − [SiO_3]_n^{2n-} [ S i O 3 ] n 2 n − 2 Pyroxenes (Diopside, C a M g ( S i O 3 ) 2 CaMg(SiO_3)_2 C a M g ( S i O 3 ) 2 , Enstatite)
Inosilicates (Double Chain) [ S i 4 O 11 ] n 6 n − [Si_4O_{11}]_n^{6n-} [ S i 4 O 11 ] n 6 n − Alternates 2 and 3 (avg 2.5) Amphiboles (Tremolite, Asbestos minerals)
Phyllosilicates (Sheet) [ S i 2 O 5 ] n 2 n − [Si_2O_5]_n^{2n-} [ S i 2 O 5 ] n 2 n − 3 Talc ( M g 3 S i 4 O 10 ( O H ) 2 Mg_3Si_4O_{10}(OH)_2 M g 3 S i 4 O 10 ( O H ) 2 ), Kaolinite clay, Micas
Tectosilicates (Framework) [ S i O 2 ] n [SiO_2]_n [ S i O 2 ] n 4 (all shared) Quartz ( S i O 2 SiO_2 S i O 2 ), Feldspars, Zeolites (molecular sieves)
Industrial Nitrogen and Phosphorus Chemistry
Haber-Bosch Process: N 2 ( g ) + 3 H 2 ( g ) ⇌ 2 N H 3 ( g ) Δ H ∘ = − 92.4 kJ/mol N_2(g) + 3\,H_2(g) \rightleftharpoons 2\,NH_3(g) \quad \Delta H^\circ = -92.4\text{ kJ/mol} N 2 ( g ) + 3 H 2 ( g ) ⇌ 2 N H 3 ( g ) Δ H ∘ = − 92.4 kJ/mol
Operating conditions: 400 – 500 ∘ C 400\text{--}500\,^\circ\text{C} 400 – 500 ∘ C , 150 – 250 atm 150\text{--}250\text{ atm} 150 – 250 atm .
Catalyst: Fused magnetite iron ( F e 3 O 4 Fe_3O_4 F e 3 O 4 ) promoted with K 2 O K_2O K 2 O and A l 2 O 3 Al_2O_3 A l 2 O 3 (structural promoter preventing sintering).
Ostwald Process for Nitric Acid:
Step 1 (Catalytic Oxidation): 4 N H 3 ( g ) + 5 O 2 ( g ) → P t / R h gauze , 850 ∘ C 4 N O ( g ) + 6 H 2 O ( g ) 4\,NH_3(g) + 5\,O_2(g) \xrightarrow{Pt/Rh\text{ gauze},\,850\,^\circ\text{C}} 4\,NO(g) + 6\,H_2O(g) 4 N H 3 ( g ) + 5 O 2 ( g ) Pt / R h gauze , 850 ∘ C 4 NO ( g ) + 6 H 2 O ( g ) (highly exothermic, contact time < 10 − 3 s < 10^{-3}\text{ s} < 1 0 − 3 s ).
Step 2 (Gas-phase Oxidation): 2 N O ( g ) + O 2 ( g ) → 2 N O 2 ( g ) 2\,NO(g) + O_2(g) \rightarrow 2\,NO_2(g) 2 NO ( g ) + O 2 ( g ) → 2 N O 2 ( g ) .
Step 3 (Aqueous Absorption): 3 N O 2 ( g ) + H 2 O ( l ) → 2 H N O 3 ( a q ) + N O ( g ) 3\,NO_2(g) + H_2O(l) \rightarrow 2\,HNO_3(aq) + NO(g) 3 N O 2 ( g ) + H 2 O ( l ) → 2 H N O 3 ( a q ) + NO ( g ) (recycled).
Phosphorus Allotropes and Oxyacids:
White Phosphorus ( P 4 P_4 P 4 ): Discrete tetrahedral molecules with acute 60 ∘ 60^\circ 6 0 ∘ P – P – P P\text{--}P\text{--}P P – P – P bond angles, exhibiting substantial angular strain. Pyrophoric in air (ignites spontaneously at 30 ∘ C 30\,^\circ\text{C} 30 ∘ C to P 4 O 10 P_4O_{10} P 4 O 10 ), highly toxic, stored under water.
Red Phosphorus: Amorphous polymeric network formed by heating white phosphorus to 250 ∘ C 250\,^\circ\text{C} 250 ∘ C in an inert atmosphere. Non-toxic, air-stable at room temperature; used in safety match striker strips.
Black Phosphorus: Puckered orthorhombic layers; thermodynamically most stable allotrope, conducting semiconductor.
Proticity of Phosphorus Oxyacids:
Hypophosphorous acid ( H 3 P O 2 H_3PO_2 H 3 P O 2 ): Monoprotic acid ( p K a ≈ 1.2 pK_a \approx 1.2 p K a ≈ 1.2 ). Structure contains one ionizable P – O H P\text{--}OH P – O H and two non-ionizable, strongly reducing P – H P\text{--}H P – H bonds ( [ H 2 P O ( O H ) ] [H_2PO(OH)] [ H 2 PO ( O H )] ).
Phosphorous acid ( H 3 P O 3 H_3PO_3 H 3 P O 3 ): Diprotic acid ( p K a 1 ≈ 1.3 , p K a 2 ≈ 6.7 pK_{a1} \approx 1.3, pK_{a2} \approx 6.7 p K a 1 ≈ 1.3 , p K a 2 ≈ 6.7 ). Contains two P – O H P\text{--}OH P – O H bonds and one reducing P – H P\text{--}H P – H bond ( [ H P O ( O H ) 2 ] [HPO(OH)_2] [ H PO ( O H ) 2 ] ).
Phosphoric acid ( H 3 P O 4 H_3PO_4 H 3 P O 4 ): Triprotic acid ( p K a 1 = 2.15 , p K a 2 = 7.20 , p K a 3 = 12.35 pK_{a1}=2.15, pK_{a2}=7.20, pK_{a3}=12.35 p K a 1 = 2.15 , p K a 2 = 7.20 , p K a 3 = 12.35 ). Contains three P – O H P\text{--}OH P – O H bonds and zero P – H P\text{--}H P – H bonds; not a reducing agent.
- Group 16, 17, and 18: Sulfur, Halogens, and Noble Gases
- Sulfuric Acid via the Contact Process
Combustion: S ( s ) + O 2 ( g ) → S O 2 ( g ) S(s) + O_2(g) \rightarrow SO_2(g) S ( s ) + O 2 ( g ) → S O 2 ( g ) .
Reversible catalytic oxidation: 2 S O 2 ( g ) + O 2 ( g ) ⇌ 2 S O 3 ( g ) 2\,SO_2(g) + O_2(g) \rightleftharpoons 2\,SO_3(g) 2 S O 2 ( g ) + O 2 ( g ) ⇌ 2 S O 3 ( g ) ( Δ H ∘ = − 198 kJ/mol \Delta H^\circ = -198\text{ kJ/mol} Δ H ∘ = − 198 kJ/mol , operated over vanadium(V) oxide, V 2 O 5 V_2O_5 V 2 O 5 on silica with potassium sulfate promoter at 450 ∘ C 450\,^\circ\text{C} 450 ∘ C ).
Absorption into existing concentrated H 2 S O 4 H_2SO_4 H 2 S O 4 : Direct hydration of S O 3 SO_3 S O 3 with water is violently exothermic and forms an unmanageable aerosol mist of acid droplets. Instead, S O 3 SO_3 S O 3 is absorbed into 98 % H 2 S O 4 98\%\text{ } H_2SO_4 98% H 2 S O 4 to produce oleum (fuming sulfuric acid, pyrosulfuric acid, H 2 S 2 O 7 H_2S_2O_7 H 2 S 2 O 7 ): S O 3 ( g ) + H 2 S O 4 ( l ) → H 2 S 2 O 7 ( l ) SO_3(g) + H_2SO_4(l) \rightarrow H_2S_2O_7(l) S O 3 ( g ) + H 2 S O 4 ( l ) → H 2 S 2 O 7 ( l )
Controlled dilution: H 2 S 2 O 7 ( l ) + H 2 O ( l ) → 2 H 2 S O 4 ( l ) H_2S_2O_7(l) + H_2O(l) \rightarrow 2\,H_2SO_4(l) H 2 S 2 O 7 ( l ) + H 2 O ( l ) → 2 H 2 S O 4 ( l ) .
Xenon Fluorides and Interhalogens
Since Neil Bartlett's 1962 discovery that P t F 6 PtF_6 Pt F 6 oxidizes elemental xenon (he formulated the orange-yellow product as X e + [ P t F 6 ] − Xe^+[PtF_6]^- X e + [ Pt F 6 ] − ; it is now understood to contain [ X e F ] + [XeF]^+ [ X e F ] + salts), noble gas compounds have occupied an essential place in advanced inorganic curricula. Xenon fluorides are synthesized by direct reaction of X e Xe X e and F 2 F_2 F 2 at controlled temperatures and stoichiometric ratios:
Species Valence Electrons / Electron Pairs Steric Number ( S N SN SN ) VSEPR Electron Geometry Molecular Shape Dipole Moment
X e F 2 XeF_2 X e F 2 8 + 2 ( 7 ) = 22 8 + 2(7) = 22 8 + 2 ( 7 ) = 22 (5 pairs) 5 (2 bonding, 3 lone pairs) Trigonal Bipyramidal Linear (lone pairs equatorial) μ = 0 \mu = 0 μ = 0 (centrosymmetric, D ∞ h D_{\infty h} D ∞ h )
X e F 4 XeF_4 X e F 4 8 + 4 ( 7 ) = 36 8 + 4(7) = 36 8 + 4 ( 7 ) = 36 (6 pairs) 6 (4 bonding, 2 lone pairs) Octahedral Square Planar (lone pairs axial) μ = 0 \mu = 0 μ = 0 (centrosymmetric, D 4 h D_{4h} D 4 h )
X e F 6 XeF_6 X e F 6 8 + 6 ( 7 ) = 50 8 + 6(7) = 50 8 + 6 ( 7 ) = 50 (7 pairs) 7 (6 bonding, 1 lone pair) Pentagonal Bipyramidal Distorted Octahedral (fluxional) μ > 0 \mu > 0 μ > 0 ( C 3 v C_{3v} C 3 v instantaneous)
X e O 3 XeO_3 X e O 3 8 + 3 ( 6 ) = 26 8 + 3(6) = 26 8 + 3 ( 6 ) = 26 (4 pairs) 4 (3 bonding, 1 lone pair) Tetrahedral Trigonal Pyramidal (explosive solid) μ > 0 \mu > 0 μ > 0 ( C 3 v C_{3v} C 3 v )
C l F 3 ClF_3 Cl F 3 7 + 3 ( 7 ) = 28 7 + 3(7) = 28 7 + 3 ( 7 ) = 28 (5 pairs) 5 (3 bonding, 2 lone pairs) Trigonal Bipyramidal T-shaped (lone pairs equatorial) μ > 0 \mu > 0 μ > 0 ( C 2 v C_{2v} C 2 v )
B r F 5 BrF_5 B r F 5 7 + 5 ( 7 ) = 42 7 + 5(7) = 42 7 + 5 ( 7 ) = 42 (6 pairs) 6 (5 bonding, 1 lone pair) Octahedral Square Pyramidal μ > 0 \mu > 0 μ > 0 ( C 4 v C_{4v} C 4 v )
I F 7 IF_7 I F 7 7 + 7 ( 7 ) = 56 7 + 7(7) = 56 7 + 7 ( 7 ) = 56 (7 pairs) 7 (7 bonding, 0 lone pairs) Pentagonal Bipyramidal Pentagonal Bipyramidal μ = 0 \mu = 0 μ = 0 ( D 5 h D_{5h} D 5 h )