General Chemistry Foundations

date2026-07-24tags:chem:

General chemistry supports every more advanced note in this wiki. Links include Electrochemistry, Corrosion, cyclic voltammetry, EIS, and OCP. General chemistry is also the layer where durable intuitions form. Most durable errors form there too.

The field fails when it treats itself as solved. The octet rule, electronegativity, and the mole are heuristics or accounting tricks. They are not laws. They break in transition metals. They break in hypervalent species. They break in relativistic effects. A working chemist spends most of their time in those broken regimes. Gold appears yellow because relativistic contraction of the 6s orbital shifts its absorption into the blue visible range. Mercury is liquid and cesium has a low melting point for the same reason. A student who treats metal color as a bulk optical property cannot predict these outcomes.

This note derives key concepts from first principles. It marks where each concept fails. It ends with a worked redox balancing example. The half reaction method is the direct prerequisite for every electrochemistry note. If you can balance this equation in acidic solution, you can read Corrosion and Electrochemical Thermodynamics without stopping.

$$\mathrm{Fe + 2H^+ \rightarrow Fe^{2+} + H_2}$$

General chemistry is the only layer most non chemists ever see. That layer determines what they think chemistry is. Engineers, biologists, and materials scientists carry the octet rule and electronegativity trends into domains where those concepts only partially work. The partial failures cause silent errors in cross discipline work.

Atomic structure

An atom has a nucleus surrounded by a probability distribution of electrons. The nucleus contains protons and neutrons. The nucleus carries almost all the mass. It contributes none of the chemistry. The electrons carry almost all the chemistry. They contribute minimal mass per atom.

Chemistry is a problem about the outer 10 to the minus 10 meters of matter. Nuclear physics is a problem about the inner 10 to the minus 15 meters. The two fields rarely interact. Radiochemistry and kinetic isotope effects are exceptions. Those effects let geochemists date rocks. For everything in this wiki, the nucleus is a point charge and a mass.

The three subatomic particles and their bookkeeping

Protons have a charge of +1 in units of e. Their mass is about 1.0073 u. The proton count defines the element. Change that count and you change the element. Chemistry preserves proton count.
Neutrons have a charge of 0. Their mass is about 1.0087 u. Neutrons stabilize the nucleus against Coulomb repulsion. The neutron count can vary for a given element. An isotope is an atom with a different neutron count.
Electrons have a charge of -1. Their mass is about 5.486 times 10 to the minus 4 u. This is roughly 1 over 1836 of a proton. Electrons determine the chemistry. Their mass is small enough to ignore in stoichiometric calculations. They are the entire substance of bonding, spectroscopy, and electrochemistry.

The atomic number Z equals the proton count. It also equals the electron count in a neutral atom. The mass number A equals the proton count plus the neutron count. The notation X with A over Z is redundant because Z fixes the symbol. It survives because it makes nuclear arithmetic clear.

Isotopes: same chemistry, different mass

Isotopes of an element share electron configuration. They therefore share chemistry in almost every way. They differ in mass. Mass matters only for inertia, vibrational zero point energy, or radioactive decay rates.

Kinetic isotope effects: a C H bond breaks faster than a C D bond. The C H stretching zero point energy is higher. This effect underlies much of mechanistic organic chemistry. It also underlies paleoclimate reconstruction from oxygen 18.
Radiometric dating: carbon 14 decays to nitrogen 14 with a half life of 5730 years. Potassium 40 decays to argon 40 with a half life of 1.25 billion years. Different isotopes date different timescales.

Isotopes are a footnote for the rest of this note. The chemistry here involves bonding, stoichiometry, and redox. That chemistry is electron driven and isotope blind to a first approximation.

Electron configuration

Electrons occupy atomic orbitals. These orbitals are the eigenfunctions of the hydrogenic Hamiltonian. They group by quantum numbers. The number n defines the shell. The symbol l defines the subshell: s, p, d, or f. The number m_l defines orientation. The number m_s defines spin at plus or minus one half. The three rules that fill these orbitals for multi electron atoms are heuristics, not laws. Each one breaks in a specific way.

Aufbau principle

Electrons fill the lowest energy available orbital first. This is the Aufbau principle. Aufbau means building up. This principle works approximately for neutral atoms in the first four periods. It depends on the claim that orbital energy ordering stays fixed regardless of occupancy. That claim is not always true.

The 4 s versus 3 d ordering in transition metals is the famous case. The 4 s orbital fills before 3 d in potassium and calcium. Once 3 d begins to fill, it drops below 4 s. Iron has the configuration with 3 d 6 and 4 s 2. The iron two plus ion has the configuration with 3 d 6 and no 4 s electrons. The 4 s electrons leave first even though they filled first. This is the most common Aufbau exception. The principle applies a static ordering to a dynamic problem. Orbital energies depend on occupancy. Memorizing a single fixed sequence fails for transition metals. Students need that sequence most for transition metals.

Hund's rule

Electrons occupy separate orbitals with parallel spins within a subshell. Pairing occurs only after all orbitals are singly occupied. The reason is Coulomb repulsion. Two electrons in the same orbital spend more time close together. They pay a pairing energy. Spreading electrons across degenerate orbitals lowers that repulsion.

Hund's rule explains why oxygen is paramagnetic. Oxygen has two unpaired electrons in the 2 p subshell. A naive Lewis structure cannot capture this. That limitation is the first hint that Lewis structures lose information about the underlying quantum state.

Pauli exclusion principle

No two electrons in an atom share all four quantum numbers. The total electronic wavefunction is antisymmetric under exchange. Two electrons with the same spin cannot share a spatial orbital.

This principle is not an empirical rule. It follows from the electron being a fermion. The deeper statement is the spin statistics theorem of quantum field theory. General chemistry textbooks present it as a prohibition. It is more accurately a symmetry constraint on allowed states.

When configurations fail

The Aufbau sequence fails for transition metals, lanthanides, and actinides. It also fails for neutral atoms with anomalously stable half filled or fully filled subshells. Chromium, molybdenum, copper, silver, and gold promote an s electron to reach d5 or d10 configurations.

Electron configurations are single configuration approximations to a multi determinant ground state. Open shell transition metal complexes require ligand field theory. Treat a configuration as a first guess, not as a fact.

The periodic table as a prediction engine

The periodic table is not a lookup chart. It is a compressed representation of the Aufbau filling pattern. Its predictive power comes entirely from that compression. Reading left to right within a period tracks increasing atomic number at fixed shell number. Reading top to bottom within a group tracks increasing shell number at fixed valence structure. These two axes give these trends:

Atomic radius decreases across a period. More protons pull the same shell tighter. The radius increases down a group because more shells add size.
Ionization energy increases across a period and decreases down a group. Local dips appear at the Group 2 to 13 and Group 15 to 16 transitions. The next electron enters a new subshell or pairs with an existing one. These dips show Hund's and Pauli's rules at the macroscopic scale.
Electronegativity increases across a period and decreases down a group. The trend holds loosely. See below for details.

The table predicts trends, not exact values. It works because the Schrodinger equation for a central Coulomb potential gives hydrogenic orbitals. Electron electron repulsion partially lifts their degeneracy. The shell structure survives. Remove that structure and the periodic table loses its organizing principle.

Electronegativity: a trend without a single definition

Electronegativity is the most useful quantity in introductory chemistry. It is also the least defined. At least four scales exist. They do not agree on all values.

Pauling scale derives from bond dissociation energies. It is unitless. Fluorine is fixed at 4.0.
Mulliken scale is the arithmetic mean of first ionization energy and electron affinity. It is physically transparent. It depends on the molecular basis set.
Allred Rochow scale uses effective nuclear charge over covalent radius squared. It gives a smooth periodic surface.
Allen scale is the weighted average valence electron ionization energy. It is the most spectroscopically direct. It is the least chemical in feel.

These scales correlate but disagree on noble gases and transition metals. Electronegativity is not a property of a single atom. It is a property of an atom in a bond. A single column in the periodic table is a pedagogical convenience. Use the trend. Do not quote a single number.

Chemical bonding

Bonding combines electrostatics and quantum mechanics. Every named bond type is a point on a continuum. The two extremes are pure ionic and pure covalent. Pure ionic means full electron transfer. The product is a pair of spherical ions held by Coulomb attraction. Pure covalent means perfect electron sharing between identical atoms. Real bonds sit between these extremes. The electronegativity difference and the availability of empty orbitals set the position on the continuum.

Ionic bonding

A large electronegativity difference, typically above 1.7 on the Pauling scale, drives electron transfer. That threshold has no theoretical justification. The resulting ions pack into a lattice. The lattice cohesion energy is the Madelung energy.

$$E_{\text{lattice}} = -\frac{N_A M z^+ z^- e^2}{4\pi\varepsilon_0 r_0}\left(1 - \frac{1}{n}\right)$$

M is the Madelung constant and depends on geometry. r0 is the nearest neighbor distance. n is the Born exponent. The lattice energy scales as one over r0. Small highly charged ions like MgO give refractory materials. Large singly charged ions like CsI give soft soluble salts. Ionic bonds are non directional. This explains why ionic crystals cleave along defined planes. It also explains why they form brittle high melting solids.

Covalent bonding

Covalent bonding shares electron density between nuclei. The simplest account comes from the variational solution of H2 plus. That system has two protons and one electron. The ground state has a bonding orbital. Its energy is lower than the isolated atom energy. The energy drop depends on overlap and nuclear nuclear repulsion.

The equilibrium bond length is where electronic stabilization cancels nuclear repulsion. Extend this to many electron molecules for molecular orbital theory. Restrict it to localized two center two electron bonds for Lewis or valence bond theory.

The octet rule compresses Lewis theory. Main group atoms tend to form bonds until they reach a noble gas valence of eight electrons. This works because a closed s and p shell is a local energy minimum. Most main group chemistry involves only s and p subshells. The rule fails in three ways:

1. Electron deficient species like BF3 and BeH2 cannot reach an octet with available electrons. These are strong Lewis acids. 2. Hypervalent species like PCl5, SF6, and IO4 minus have 10, 12, or 14 valence electrons. The classical d orbital explanation is largely wrong. The modern account uses 3 center 4 electron bonding with negligible d orbital contribution. Textbooks keep the d orbital explanation because it preserves the octet rule as an axiom. The actual hypervalent bonding in SF6 uses only s and p orbitals on sulfur. The sulfur 3 d orbitals are too high in energy to contribute. Preserving a simple rule required a wrong mechanism. The field has spent decades correcting this. 3. Transition metal complexes ignore the octet rule entirely. The 18 electron rule or ligand field theory applies instead.

Metallic bonding

Valence electrons delocalize over the entire metal lattice. The electron sea picture describes this. Bonding trades localization energy for kinetic energy lowering and Coulomb stabilization. Each electron spreads over about 10 to the 23 atoms. The consequences are the macroscopic properties of metals. These include electrical and thermal conductivity from delocalized carriers. They include malleability from non directional bonds that slip without breaking. They include metallic luster from collective electron oscillation, also called plasmon response.

The continuum and the bond type triangle

The van Arkel Ketelaar triangle makes the continuum explicit. Any bond is a mix of metallic, ionic, and covalent character. NaCl is ionic dominant. Diamond is covalent dominant. Sodium is metallic dominant. GaAs, InP, and many oxides sit in the middle. They are polar covalent with partial ionic and partial metallic character.

Material properties depend on where a compound sits on this triangle. Small composition changes can move a material across the triangle. Doping GaAs or ordering oxygen vacancies in SrTiO3 can change a conductor into an insulator.

Stoichiometry

Stoichiometry accounts for atoms. Its key trick is the mole. One mole equals 6.02214076 times 10 to the 23 entities. This number makes one mole of carbon 12 atoms weigh exactly 12 grams.

The mole is not a physical quantity. It is a counting unit like a dozen. It scales to make atomic masses come out in grams. The trick converts between the atomic world and the laboratory world. A single multiplication bridges one collision at a time with weighing on a balance.

The mole is a counting trick

The mole is the most confused quantity in introductory chemistry. It is not the amount of substance in a physical sense. It is a defined counting unit. When you write 2 mol H2, you mean 2 times 6.022 times 10 to the 23 molecules of H2. The Avogadro constant is now a defined exact quantity since the 2019 SI redefinition. The mole is pinned to a counting integer. This is a clean statement that the mole is a bookkeeping convention.

Balancing chemical equations

A balanced equation states that atoms are conserved. Follow these steps:

1. Write the skeleton with correct formulas. Never alter subscripts to balance. That changes the species. 2. Count each element on both sides. 3. Adjust stoichiometric coefficients to whole numbers until counts match. 4. Verify the balance. Check charge conservation if ions appear.

For propane combustion:

$$\mathrm{C_3H_8 + 5\,O_2 \rightarrow 3\,CO_2 + 4\,H_2O}$$

One mol of C3H8 weighs 44.10 g. Five mol of O2 weigh 160.0 g. Three mol of CO2 weigh 132.0 g. Four mol of H2O weigh 72.06 g. Total mass in is 204.1 g. Total mass out is 204.1 g. This is not an additional constraint. It follows from atom conservation. Each mol is a fixed count of atoms with fixed mass.

Limiting reagent and yield

One reagent runs out first in any real synthesis. That reagent is the limiting reagent. The theoretical yield comes from its mole count. Percent yield is actual yield divided by theoretical yield. The gap comes from side reactions, equilibrium, separation losses, and human error.

Carrying the limiting reagent calculation through every step is a transferable skill. It is mass balance accounting. The same skill appears in process engineering, pharmacokinetics, and life cycle analysis.

Balancing redox equations: the half reaction method

Redox reactions change oxidation states. Oxidation loses electrons. Reduction gains electrons. The underlying rule is that electrons are conserved. Every electron lost by the oxidized species is gained by the reduced species.

The half reaction method enforces this rule by construction:

1. Split the overall reaction into an oxidation half reaction and a reduction half reaction. 2. Balance all atoms except O and H in each half reaction. 3. Balance O by adding H2O. 4. Balance H by adding H+ for acidic solutions. For basic solutions add OH- instead, then neutralize excess H+ with OH- on both sides. 5. Balance charge by adding electrons to the more positive side. 6. Scale the two half reactions until the electron counts match. Use the lowest common multiple. 7. Add the half reactions. Cancel species appearing on both sides. Electrons must cancel completely. H2O, H+, and OH- often partially cancel.

The method is mechanical. It is the key mechanical skill for everything that follows. The half reactions are the electrode reactions in a galvanic cell. A Pourbaix diagram plots their equilibrium potentials versus pH. Cyclic voltammetry measures their kinetics in situ. Without fluency in the half reaction method, none of those notes will make sense.

Worked example: iron in acidic solution

Iron dissolution in acid is the canonical corrosion reaction. It is also a canonical redox balancing exercise. Corrosion is redox chemistry with an environmental electrolyte.

Skeleton:

$$\mathrm{Fe + H^+ \rightarrow Fe^{2+} + H_2}$$

Step 1: Split into half reactions. Iron oxidizes from zero to plus two. Hydrogen reduces from plus one to zero:

$$\text{ox:}\quad \mathrm{Fe \rightarrow Fe^{2+}}$$ $$\text{red:}\quad \mathrm{H^+ \rightarrow H_2}$$

Step 2: Balance non O and non H atoms. Iron is balanced with one atom on each side. Hydrogen needs two on the left. Place a 2 before H+:

$$\mathrm{2\,H^+ \rightarrow H_2}$$

Step 3: Balance O with H2O. No oxygen is present. Skip.

Step 4: Balance H with H+. Already balanced by the coefficient above.

Step 5: Balance charge with electrons.

Oxidation: Left charge is zero. Right charge is plus two. Add 2 electrons to the right: $\mathrm{Fe \rightarrow Fe^{2+} + 2\,e^-}$.
Reduction: Left charge is plus two. Right charge is zero. Add 2 electrons to the left: $\mathrm{2\,H^+ + 2\,e^- \rightarrow H_2}$.

Step 6: Equalize electrons. Both half reactions transfer 2 electrons. The lowest common multiple is 2. No scaling is needed.

Step 7: Add and cancel:

$$\mathrm{Fe + 2\,H^+ + 2\,e^- \rightarrow Fe^{2+} + 2\,e^- + H_2}$$

Cancel the electrons on both sides:

$$\boxed{\mathrm{Fe + 2\,H^+ \rightarrow Fe^{2+} + H_2}}$$

Unit check: 1 mol Fe weighs 55.85 g. It consumes 2 mol H+ weighing 2.016 g. It yields 1 mol Fe2+ weighing 55.85 g and 1 mol H2 weighing 2.016 g. Mass in is 57.87 g. Mass out is 57.87 g. Charge in is plus two. Charge out is plus two. Both conservations hold by construction.

The same reaction in basic solution

Iron corrodes in neutral or basic media. This is the regime of Corrosion and Pourbaix diagrams. Balance as if in acid first. Then add OH- to both sides equal to the H+ count. Combine H+ and OH- to form H2O. Cancel resulting H2O.

The acid step gives Fe + 2 H+ forming Fe2+ + H2. Adding 2 OH- to both sides gives:

$$\mathrm{Fe + 2\,H_2O \rightarrow Fe^{2+} + H_2 + 2\,OH^-}$$

This form appears in Pourbaix analysis. The oxidation half reaction becomes Fe + 2 OH- forming Fe(OH)2 + 2 e- if iron precipitates as hydroxide. Write either Fe2+ or Fe(OH)2. The choice depends on pH and the downstream electrochemistry question. That is why the half reaction method must be fluent and not memorized as a single form.

Why this matters downstream

The half reaction method is not a chapter end exercise. Each electrochemistry note starts from balanced half reactions:

Corrosion: the anodic dissolution pairs with cathodic oxygen reduction. The galvanic couple between them is the corrosion cell.
Electrochemistry: the three electrode cell measures one half reaction potential against a reference.
Electrochemical Thermodynamics: the Nernst equation comes from the mass action expression for a balanced half reaction.
Cyclic voltammetry: the peak current ratio depends on the electron count n. Mis count by two and the inferred diffusion coefficient is off by four.

The half reaction method is the prerequisite, not the application.

What general chemistry is actually for

General chemistry installs defaults. These are rules of thumb you apply before reaching for a refined model. The defaults are: atoms are conserved, electrons are conserved, charge is conserved, energy is conserved, and the periodic table predicts trends.

More sophisticated theories refine these defaults. Molecular orbital theory, ligand fields, statistical mechanics, and density functional theory all refine one default. They activate when the default fails quantitatively.

Treat the defaults as provisional, not as laws. The octet rule has three named exception classes. Electronegativity has four non equivalent definitions. The mole is a counting convention with no physical content. Aufbau is a static approximation to an occupancy dependent ordering. Internalize these as useful until the next theory level. The transition to transition metal chemistry, hypervalency, and relativistic effects then becomes a smooth refinement. Gold is yellow and mercury is liquid in that regime.