Gen Chem MCAT

Subatomic Particles

Particle	Charge	Mass	Location
Proton (p+)	Positive (+1)	~1 amu*	In the nucleus
Neutron (n0)	Neutral (0)	~1 amu*	In the nucleus
Electron (e-)	Negative (-1)	~0 amu (negligible)	Orbiting the nucleus

*amu = atomic mass unit. It’s the standard unit for measuring mass at the atomic scale.

Key Terms

• Atomic Number (Z): The number of protons in an atom's nucleus. This is the atom's identity card. If you change the number of protons, you change the element. For example, every hydrogen atom has 1 proton; every helium atom has 2.

• Mass Number (A): The total number of protons AND neutrons in the nucleus. It’s essentially the atom's total mass. Since electrons weigh almost nothing, they aren't counted.

Atomic Mass

• Atomic Mass: The mass of a single, specific atom. It's essentially equal to the mass number (protons + neutrons). A carbon-12 atom has an atomic mass of exactly 12 amu.

• Isotopes: Atoms of the same element (same number of protons) that have a different number of neutrons. They are twins with different weights.

  • Analogy: Think of a 2010 Honda Civic (the element). They can come in red, blue, or silver (the isotopes). They’re all Honda Civics, but look slightly different.

  • Example: Carbon has three main isotopes:

    • Carbon-12: 6 protons + 6 neutrons (the most common one)

    • Carbon-13: 6 protons + 7 neutrons

    • Carbon-14: 6 protons + 8 neutrons (this one is radioactive)

  • Hydrogen’s Special Names: Hydrogen's isotopes are so important they have unique names:

    • Protium: 1 proton, 0 neutrons (standard hydrogen)

    • Deuterium: 1 proton, 1 neutron

    • Tritium: 1 proton, 2 neutrons

Atomic Weight

• Atomic Weight: The weighted average mass of all the naturally occurring isotopes of an element. This is the number you see on the periodic table.

  • Why a decimal? Carbon's atomic weight is 12.011 amu. That's because it’s an average of mostly carbon-12 (mass 12) and a tiny bit of carbon-13 (mass 13). You won't find a single carbon atom with a mass of 12.011.

  • Key takeaway: The periodic table lists atomic weights, not atomic masses.

Rutherford to Bohr

• Rutherford’s Gold Foil Experiment (1911): Fired positively charged particles at a thin sheet of gold. Most passed right through, but a few bounced back dramatically. This led him to postulate that the atom is mostly empty space with a tiny, dense, positively charged core called the nucleus.

• Bohr Model (1913): Refined Rutherford’s model by fixing a major problem. He proposed that electrons orbit the nucleus at fixed distances, like planets around the sun. These orbits represent specific energy levels. An electron cannot exist between these levels.

• Planck & The Quantum: The energy difference between these fixed levels is called a quantum (plural: quanta). Max Planck first described this idea, which gave birth to quantum theory—the idea that energy on the atomic scale exists in discrete packets, not as a smooth, continuous flow.

• Quantization Explained: Think of a ladder. You can stand on rung 1 or rung 2, but you cannot float in the air halfway between them. Electron energy levels are quantized. The further the electron is from the nucleus, the higher its energy (like a rung higher up the ladder).

Absorption and Emission Spectra

• Absorption: To jump up a ladder rung (to an excited state), an electron must absorb a specific amount of energy that exactly matches the gap between the two levels.

• Emission: When it falls back down to its original rung (ground state), it releases that same exact amount of energy, often as light. Because every element has a unique set of energy levels, each element has a unique "fingerprint" of light it emits—its atomic emission spectrum.

Quantum Mechanical Model: The Modern View

The Bohr model was a good start, but it turned out to be wrong about one key thing: electrons don't travel in neat planetary orbits.

• Orbitals, Not Orbits: The quantum mechanical model posits that we can’t know an electron’s exact path. Instead, an orbital is a 3D region of space around the nucleus where there’s a high probability (usually 90%) of finding an electron. Think of it as a “cloud” of negative charge.

• Heisenberg Uncertainty Principle: This is the fundamental reason we talk about orbitals. It states you cannot simultaneously know both the exact position and the exact momentum (speed and direction) of an electron. If you measure its position precisely, you disturb its momentum, and vice-versa.

 The Four Quantum Numbers

These four numbers are like a complete mailing address for each electron in an atom.

1. Principal Quantum Number (n): The Shell (Energy Level)

   • Think: The city.

   • Values: 1, 2, 3, 4...

   • Describes the main energy level and relative size. Higher n means higher energy and a larger orbital (the electron is usually farther from the nucleus).

2. Azimuthal Quantum Number (l): The Subshell (Orbital Shape)

   • Think: The street within the city.

   • Values: 0 to (n-1).

   • Defines the shape of the orbital.

     • l = 0 → s subshell (spherical shape)

     • l = 1 → p subshell (dumbbell shape)

     • l = 2 → d subshell (cloverleaf shape)

     • l = 3 → f subshell (complex shape)

3. Magnetic Quantum Number (ml): The Orbital (Orientation in Space)

   • Think: The house number on the street.

   • Values: -l to +l, including 0.

   • Specifies the exact orbital within a subshell. For example, the p subshell (l=1) has three possible ml values: -1, 0, +1. These correspond to the px, py, and pz orbitals that align along the x, y, and z axes.

4. Spin Quantum Number (ms): The Electron’s Spin

   • Think: The apartment occupant (each orbital can hold max two occupants, and they must be different).

   • Values: +½ or -½ (often drawn as an up or down arrow: ↑ and ↓).

   • An electron behaves like a tiny spinning magnet, creating a spin orientation.

Electron Configuration

• Spectroscopic Notation: Uses the n and l values (number and letter). A superscript tells you how many electrons are in that subshell.

  • Example: Magnesium (Mg)

    • Magnesium has 12 electrons.

    • Configuration: 1s² 2s² 2p⁶ 3s²

    • Translation:

      • 1s²: 2 electrons in the first shell's s subshell.

      • 2s²: 2 electrons in the second shell's s subshell.

      • 2p⁶: 6 electrons in the second shell's p subshell.

      • 3s²: 2 electrons in the third shell's s subshell.

    • Valence Electrons: The two electrons in the outermost shell (3s²) are the valence electrons for magnesium.

• Filling Order Rules:

  • (n + l) Rule: Orbitals fill from lowest energy to highest. The energy ranking is predicted by adding the n and l values. 1s (1+0=1) fills before 2s (2+0=2). If there's a tie, like 2p (2+1=3) and 3s (3+0=3), the one with the lower n (2p) fills first.

  • Hund’s Rule: When filling a subshell with multiple orbitals (p, d, or f), electrons will fill each empty orbital singly with parallel spins before pairing up in an orbital. It's like placing one person on each seat on a bus before asking anyone to share.

Magnetic Properties from Electron Config

• Paramagnetic: An atom or material with at least one unpaired electron. These unpaired electrons act like tiny magnets and are weakly attracted to an external magnetic field.

• Diamagnetic: An atom or material where all electrons are paired (↑↓). The paired spins cancel out the magnetic field, and these materials are weakly repelled by a magnet.

Valence Electrons

• Definition: The electrons in the outermost principal energy level (the highest n value). They are the most important electrons because they participate in chemical bonding.

• Location:

  • Representative Elements (Groups 1, 2, 13-18): Valence electrons are only in the outermost s and p subshells.

  • Transition Elements: Valence electrons are in the outermost s subshell AND the (n-1) d or (n-2) f subshells.

• The Octet Rule: The driving force for most bonding. Many atoms interact with other atoms to gain, lose, or share electrons in order to achieve a stable valence shell with eight electrons (a complete octet), just like the noble gases.

Periodic Table

The periodic table isn't just a random chart; it’s a masterfully organized grid that predicts how elements behave.

• Organization Principle: Elements are arranged by increasing atomic number(number of protons). The layout reveals repeating patterns in their chemical and physical properties.

• Rows (Periods): Horizontal rows. All elements in a period have their valence electrons in the same principal energy level (n). As you move across Period 2 (Li to Ne), you’re filling the n=2 shell.

• Columns (Groups): Vertical columns. Elements in the same group have the same number and arrangement of valence electrons, which gives them very similar chemical properties.

  • Analogy: A period is like a school grade level (everyone is roughly the same age/size). A group is like a family with shared traits.

Types of Elements

The table is broadly divided into three categories based on physical and chemical properties.

Type	Properties	Location on Table
Metals	Shiny (lustrous), excellent conductors of heat/electricity, malleable (can be hammered into sheets), ductile (can be drawn into wires).	Left side and the middle (transition metals).
Nonmetals	Dull appearance, poor conductors (insulators), brittle if solid.	Right side (upper right corner).
Metalloids (Semimetals)	Possess a mix of metal and nonmetal properties. They’re the “middle children” and often make good semiconductors (like silicon in computer chips).	In a "stair-step" line starting from Boron (B) down to Astatine (At).

Trends of the Table

The Foundation: Two Key Players

1. Effective Nuclear Charge (Zeff): This is the "felt" positive charge that a valence electron experiences from the nucleus. It's the actual nuclear charge (+Z) minus the shielding effect of the inner "core" electrons that block the valence electron from the full nuclear attraction.

   • Analogy: Imagine a bonfire (the nucleus). You’re in the front row (valence electron). The people in front of you (core electrons) are blocking some of the heat. The heat you actually feel is the Zeff.

   • Core Trend: The main driver of horizontal trends.

     • Across a Period (→): Zeff increases. You add a proton to the nucleus (+1 charge) and an electron to the same outer shell. The shielding doesn't increase much, so the pull on each valence electron gets stronger.

     • Down a Group (↓): Zeff stays relatively constant. The nuclear charge increases, but so does the number of inner shielding shells, effectively canceling out.

2. Increasing Principal Energy Level (n): The main driver of vertical trends.

   • Down a Group (↓): The valence electrons are placed in shells with a higher n value, meaning they are physically farther from the nucleus. A greater distance weakens the electrostatic attraction, even if Zeff is similar.

The Trends Themselves

Atomic Radius (Size of the Neutral Atom)

• Across a Period (→): DECREASES. Zeff pulls the electrons in tighter, shrinking the atom.

• Down a Group (↓): INCREASES. Electrons are added to new, larger shells farther from the nucleus.

Ionic Radius (Size of a Charged Ion)

• Cations (+): Smaller than their neutral parent atom. Losing electrons means the remaining electrons are held more tightly by the same nuclear charge. Often, the entire outer shell is lost.

• Anions (-): Larger than their neutral parent atom. Gaining electrons increases electron-electron repulsion and Zeff decreases, causing the cloud to expand.

• Trend Boundary: The largest nonmetal anions (very puffed up) and the smallest metal cations (very shrunken) are found near the metalloid "stair-step" line.

Ionization Energy (IE) — Energy required to remove an e-

• Definition: How much energy it takes to pluck away a valence electron from a gaseous atom. A high IE means the atom holds onto its electrons tightly.

• Across a Period (→): INCREASES. Increasing Zeff means a stronger hold on the electrons, making them harder to remove.

• Down a Group (↓): DECREASES. Electrons are farther from the nucleus and more shielded, making them easier to remove.

Electron Affinity (EA) — Energy released when gaining an e-

• Definition: The energy change (usually an energy release) when a gaseous atom gains an electron. A more negative value (releasing more energy) means the atom strongly "wants" to grab an electron.

• Across a Period (→): INCREASES (releases more energy). Increasing Zeff creates a stronger attraction for an incoming electron.

• Down a Group (↓): DECREASES (releases less energy). Electrons are being added farther from the nucleus, so the attractive pull is weaker.

Electronegativity (EN) — Pull on electrons within a bond

• Definition: A measure of how strongly an atom's nucleus attracts shared electrons when it forms a chemical bond. Think of it as a tug-of-war. This is a bonding concept, not a property of an isolated atom.

• Across a Period (→): INCREASES. Higher Zeff means a stronger pull on bonding electrons.

• Down a Group (↓): DECREASES. Greater distance from the nucleus means a weaker pull on bonding electrons.

Trend Summary Table

Across Period vs Down Group

Property	Trend Across a Period (→)	Trend Down a Group (↓)
Zeff	Increases	Stays Relatively Constant
Atomic Radius	Decreases	Increases
Ionization Energy	Increases	Decreases
Electron Affinity	Increases	Decreases
Electronegativity	Increases	Decreases

Chemistry of Groups

• Group 1: Alkali Metals

  • Oxidation State: +1. They lose one electron easily (very low IE) to form a +1 cation with a noble gas configuration.

  • Reactivity: The most reactive of all metals. Reactivity increases down the group as IE decreases.

• Group 2: Alkaline Earth Metals

  • Oxidation State: +2. They lose two electrons to achieve a noble gas configuration.

  • Reactivity: Highly reactive, but less so than alkali metals.

• Group 16: Chalcogens

  • Oxidation States: They have two common ways to achieve an octet, depending on their metallic character.

    • -2: Gaining two electrons (common for nonmetals like oxygen).

    • +6: Losing or sharing six electrons (possible for larger metalloids/metals like polonium).

  • Biological Importance: Crucial for life (Oxygen for water/respiration, Sulfur in proteins).

• Group 17: Halogens

  • Oxidation State: -1. They are one electron short of an octet, so they very aggressively gain an electron to form a -1 anion.

  • Properties: Nonmetals with the highest electronegativities in their respective periods. Fluorine is the most electronegative element on the table.

• Group 18: Noble Gases

  • Oxidation State: 0. Their valence shell is already full. They are chemically inert (unreactive) under standard conditions.

  • Properties: Have extremely high ionization energies (won't give up electrons) and, for the smaller ones (He, Ne, Ar), virtually zero electronegativity or electron affinity (won't take on electrons either).

• Transition Metals (The 'd' Block)

  • Unique Feature: Multiple oxidation states. Because their s and d orbitals are close in energy, they can lose different numbers of electrons (e.g., Iron can be +2 or +3, Copper can be +1 or +2).

  • Consequences: This makes them excellent catalysts and allows them to form colorful complexes with nonmetals in solution (e.g., permanganate is deep purple, dichromate is orange), which is essential in both industrial chemistry and biological systems (like iron in hemoglobin).

Bonding

Atoms bond to achieve a more stable, lower-energy state, almost always by getting a full valence shell like a noble gas.

• The Octet Rule: The guiding principle that atoms are most stable with eight valence electrons.

• EXCEPTIONS TO THE OCTET RULE (Key to Know):

  1. Incomplete Octet: Some small atoms are stable with fewer than eight. These are: Hydrogen (H, stable with 2), Helium (He, 2), Lithium (Li, 2), Beryllium (Be, 4), and Boron (B, 6).

  2. Expanded Octet: Elements in Period 3 or higher can hold more than eight electrons because they have empty d orbitals available. Examples: Phosphorus (PCl₅ has 10), Sulfur (SF₆ has 12).

  3. Odd-Electron Species (Radicals): Molecules with an odd number of total valence electrons (like NO, which has 11) cannot possibly give every atom an octet. One electron will be unpaired.

Ionic Bonds

This is an extreme transfer of electrons, like one person giving a dollar to another.

• Mechanism: An element with a very low ionization energy (a metal) transfersone or more electrons to an element with a very high electron affinity (a nonmetal).

• The Ions Formed:

  • Cation: The atom that lost an electron(s) becomes positively charged (+).

  • Anion: The atom that gained an electron(s) becomes negatively charged (-).

• The Bond: The strong electrostatic attraction between the oppositely charged ions holds them together.

• Key Condition: Large difference in electronegativity (ΔEN > 1.7), typically a metal + nonmetal.

• Properties of Ionic Compounds:

  • Form crystalline lattices—a rigid, repeating, organized 3D array of ions.

  • Have high melting and boiling points (strong attraction requires a lot of energy to overcome).

  • Dissociate (break apart into their ions) in polar solvents like water. This makes the solution conduct electricity.

Covalent Bonds

This is a bond where electrons are shared, like a joint bank account between two people of similar financial habits.

• Mechanism: Elements with similar electronegativities share one or more pairs of electrons to complete their octets. Typically nonmetal + nonmetal.

• Bond Order:

  • Single Bond: 1 shared pair (longest, weakest).

  • Double Bond: 2 shared pairs.

  • Triple Bond: 3 shared pairs (shortest, strongest).

  • Trend: As bond order increases, bond strength (energy) increases and bond length decreases.

• Types of Covalent Bonds (by Polarity):

  • Nonpolar Covalent: Electrons are shared equally or near-equally. ΔEN is approximately 0 to less than 0.5. Example: C—H, H—H.

  • Polar Covalent: Electrons are shared unequally. ΔEN is between 0.5 and 1.7. The more electronegative atom hogs the electrons and gets a partial negative charge (δ-). The less electronegative atom gets a partial positive charge (δ+). Example: H—Cl.

• Coordinate Covalent Bond: A special case where one atom donates BOTH electrons for a shared pair. The other atom contributes nothing but an empty orbital.

  • Clue: Often forms between a Lewis acid (electron-pair acceptor) and a Lewis base (electron-pair donor).

Lewis Structures

These are the blueprints for showing valence electrons in a molecule.

• Lewis Dot Symbol: The elemental symbol surrounded by dots, each representing a valence electron.

• Rules for Drawing Lewis Structures:

  1. Count total valence electrons in the molecule/ion.

  2. Draw a skeleton structure (least electronegative atom in the center, except H).

  3. Connect atoms with single bonds (lines).

  4. Complete octets of outer atoms with lone pairs (dots).

  5. Place any remaining electrons on the central atom.

Formal Charge (FC)

• Formal Charge (FC): A bookkeeping tool to decide the best Lewis structure. It tells you if an atom in the molecule has more or fewer electrons than it had as a neutral atom, assuming equal sharing.

  • Formula: FC = (Valence electrons of free atom) – (Dots) – (Lines)

    • Dots = nonbonding electrons owned entirely by the atom.

    • Lines = bonding electrons shared equally (one electron per bond to the atom).

  • Goal: The best structure minimizes formal charges, and any negative formal charges should be on the most electronegative atoms.

Resonance Structures

Resonance Structures: When a molecule has a pi (π) system (double/triple bonds), one Lewis structure often isn't enough. The electrons are actually delocalized across multiple positions.

• Analogy: A hybrid car is not a gas car one moment and an electric car the next; it's a blend of both at all times. Resonance is the actual, stable hybrid of all valid Lewis structures. The classic example is the carbonate ion (CO₃²⁻), which has three resonance structures with the double bond in a different position each time.

VSEPR Theory: Predicting 3D Shape

Valence Shell Electron Pair Repulsion. The "family reunion" theory of molecular shape.

• Core Idea: Electron pairs (both bonding pairs in lines and nonbonding lone pairs) are negatively charged and repel each other. They will arrange themselves in 3D space to be as far apart as possible to minimize this repulsion.

• Key Hierarchy of Repulsion:
  Lone Pair–Lone Pair > Lone Pair–Bonding Pair > Bonding Pair–Bonding Pair
  (Lone pairs are held closer to the nucleus and take up more space, so they "push" harder.)

• Two Key Geometries (Don't Confuse Them!):

  • Electronic Geometry: The shape including all electron pairs (bonds AND lone pairs). The "family tree" that dictates the overall arrangement.

  • Molecular Geometry: The shape of the actual atoms. This is what we name the molecule's shape. Lone pairs are invisible in this shape.

• Polarity of Molecules: Must check the whole 3D structure.

  • A molecule with only nonpolar bonds is nonpolar.

  • A molecule with polar bonds can still be nonpolar if the geometry is perfectly symmetric and the individual bond dipole moments (vectors) cancel each other out (like a perfect tug-of-war tie). Example: CO₂ (linear) is nonpolar, but H₂O (bent) is polar.

VSEPR - Simplified

• Electron Groups: Any bond (single, double, or triple) or lone pair. A double bond counts as ONE group here for determining shape.

• Bonded Pairs: Atoms attached to the central atom.

• Lone Pairs: Nonbonding electrons that take up space and repel strongly.

sp Hybridization (2 Electron Groups)

Think of this as two balloons tied together. They want to be on opposite sides.

Bonded	Lone	Electronic Geometry	Molecular Shape	Bond Angle
Bonded: 2	Lone: 0	EG: Linear	MS: Linear	180°
Bonded: 1	Lone: 1	EG: Linear	MS: Linear	180°

Simply Put: With only two things around the atom, the only way to get them far apart is a straight line.

sp² Hybridization (3 Electron Groups)

Think of three balloons tied together. They spread out flat in a circle (trigonal planar, 120° apart).

Bonded	Lone	Electronic Geometry	Molecular Shape	Bond Angle
Bonded: 3	Lone: 0	EG: Trigonal Planar	MS: Trigonal Planar	120°
Bonded: 2	Lone: 1	Trigonal Planar	Bent (or Angular)	< 120°
Bonded: 1	Lone: 2	Trigonal Planar	Linear	180°

How to Visualize It:

• 3 bonds, 0 lone pairs: All three corners of the triangle have an atom. Perfectly flat and even.

• 2 bonds, 1 lone pair: One corner of the triangle is just an invisible lone pair, pushing the two actual atoms closer together. The molecule looks bent. The angle is squeezed to less than 120°.

• 1 bond, 1 lone pair: This is rare. Two lone pairs fill two corners of the triangle, leaving just one straight line for atoms, so it's linear.

sp³ Hybridization (4 Electron Groups)

Think of four balloons tied together. They form a 3D tetrahedron (like a tripod). The ideal angle is 109.5°.

Bonded	Lone	Electronic Geometry	Molecular Shape	Bond Angle
Bonded: 4	Lone: 0	EG: Tetrahedral	MS: Tetrahedral	109.5°
3	1	Tetrahedral	Trigonal Pyramidal	< 109.5°
2	2	Tetrahedral	Bent (or Angular)	< 109.5°
1	3	Tetrahedral	Linear	180°

How to Visualize It:

• 4 bonds, 0 lone pairs: Perfect, symmetric 3D shape. Methane (CH₄).

• 3 bonds, 1 lone pair: Imagine removing one leg of a tripod. The lone pair sits at the top, pushing the three bonds down, making a pyramid shape. Ammonia (NH₃). The angle is slightly less than 109.5°.

• 2 bonds, 2 lone pairs: Two corners of the tetrahedron are lone pairs. They push the two remaining bonds into a bent shape, like water (H₂O). The angle is squeezed even more.

• 1 bond, 3 lone pairs: Very rare. The lone pairs fill the base of the tetrahedron, forcing the single bond straight up, making it linear (like HF).

 sp³d Hybridization (5 Electron Groups)

Think of five balloons. They form a trigonal bipyramid—a flat triangle in the middle (equatorial) with one atom above and one below (axial). The angles are 90° and 120°.

The Golden Rule for Lone Pairs Here: Lone pairs ALWAYS go in the equatorial plane (the flat triangle) first because that gives them the most space from other groups.

Bonded	Lone	Electronic Geometry	Molecular Shape	Bond Angle
Bonded: 5	Lone: 0	EG: Trigonal Bipyramidal	MS: Trigonal Bipyramidal	120° and 90°
4	1	Trigonal Bipyramidal	Seesaw	< 120° and < 90°
3	2	Trigonal Bipyramidal	T-Shaped	< 90°
2	3	Trigonal Bipyramidal	Linear	180°

How to Visualize It:

• 5 bonds: Full, symmetrical shape.

• 4 bonds, 1 lone pair: A lone pair replaces one equatorial atom. The two remaining equatorial atoms and two axial atoms look like a playground seesaw.

• 3 bonds, 2 lone pairs: Two equatorial lone pairs leave one equatorial and two axial atoms. They form a T-shape in 3D.

• 2 bonds, 3 lone pairs: All three equatorial spots are lone pairs, leaving just the two axial atoms. They form a straight 180° line.

sp³d² Hybridization (6 Electron Groups)

Think of six balloons tied together. They form an octahedron—like two pyramids stuck base-to-base. All angles are exactly 90°.

Bonded	Lone	Electronic Geometry	Molecular Shape	Bond Angle
Bonded: 6	Lone: 0	EG: Octahedral	MS: Octahedral	90°
5	1	Octahedral	Square Pyramidal	< 90°
4	2	Octahedral	Square Planar	90°

How to Visualize It:

• 6 bonds: Perfectly symmetric.

• 5 bonds, 1 lone pair: Remove one of the six positions. The lone pair sits at one pole, and the base of the pyramid is a square of atoms.

• 4 bonds, 2 lone pairs: The two lone pairs want to be as far apart as possible, so they go at opposite poles (180°). This leaves the four atoms in a perfect flat square around the middle (equator). A totally flat molecule.

Memorize VSEPR

Step 1: Start with the “Balloon” Geometry (Electronic Shape)

This is based purely on the number of electron groups (things around the central atom).

# of Groups	Think of This Shape
2	A straight line (Linear)
3	A flat triangle (Trigonal Planar)
4	A 3D tripod (Tetrahedral)
5	A triangle with two poles (Trigonal Bipyramidal)
6	Two pyramids base-to-base (Octahedral)

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Step 2: The Lone Pair Deletion Rule

To get the molecular shape, take the starting shape and mentally "erase" one atom spot for each lone pair. The remaining atom positions define the shape.

• 4 groups (Tetrahedral)

  • 4 atoms = Tetrahedral

  • Erase 1 atom (3 left) = Trigonal Pyramidal

  • Erase 2 atoms (2 left) = Bent

• 5 groups (Trigonal Bipyramidal)

  • Crucial: Always erase from the flat triangle (equatorial) first.

  • Erase 1 equatorial (4 left) = Seesaw

  • Erase 2 equatorial (3 left) = T-shaped

  • Erase all 3 equatorial (2 left) = Linear

• 6 groups (Octahedral)

  • Crucial: Erase from opposite poles first to minimize repulsion.

  • Erase 1 (5 left) = Square Pyramidal

  • Erase 2 opposite poles (4 left in a flat square) = Square Planar

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Step 3: The Angle Squeeze Rule

• Lone pairs push harder than bonds.

• If there are NO lone pairs, the angles are the ideal, maximum spread.

• For every lone pair you add to the central atom, squeeze the bond angle a little bit (less than 120°, less than 109.5°, etc.).

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The “Family Name” Trick (Memorize the Sequence)

Instead of a chart, just memorize the names in order for the most common hybridizations:

• sp³ (4 groups): Tetrahedral → Trig. Pyramidal → Bent

• sp³d (5 groups): Trig. Bipyramidal → Seesaw → T-shaped → Linear

• sp³d² (6 groups): Octahedral → Sq. Pyramidal → Sq. Planar

Think of it as each lone pair "eating" one atom position, and the name changes as the shape shrinks.

Sigma (σ) and Pi (π) Bonds

This describes how the electron clouds physically overlap to form a bond.

• Sigma (σ) Bond: Formed by head-to-head overlap of orbitals directly along the internuclear axis (the line connecting the two nuclei). This is the strongest type of covalent interaction.

  • All single bonds are sigma bonds.

  • In a double or triple bond, the first bond is always a sigma bond.

• Pi (π) Bond: Formed by the side-to-side overlap of two parallel, unhybridized p-orbitals. The electron density is above and below the internuclear axis. They are weaker than sigma bonds.

  • A double bond consists of one σ + one π bond.

  • A triple bond consists of one σ + two π bonds.

Intermolecular Forces (IMFs)

These are NOT bonds within a molecule. They are weaker attractions between one molecule and its neighbor. They dictate physical properties like boiling point, melting point, and viscosity.

Strength Ranking (Weakest to Strongest):

1. London Dispersion Forces (LDFs):

   • Present in: ALL molecules and atoms.

   • Cause: Random, fleeting asymmetries in electron clouds create temporary, instantaneous dipoles that induce dipoles in neighbors. It's the only force holding nonpolar molecules together.

   • Trend: Strength increases with the size and polarizability of the electron cloud. Larger, heavier atoms/molecules have stronger LDFs.

2. Dipole–Dipole Interactions:

   • Present in: Only polar molecules.

   • Cause: The positive end (δ+) of one polar molecule is attracted to the negative end (δ-) of its neighbor. This is a permanent, not temporary, arrangement.

   • Note: These are strong in solids/liquids but negligible in gases because the molecules are too far apart.

3. Hydrogen Bonds:

   • Present in: A special, extra-strong subset of dipole-dipole interactions.

   • Condition: A hydrogen atom must be covalently bonded to a very small, highly electronegative atom with a lone pair. That's only Fluorine (F), Oxygen (O), or Nitrogen (N). (The acronym is FON).

   • Why it's strong: The massive ΔEN makes the H very δ+, and the lone pair on the F/O/N is very concentrated and negative. This is why water has a surprisingly high boiling point for such a small molecule.

Key Equations

• Dipole Moment (p): p = qd

  • p = dipole moment (a vector quantifying bond polarity)

  • q = magnitude of the partial charges

  • d = distance between the charges

• Formal Charge (FC): FC = Valence electrons – dots – lines

  • A quick way to count: Look at an atom in a Lewis structure. From its normal number of valence electrons, subtract every electron it owns (lone pair dots count as two, each bond line counts as one).

Molecules and Moles

Atoms are too small to count one by one, so we use these concepts to "scale up" to measurable quantities.

• Compound: A substance made of two or more elements chemically combined in a fixed, definite proportion (e.g., water is always H₂O, never H₂.₅O).

• Molecular Weight: The mass of one molecule, found by adding the atomic weights of all atoms in the molecular formula. Units are amu.

  • Example: H₂O = (2 × 1.0) + (1 × 16.0) = 18.0 amu.

• Molar Mass: The mass of one mole of a substance. The mole is the chemist's "dozen."

  • Avogadro's Number (NA): 6.022 × 10²³ particles. One mole of anything contains this many of that thing.

  • The Beautiful Connection: The molar mass of a compound in grams is numerically equal to its molecular weight in amu. Water's molecular weight is 18.0 amu; its molar mass is 18.0 g/mol.

Gram Equivalent Weight & Normality 

• Equivalent: The "moles of the species of interest" in a reaction. What that species is depends on the reaction type.

  • In acid-base reactions: Moles of H⁺ (or OH⁻) donated/accepted.

  • In redox reactions: Moles of electrons transferred.

• Gram Equivalent Weight: The mass of a substance that provides one equivalent of the species of interest.

• Normality (N): A concentration unit based on equivalents. Normality = equivalents of solute / liters of solution.

• Formula Connection: Normality (N) = Molarity (M) × n, where n is the number of equivalents per mole of compound. For H₂SO₄ (which has 2 H⁺), a 1 M solution is 2 N.

Representation of Compounds

• Law of Constant Composition: A pure compound always contains the exact same elements in the exact same mass ratio, regardless of the source. Water from a glacier and water from a desert spring are both 88.9% oxygen and 11.1% hydrogen.

• Empirical Formula: The simplest, smallest whole-number ratio of atoms in a compound. It's the reduced form. Glucose has a molecular formula C₆H₁₂O₆, but its empirical formula is CH₂O.

• Molecular Formula: The exact number of atoms of each element in a molecule. It is always a whole-number multiple of the empirical formula.

• Percent Composition: The mass percentage of each element in a compound.

  • Formula:(Mass of element in 1 mole of compound / Molar mass of compound) × 100%

Types of Chemical Reactions

• Combination (Synthesis): A + B → AB

  • Two or more simple substances combine to form one more complex product.

  • Example: 2H₂ + O₂ → 2H₂O

• Decomposition: AB → A + B

  • One complex substance breaks down into two or more simpler ones. Usually requires heat, light, or electricity.

  • Example: 2H₂O → 2H₂ + O₂

• Combustion: Fuel + O₂ → CO₂ + H₂O

  • A rapid reaction with oxygen that releases heat and light. For hydrocarbons, the products are ALWAYS carbon dioxide and water.

  • Example: CH₄ + 2O₂ → CO₂ + 2H₂O

• Displacement (Replacement):

  • Single-Displacement: A + BC → B + AC. One element replaces another in a compound. Often involves a metal replacing another metal.

    • Example: Zn + CuSO₄ → Cu + ZnSO₄

  • Double-Displacement (Metathesis): AB + CD → AD + CB. Two compounds trade partners. Often occurs to form a precipitate, a gas, or water.

    • Example: NaCl + AgNO₃ → NaNO₃ + AgCl (solid)

• Neutralization: Acid + Base → Salt + Water

  • A specific, critically important double-displacement reaction.

  • Example: HCl + NaOH → NaCl + H₂O

Balancing Chemical Equations

Matter cannot be created or destroyed, so a balanced equation must have the same number of each type of atom on both sides of the arrow.

• Balancing Steps (The Practical Order):

  1. Balance the least common atoms first (usually metals, carbon, or other elements aside from H and O).

  2. Balance the more common atoms next (almost always hydrogen and then oxygen last).

  3. Balance charge, if writing a net ionic equation or half-reaction.

  • Pro Tip: Never change subscripts to balance; only change the coefficients in front.

 Applications of Stoichiometry

Stoichiometry uses the balanced equation to predict quantities of reactants consumed and products formed.

• Limiting Reagent (Limiting Reactant): The reactant that runs out first during a reaction. It completely determines the maximum amount of product that can be formed. Like having eight slices of bread but only one slice of cheese—you can only make one grilled cheese.

• Excess Reagent: Any reactant present in a quantity greater than needed to react with the limiting reagent. You'll have some left over.

• Theoretical Yield: The maximum amount of product predicted by stoichiometry, assuming the limiting reagent is 100% converted with no side reactions.

• Actual Yield: The amount of product you actually measure when you do the experiment in the lab. It is almost always less than the theoretical yield due to incomplete reactions, side reactions, or loss during purification.

• Percent Yield: The efficiency of a reaction.

  • Formula: (Actual Yield / Theoretical Yield) × 100%

Nomenclature

A systematic set of rules for naming charged species.

• General Rules for Metals (Cations):

  • For metals that can have multiple charges (nonrepresentative/transition metals), use Roman numerals in parentheses to denote the charge. Example: Iron(III) is Fe³⁺.

  • An older system uses -ous for the lesser charge and -ic for the greater. Example: Ferrous (Fe²⁺) vs. Ferric (Fe³⁺).

• Rules for Nonmetals (Anions):

  • Monatomic anions (single atom) end in –ide. Example: Cl⁻ is chloride, O²⁻ is oxide.

  • Oxyanions (contain oxygen and another central atom):

    • The most common "base" form ends in –ate. Example: SO₄²⁻ is sulfate.

    • If there's a form with one less oxygen, it ends in –ite. Example: SO₃²⁻ is sulfite.

    • Extended Series (for halogens):

      • Per–...–ate : Most oxygen atoms. (ClO₄⁻ is perchlorate)

      • –ate : One fewer than per-. (ClO₃⁻ is chlorate)

      • –ite : One fewer than -ate. (ClO₂⁻ is chlorite)

      • Hypo–...–ite : Fewest oxygen atoms. (ClO⁻ is hypochlorite)

• Polyatomic Ions with Hydrogen:

  • Adding "hydrogen" (or the prefix "bi–") means one H⁺ has been added to the anion. Example: HCO₃⁻ is hydrogen carbonate or bicarbonate.

  • "Dihydrogen" means two H⁺ have been added. Example: H₂PO₄⁻ is dihydrogen phosphate.

Predicting Ionic Charges

• Representative Metals (Groups 1, 2, 13): Charge is simply their group number (Na⁺, Mg²⁺, Al³⁺).

• Representative Nonmetals (Groups 15-17): Charge is (group number – 18) to show how many electrons they gain to reach an octet (N³⁻, O²⁻, Cl⁻).

• Transition/Nonrepresentative Metals: Unpredictable; must be given or memorized (e.g., Cu⁺ and Cu²⁺).

Electrolytes

• Electrolytes: Solutes that dissolve in water to form ions, making the solution conductive.

  • Strong Electrolytes: Dissociate completely (soluble ionic compounds like NaCl, strong acids, strong bases).

  • Weak Electrolytes: Dissociate only partially (weak acids and bases). The degree of dissociation determines their strength.

Chemical Kinetics

Thermodynamics (ΔG) tells us if a reaction will happen spontaneously. Kinetics tells us how fast it will happen. A spontaneous reaction could take one second or one million years.

• Chemical Mechanism: The detailed, step-by-step sequence of elementary reactions that makes up the overall reaction. Think of it as the turn-by-turn GPS directions, not just the starting point and destination.

• Intermediates: Molecules that are produced in one step and then consumed in a later step. They exist in the middle of the mechanism but do not appear in the overall balanced equation.

• Rate-Determining Step: The slowest step in the mechanism. Like a single-lane bottleneck on a highway, this step sets the maximum speed for the entire reaction flow. No step can proceed faster than the slowest one.

Theories of How Reactions Happen

Collision Theory

For a reaction to occur, molecules must physically collide. But not just any collision works.

• Two Requirements for an Effective Collision:

  1. Proper Orientation: The molecules must hit each other with the reactive parts aligned. It's like a key needing to be inserted correctly into a lock.

  2. Sufficient Energy: The colliding molecules' combined kinetic energy must be equal to or greater than the activation energy (Ea).

• Rate Equation: rate = Z × f

  • Z = Total number of collisions per second.

  • f = Fraction of those collisions that are effective (have correct orientation and enough energy).

Arrhenius Equation (Collision Theory in Math Form)

This equation quantifies the effect of temperature on the rate constant k.

• Equation: k = Ae^(-Ea/RT)

  • k = rate constant (a higher k means a faster reaction).

  • A = frequency factor (how often molecules collide with the right orientation).

  • Ea = activation energy.

  • R = ideal gas constant.

  • T = temperature in Kelvin.

• Key Takeaway: As temperature (T) increases, the exponent (-Ea/RT) gets smaller (less negative), so k increases significantly. Conversely, a higher activation energy (Ea) makes k much smaller.

Transition State Theory

• As molecules collide effectively, they form an unstable, high-energy transition state (or activated complex) where old bonds are half-broken and new bonds are half-formed. This is not a stable intermediate you can isolate.

• The transition state is the highest energy point on the reaction pathway (the peak of the energy diagram hill). From this peak, the reaction can "slide down" to form products or fall back to reactants.

Factors Affecting Reaction Rate

• Concentration of Reactants: More reactant molecules in the same volume = more frequent collisions. Increasing concentration increases rate for all reactions except zero-order ones.

• Temperature: Higher temperature means molecules move faster. This increases both the frequency of collisions and, crucially, the energy of those collisions. Increases rate.

• Medium (Solvent): The environment matters. A reaction might be fast in one solvent but slow in another due to how the solvent stabilizes reactants, intermediates, or the transition state.

• Catalysts: Substances that increase the reaction rate without being consumed.

  • Mechanism: They provide an alternative reaction pathway with a lower activation energy (Ea). A lower "hill" to climb means more collisions have enough energy to get over it.

  • Homogeneous Catalysts: In the same phase (e.g., liquid) as the reactants.

  • Heterogeneous Catalysts: In a different phase (e.g., a solid metal catalyst with gaseous reactants).

Reaction Rates

• Definition of Rate: How fast a reactant disappears or a product appears over a specific time period (Δt). The stoichiometric coefficients a, b, c, d are used to normalize the rate.

  • Rate = – (1/a) Δ[A]/Δt = – (1/b) Δ[B]/Δt = (1/c) Δ[C]/Δt = (1/d) Δ[D]/Δt

  • The minus sign for reactants makes the rate a positive number, as Δ[A] is negative.

• The Rate Law: An equation that links the reaction rate to the concentrations of reactants and a rate constant k.

  • General Form: Rate = k [A]^x [B]^y

    • k: The rate constant (temperature-dependent).

    • [A], [B]: Molar concentrations of reactants.

    • x, y: The rate orders for each reactant. These are determined experimentally and DO NOT necessarily equal the stoichiometric coefficients from the balanced equation.

• Overall Reaction Order: The sum of all individual rate orders (x + y + ...).

Identifying Reaction Order from Data

Reaction orders (0th, 1st, 2nd) have distinct patterns in how concentration changes over time. This is how we determine the rate law experimentally.

Reaction Order	Rate Law (simplified)	Meaning	Concentration vs. Time Plot	Straight-Line Plot	Slope of Straight Line
Zero-Order	Rate = k	Rate is constant and independent of [A]. Only T or a catalyst changes it.	Linear, decreasing	[A] vs. time	Slope = –k
First-Order	Rate = k[A]	Rate is directly proportional to [A]. If [A] doubles, rate doubles. A common pattern for radioactive decay.	Nonlinear curve	ln[A] vs. time	Slope = –k
Second-Order	Rate = k[A]²	Rate is proportional to the square of [A]. If [A] doubles, rate quadruples.	Nonlinear curve	1/[A] vs. time	Slope = +k

• Broken-Order Reactions: Have fractional orders (e.g., rate = k[A]^0.5). No theoretical meaning is implied; just an empirical fit.

• Mixed-Order Reactions: The reaction order changes over the course of the reaction as conditions change.

Key Equations Summary

• Collision Theory: rate = Z × f (total collisions × fraction effective)

• Arrhenius Equation: k = Ae^(-Ea/RT) (relates k, Ea, and T)

• General Definition of Rate:Rate = – Δ[A]/ aΔt = – Δ[B]/ bΔt = Δ[C]/ cΔt = Δ[D]/ dΔt

• Generic Rate Law: Rate = k[A]^x [B]^y

• First-Order Decay (Radioactive Decay): [A]_t = [A]_0 e^{-kt} (calculates concentration remaining after time t)

Equilibrium: The Dynamic Balance

Many reactions are reversible; they can go both forward (reactants → products) and backward (products → reactants). Equilibrium is the state where these two opposing processes are perfectly balanced.

• Dynamic, Not Static: At equilibrium, the reaction hasn't stopped. The forward and reverse reactions are still occurring, but at exactly the same rate. It's like a crowded room where people are constantly entering and leaving, but the total number of people inside stays the same.

• Constant Concentrations: Because the forward and reverse rates are equal, the macroscopic concentrations of all reactants and products remain constant over time.

• Why It Happens: Systems naturally tend toward a state of minimum energy and maximum entropy (disorder) . Equilibrium is the compromise between these two driving forces.

The Equilibrium Constant (Keq) and Reaction Quotient (Q)

The Law of Mass Action

This law provides the mathematical formula to describe an equilibrium state. For a generic reaction:
aA + bB ⇌ cC + dD

• Equilibrium Constant (Keq or Kc):

  • Keq = ([C]^c [D]^d) / ([A]^a [B]^b)

  • This ratio uses the concentrations of products over reactants, each raised to the power of its stoichiometric coefficient.

  • Critical Rule: Keq is a constant value at a given temperature. It does not change unless the temperature changes.

  • What to Include: ONLY gases (g) and aqueous solutes (aq) appear in the expression. Pure solids (s) and pure liquids (l) are omitted because their concentrations are essentially constant.

• Reaction Quotient (Q):

  • Q = ([C]^c [D]^d) / ([A]^a [B]^b)

  • It has the exact same mathematical form as Keq, but you calculate it using concentrations at any point in time, not just at equilibrium.

Using Q to Predict Direction (The Q vs. K Test)

Comparing Q to Keq tells you which way a reaction must shift to reach equilibrium and also relates directly to Gibbs free energy (ΔG).

Comparison	Meaning	Reaction Direction	ΔG
Q < Keq	Not enough products yet. The ratio is too small.	Forward (→) to make more products.	ΔG < 0 (Spontaneous)
Q = Keq	The system is at the perfect balance.	At Equilibrium. No net change.	ΔG = 0
Q > Keq	Too many products. The ratio is too large.	Reverse (←) to make more reactants.	ΔG > 0 (Non-spontaneous)

What the Magnitude of Keq Tells You

The value of Keq is a snapshot of the equilibrium mixture's composition.

Magnitude of Keq	Composition at Equilibrium
Keq >> 1 (Large)	Product-favored. The equilibrium lies far to the right. Reaction essentially goes to completion.
Keq ≈ 1	Significant amounts of both reactants and products are present.
Keq << 1 (Small)	Reactant-favored. The equilibrium lies far to the left. Reaction barely proceeds.
Keq <<< 1 (Very Small)	Negligible product forms. In calculations, the change x in reactant concentration can be treated as negligible compared to the initial concentration.

Le Châtelier’s Principle

If you apply a stress to a system at dynamic equilibrium, the system will shift its equilibrium position to relieve that stress and re-establish equilibrium. Think of it as a "chemical reflex."

The three main stresses:

1. Change in Concentration:

   • Add Reactant or Remove Product: The system will "use up" what you added or "replace" what you removed. Shifts RIGHT (→) .

   • Add Product or Remove Reactant: The system works in reverse to consume the excess. Shifts LEFT (←) .

2. Change in Pressure/Volume (for gases only):

   • The stress is a change in the number of gas molecules. The system shifts to counteract the volume change.

   • Increase Pressure (Decrease Volume): System shifts toward the side with FEWER moles of gas to lower the pressure.

   • Decrease Pressure (Increase Volume): System shifts toward the side with MORE moles of gas to raise the pressure.

   • Note: If both sides have equal moles of gas, pressure changes have NO effect on equilibrium.

3. Change in Temperature:

   • This is the ONLY stress that changes the value of Keq itself. Treat heat as a reactant (for endothermic) or product (for exothermic).

   • Exothermic Reaction (Heat is a product): Reactants ⇌ Products + Heat

     • Increase T: Adding heat shifts the reaction LEFT (←) . Keq decreases.

     • Decrease T: Removing heat shifts the reaction RIGHT (→) . Keq increases.

   • Endothermic Reaction (Heat is a reactant): Reactants + Heat ⇌ Products

     • Increase T: Adding heat shifts the reaction RIGHT (→) . Keq increases.

     • Decrease T: Removing heat shifts the reaction LEFT (←) . Keq decreases.

Kinetic vs. Thermodynamic Control

For reactions that can form two different products, the outcome can depend on the conditions.

• Kinetic Product: The product that forms fastest. It has a lower activation energy (Ea) barrier to its formation.

  • Properties: Higher in free energy (less stable), favored at low temperatures(where the energy to overcome the higher Ea for the thermodynamic product is insufficient).

  • Often called the "fast" product.

• Thermodynamic Product: The most stable product. It has the lowest overall free energy (most negative ΔG).

  • Properties: Lower in free energy (more stable). It often has a higher activation energy barrier, meaning it forms more slowly. Favored at higher temperatures (which provide enough energy to overcome the barrier and allow the reaction to reach the true equilibrium state).

Key Equations

• Equilibrium Constant: Keq = ([C]^c [D]^d) / ([A]^a [B]^b)
  (Concentrations at equilibrium only)

• Reaction Quotient: Q = ([C]^c [D]^d) / ([A]^a [B]^b)
  (Concentrations at any point in time)

Systems

Thermodynamics is the study of energy and its transformations. We start by defining the "stage" (the system) and the "play" (the process).

• Types of Systems (Defined by boundaries):

  • Isolated System: Completely sealed off. Exchanges neither matter nor energy with the surroundings. The theoretical ideal; a perfect, sealed, perfectly insulated thermos.

  • Closed System: Can exchange energy (heat, work) but NOT matter. Like a sealed piston or a sealed water bottle being heated. Most common system in basic chemistry.

  • Open System: Exchanges both matter and energy freely. Like a pot of boiling water on a stove (steam escapes, heat enters).

Types of Processes 

 (Defined by a constant property):

• Isothermal: Occurs at a constant temperature (ΔT = 0).

• Adiabatic: Exchanges no heat with the surroundings (q = 0). Achieved by perfect insulation or a very rapid process.

• Isobaric: Occurs at a constant pressure (ΔP = 0). Common in open lab settings.

• Isovolumetric (Isochoric): Occurs at a constant volume (ΔV = 0). Reactions in sealed, rigid containers.

States and State Functions

A state function is a property whose value depends only on the current state of the system, not on the path taken to get there. They are the "altitude" of thermodynamics—your altitude on a mountain depends only on where you're standing, not on the trail you hiked to get there.

• Key State Functions: Pressure (P), Volume (V), Temperature (T), Density (ρ), Internal Energy (U), Enthalpy (H), Entropy (S), Gibbs Free Energy (G).

• Path Functions: In contrast, these do depend on the path taken. The two primary ones are heat (q) and work (w) .

• Standard Conditions (The Reference Point): To compare substances and reactions fairly, we use a standard state defined as:

  • Temperature: 298 K (25°C)

  • Pressure: 1 atm

  • Concentration: 1 M (for solutions)

  • A substance's standard state is its most stable form under these conditions (e.g., O₂ gas, H₂O liquid, solid carbon is graphite).

Phase Changes and Phase Diagrams

Matter isn't just solid, liquid, or gas. The transitions between them are physical processes with specific names and energy changes.

• The Six Key Phase Transitions:

  1. Fusion (Melting): Solid → Liquid

  2. Freezing (Crystallization): Liquid → Solid

  3. Vaporization (Boiling/Evaporation): Liquid → Gas

  4. Condensation: Gas → Liquid

  5. Sublimation: Solid → Gas (e.g., dry ice)

  6. Deposition: Gas → Solid (e.g., frost forming)

• Critical Points on a Phase Diagram:

  • Triple Point: The unique temperature and pressure where all three phases (solid, liquid, gas) co-exist in perfect equilibrium.

  • Critical Point: Above this temperature and pressure, a distinct liquid and gas phase cease to exist. The substance becomes a supercritical fluid.

Heat vs. Temperature: The Crucial Distinction

• Temperature (T): A measure of the average kinetic energy of the particles in a substance. It's an intensive property. Units: Kelvin (K), Celsius (°C).

• Heat (q): The transfer of thermal energy from a hotter object to a colder one. It's an extensive property—a process, not a possession. "A hot coffee cup contains high thermal energy, not 'heat'."

Calorimetry Equations (Measuring Heat):

• No Phase Change (Temperature Change): q = mcΔT

  • m = mass, c = specific heat capacity (energy to raise 1g by 1°C).

  • ΔT = change in temperature.

• During a Phase Change (No Temperature Change): q = mL

  • L = latent heat (heat of fusion or vaporization). Energy breaks intermolecular forces, not raises kinetic energy.

Enthalpy (H): Heat of Reaction

Enthalpy is a state function measuring the total heat content/potential energy stored in chemical bonds and intermolecular forces.

• General Enthalpy of Reaction: ΔH_rxn = H_products – H_reactants

  • ΔH > 0 (+): Endothermic. The system absorbs heat from the surroundings (feels cold). Energy is a reactant.

  • ΔH < 0 (-): Exothermic. The system releases heat to the surroundings (feels hot). Energy is a product.

• Ways to Calculate ΔH:

  1. Hess's Law: If a reaction is the sum of two or more steps, the overall ΔH is the algebraic sum of the ΔH for those individual steps.

  2. Standard Heats of Formation (ΔH°f):ΔH°_rxn = Σ ΔH°_f(products) – Σ ΔH°_f(reactants)

     • The ΔH°f of a pure element in its standard state is always zero.

  3. Bond Dissociation Energies:ΔH°_rxn = Σ (Bond energies of bonds broken) – Σ (Bond energies of bonds formed)

     • Breaking bonds requires energy (endothermic, +).

     • Forming bonds releases energy (exothermic, -).

Entropy (S): The Measure of Dispersal

• Definition: Entropy is a measure of the dispersal of energy and matter within a system. It's a statistical tendency toward the most probable state. High entropy = high dispersal (e.g., gas is more dispersed than a solid).

• Key Principle: The universe naturally tends toward maximum entropy.

• Calculating Entropy Change: ΔS = Q_rev / T. A small amount of heat added at a low temperature causes a large entropy increase.

• Second Law of Thermodynamics: For any spontaneous process, the total entropy of the universe must increase.

  • ΔS_universe = ΔS_system + ΔS_surroundings > 0

• Standard Entropy Change of Reaction:ΔS°_rxn = Σ S°(products) – Σ S°(reactants)

Gibbs Free Energy (G)

Gibbs free energy elegantly combines enthalpy, entropy, and temperature into a single state function to predict spontaneity at constant pressure and temperature.

• The Master Equation: ΔG = ΔH – TΔS

• Interpreting ΔG:

  • ΔG < 0: The process is spontaneous (thermodynamically favorable) in the forward direction.

  • ΔG = 0: The system is at dynamic equilibrium.

  • ΔG > 0: The process is nonspontaneous in the forward direction (but spontaneous in reverse).

The Temperature Dependence (How ΔH and TΔS fight)

Sign of ΔH	Sign of ΔS	ΔG = ΔH – TΔS	Spontaneity
Sign of ΔH: – (favorable)	Sign of ΔS: + (favorable)	Always negative (–)	Spontaneous at ALL temperatures
Sign of ΔH: + (unfavorable)	Sign of ΔS: – (unfavorable)	Always positive (+)	Nonspontaneous at ALL temperatures
Sign of ΔH: – (favorable)	Sign of ΔS: – (unfavorable)	Negative at low T, Positive at high T	Spontaneous only at LOW temperatures
Sign of ΔH: + (unfavorable)	Sign of ΔS: + (favorable)	Positive at low T, Negative at high T	Spontaneous only at HIGH temperatures

Gibbs Free Energy

• Standard Gibbs Free Energy from Keq: ΔG°_rxn = –RT ln(Keq)

  • This is the crucial link between thermodynamics and equilibrium. A large Keq corresponds to a very negative ΔG°.

• Non-Standard Gibbs Free Energy:ΔG_rxn = ΔG°_rxn + RT ln(Q) = RT ln(Q/Keq)

  • This equation is the mathematical proof of the Q vs. Keq test for spontaneity.

Key Equations Summary

• First Law (Conservation of Energy): ΔU = Q – W (Internal Energy Change = Heat added to system – Work done by system)

• Heat Transfer (no phase change): q = mcΔT

• Heat Transfer (phase change): q = mL

• Standard Enthalpy Change:ΔH°_rxn = ΣΔH°_f(products) – ΣΔH°_f(reactants)

• Bond Enthalpy: ΔH°_rxn = Σ BE(bonds broken) – Σ BE(bonds formed)

• Entropy Definition: ΔS = Q_rev / T

• Second Law: ΔS_universe = ΔS_system + ΔS_surroundings > 0

• Gibbs Free Energy: ΔG = ΔH – TΔS

• Standard Free Energy from Keq: ΔG°_rxn = –RT ln(Keq)

• Nonstandard Free Energy: ΔG_rxn = ΔG°_rxn + RT lnQ

The Gas Phase

Gases represent the state of matter where particles have enough kinetic energy to overcome nearly all intermolecular forces.

• General Properties of Gases:

  • Low Density: Particles are very spread out with lots of empty space between them.

  • Fluidity: Gases flow and completely fill any container they're in, taking its shape.

  • Compressibility: Due to the large empty space between particles, gases can be squeezed into a smaller volume easily.

• Four Key Variables Describe a Gas:

  1. Temperature (T): Must always be in Kelvin.

  2. Pressure (P): The force per unit area from gas collisions with container walls.

  3. Volume (V): The space the gas occupies.

  4. Number of Moles (n): The amount of gas particles.

• Pressure Units (Memorize These Equivalencies):

  • 1 atm = 760 mmHg = 760 torr = 101.325 kPa

  • The "mmHg" and "torr" are identical units, named for the use of mercury in barometers.

• The Mercury Barometer: Atmospheric pressure pushes down on a pool of mercury, forcing it up a sealed tube. Higher atmospheric pressure pushes the mercury higher up the column.

Ideal Gases

An ideal gas is a theoretical model that makes two simplifying assumptions: gas particles have negligible volume themselves, and they have no intermolecular forces. This model works well under normal conditions.

• Standard Temperature and Pressure (STP): The reference point for gases.

  • Temperature: 273 K (0°C)

  • Pressure: 1 atm

  • Molar Volume at STP: One mole of ANY ideal gas occupies exactly 22.4 L.

• The Ideal Gas Law (The Master Equation): PV = nRT

  • R is the universal gas constant. The most common value is 0.0821 L·atm / (mol·K).

  • This single equation links all four gas variables. You can also derive gas density from it: ρ = m/V = (PM) / (RT), where M is molar mass.

The Special Case Laws (Holding Two Variables Constant)

Each of these is derived from the ideal gas law by canceling out constant terms.

Law	Constant Variables	Relationship	The Formula(s)
Boyle's Law	n, T	P and V are inversely proportional	P₁V₁ = P₂V₂
Charles's Law	n, P	V and T are directly proportional	V₁/T₁ = V₂/T₂
Gay-Lussac's Law	n, V	P and T are directly proportional	P₁/T₁ = P₂/T₂
Avogadro's Principle	P, T	V and n are directly proportional	n₁/V₁ = n₂/V₂

• The Combined Gas Law: Integrates Boyle's, Charles's, and Gay-Lussac's laws into one equation for when n is constant.

  • P₁V₁ / T₁ = P₂V₂ / T₂

Dalton's Law

• Dalton's Law of Partial Pressures: In a mixture of gases, each gas exerts a pressure as if it were alone in the container. The total pressure is the sum of these partial pressures.

  • P_total = P_A + P_B + P_C + ...

  • Mole Fraction Connection: The partial pressure of gas A equals its mole fraction (X_A) times the total pressure. P_A = X_A × P_total.

Henry's Law

• Henry's Law: Deals with gases dissolving in liquids. The concentration of a dissolved gas is directly proportional to the partial pressure of that gas above the liquid's surface.

  • [A] = k_H × P_A (or [A]₁/P₁ = [A]₂/P₂ = k_H)

  • This is why a soda fizzes when opened: the pressure of CO₂ above the liquid drops drastically, so the dissolved CO₂ comes out of solution.

Kinetic Molecular Theory (KMT)

This is the set of assumptions that explains why the ideal gas laws work.

• The Five Postulates of KMT:

  1. Gas particles have negligible volume compared to the container.

  2. Gas particles have no intermolecular attractions or repulsions.

  3. Particles undergo random, continuous motion, colliding with container walls (creating pressure).

  4. All collisions are perfectly elastic (total kinetic energy is conserved; no energy is lost).

  5. The average kinetic energy (KE) is directly proportional to the absolute temperature (T) . This is the crucial link.

• Key KMT Math:

  • Average KE: KE = ½ mv² = ³⁄₂ k_B T (k_B is Boltzmann's constant). All gases at the same temperature have the same average KE.

  • Root-Mean-Square Speed (u_rms): A measure of the average speed of gas particles. u_rms = √(3RT / M) . At a constant T, lighter gas particles (lower M) move faster.

Graham's Law

• Graham's Law of Effusion/Diffusion: Rates of effusion and diffusion are inversely proportional to the square root of the molar mass. Lighter gases move faster.

  • Formula: r₁ / r₂ = √(M₂ / M₁)

  • Diffusion: The spreading of gas particles from high concentration to low concentration.

  • Effusion: The escape of a gas through a tiny pinhole into a vacuum.

Real Gases

Real gases deviate from ideal behaviour when the two core assumptions (no volume, no forces) become invalid. This happens under high pressure and/or low temperature.

• Conditions for Deviation:

  • High Pressure (Low Volume): Molecules are squeezed closer together.

  • Low Temperature: Molecules slow down and intermolecular forces become significant.

• Two Types of Deviation (in PV = nRT terms):

  1. Intermolecular Attraction: At moderately high pressures/low temps, attractive forces cause particles to "stick" a bit when they hit the walls. This means the pressure is slightly lower than predicted. V_real < V_ideal.

  2. Molecular Volume: At extremely high pressures, the particles themselves are taking up a significant fraction of the container's volume. The space for them to move is less than the container volume. V_real > V_ideal.

• The van der Waals Equation of State: This equation corrects the ideal gas law with two substance-specific constants.

  • (P + n²a/V²) (V – nb) = nRT

  • a : Corrects for intermolecular attractions. The + n²a/V² term adds a little back to the measured pressure.

  • b : Corrects for the physical volume of the particles. The – nb term subtracts the space the particles occupy from the container's volume.

  • For large, "sticky" molecules, a and b are large. For small, nonpolar molecules like He, they are very small.

Key Equations Summary

• Ideal Gas Law: PV = nRT

• Gas Density: ρ = m/V = PM / RT

• Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂

• Boyle's Law (constant n, T): P₁V₁ = P₂V₂

• Charles's Law (constant n, P): V₁/T₁ = V₂/T₂

• Gay-Lussac's Law (constant n, V): P₁/T₁ = P₂/T₂

• Avogadro's Principle (constant P, T): n₁/V₁ = n₂/V₂

• Dalton's Law (Partial Pressures): P_A = X_A P_total and P_total = P_A + P_B + ...

• Henry's Law: [A] = k_H × P_A

• Average Kinetic Energy: KE = ½ mv² = ³⁄₂ k_B T

• Root-Mean-Square Speed: u_rms = √(3RT / M)

• Graham's Law: r₁ / r₂ = √(M₂ / M₁)

• van der Waals Equation: (P + n²a/V²) (V – nb) = nRT

Nature of Solutions

A solution is a special type of mixture at the molecular level.

• Homogeneous Mixture: A solution is uniform throughout. Its composition and properties are the same in every sample. It forms a single phase, most commonly liquid.

• Solvation (Dissolution): The process of dissolving. Solvent particles surround and pull apart solute particles through electrostatic interactions.

  • In water, this is specifically called hydration (the water molecules form a "hydration shell" around the solute).

• Energetics of Dissolution:

  • Most dissolutions of solids/liquids are endothermic (absorb heat, feel cold).

  • The dissolution of a gas into a liquid is exothermic (releases heat). This is why gas solubility decreases as temperature rises.

Solubility and rules

• The maximum amount of solute that can dissolve in a solvent at a specific temperature. It defines the saturated concentration. Molar solubility is this limit expressed in mol/L

Soluble

Group 1 ions, C₃H₃O₂^-, and NH₄⁺ = Always soluble

Cl-, Br-, I- = Generally soluble except in Ag⁺, Pb²⁺, and Hg²⁺

SO4^2- = Generally soluble except in Ca²⁺, Ba²⁺, Pb²⁺ and Sr²⁺

Insoluble

OH- = General insoluble except in Na⁺, NH4⁺, Ca²⁺, Ba²⁺, Sr²⁺

S^2-, CO3^2-, PO4^3-, CrO4^2- = General insoluble except in Na⁺, NH4⁺, K⁺, Li²⁺

Complex Ions 

• Complex Ions (Coordination Compounds):

  • A central metal ion bonded to surrounding molecules or anions called ligands. The bond is a coordinate covalent bond where the ligand donates both electrons.

  • Effect on Solubility: Forming a complex ion drastically increases the solubility of otherwise insoluble salts. It consumes the free metal ion product, pulling the dissolution equilibrium to the right. This is the opposite of the common ion effect.

Concentration

These are the different "units" for measuring concentration. Each has a specific use-case.

Unit	Formula	What It's Based On	Best Used For
Percent by Mass	(mass solute / mass solution) × 100%	Based On: Mass	Simple recipes, solid mixtures.
Mole Fraction (X)	X_A = moles A / total moles	Based On: Moles	Gas partial pressures (Dalton's Law), vapor pressure depression (Raoult's Law).
Molarity (M)	M = moles solute / L solution	Based On: Volume of solution	THE most common unit. Used for kinetics, equilibrium (Keq), pH, osmotic pressure.
Molality (m)	m = moles solute / kg solvent	Based On: Mass of solvent	Temperature-dependent properties like boiling point elevation and freezing point depression.
Normality (N)	N = equivalents / L solution	Based On: Equivalents of interest	Acid-base and redox reactions. N = M × n (where n = H⁺, OH⁻, or e⁻).

• Dilution Formula: When you add solvent to a stock solution, the moles of solute stay the same.

  • M_i V_i = M_f V_f

Solution Equilibria

Dissolution of a slightly soluble ionic solid is an equilibrium process.

• Saturated Solution: A solution at equilibrium with undissolved solute. The maximum amount is dissolved. Dissolution and precipitation rates are equal.

• The Solubility Product Constant (Ksp): The equilibrium constant for the dissociation of an ionic solid.

  • For A_m B_n (s) ⇌ m A^{n+} (aq) + n B^{m-} (aq)

  • Ksp = [A^{n+}]^m [B^{m-}]^n (The pure solid reactant is omitted).

• The Ion Product (IP): The same formula as Ksp, but calculated for the current concentrations, not just at equilibrium. It tells you the saturation state.

  • IP < Ksp: Unsaturated. More solid can dissolve.

  • IP = Ksp: Saturated. At equilibrium. No net change.

  • IP > Ksp: Supersaturated. Precipitation will occur to lower the IP to Ksp.

• Factors Affecting Solubility:

  1. Common Ion Effect: Adding a soluble salt that shares an ion with the insoluble salt decreases the solubility of the insoluble salt. It's a direct application of Le Châtelier's principle—adding a product shifts equilibrium left.

  2. Complex Ion Formation: The opposite effect. Adding a ligand that forms a complex with the metal ion increases solubility by consuming the free metal ion product. The formation constant (Kf) for complex ions is usually very large, pulling the equilibrium far to the right.

Colligative Properties

Depend Only on Particle COUNT

Colligative properties are physical changes that depend only on the concentration (number) of dissolved solute particles, not on the chemical identity of those particles.

Vapor Pressure Depression (Raoult's Law)

A nonvolatile solute blocks some solvent molecules from escaping the liquid surface, lowering the evaporation rate while condensation rate remains unchanged.

• Formula: P_A = X_A × P_A° (The new vapor pressure equals the pure solvent vapor pressure times the solvent's mole fraction).

• Since X_A < 1, the vapor pressure is always lowered.

Elevation and Depression

• Boiling Point Elevation: Because vapor pressure is lowered, a higher temperature is required to make it equal atmospheric pressure (the definition of boiling). The boiling point goes up.

  • Formula: ΔT_b = i × K_b × m

    • K_b = ebullioscopic constant (property of the solvent).

    • m = molality.

• Freezing Point Depression: The solute particles disrupt the solvent's ability to form a perfect crystal lattice, requiring a lower temperature to freeze. The freezing point goes down.

  • Formula: ΔT_f = i × K_f × m

    • K_f = cryoscopic constant (property of the solvent).

Osmotic Pressure

• Osmotic Pressure (Π): The pressure required to stop the flow of solvent across a semipermeable membrane. Solvent flows spontaneously from low solute concentration to high solute concentration (osmosis) to try to equalize concentrations.

  • Formula: Π = i × M × R × T (Note the use of Molarity, M).

• The van't Hoff Factor (i): This is the "fudge factor" for solutes that dissociate into multiple particles (like ionic salts).

  • For a non-dissociating covalent solute (like glucose), i = 1.

  • For NaCl, which ideally dissociates into Na⁺ and Cl⁻, i = 2.

  • For CaCl₂, which ideally dissociates into Ca²⁺ and 2Cl⁻, i = 3.

Key Equations Summary

• Percent Composition by Mass: (mass solute / mass solution) × 100%

• Mole Fraction: X_A = moles A / total moles

• Molarity: M = moles solute / L solution

• Molality: m = moles solute / kg solvent

• Dilution: M_i V_i = M_f V_f

• Solubility Product Constant (for AmBn): Ksp = [A^{n+}]^m [B^{m-}]^n

• Ion Product: IP = [A^{n+}]^m [B^{m-}]^n (compare to Ksp)

• Raoult's Law: P_A = X_A × P_A°

• Boiling Point Elevation: ΔT_b = i × K_b × m

• Freezing Point Depression: ΔT_f = i × K_f × m

• Osmotic Pressure: Π = i × M × R × T

Definitions of Acids and Bases

There are three key definitions, each broader and more inclusive than the last.

1. Arrhenius (The Most Specific):

   • Acid: Dissociates in water to produce an excess of H⁺ ions (protons).

   • Base: Dissociates in water to produce an excess of OH⁻ ions (hydroxide).

   • Limitation: Must be in an aqueous solution. Doesn't explain bases like NH₃ without OH⁻.

2. Brønsted–Lowry (The Proton Transfer Definition):

   • Acid: A species that donates a hydrogen ion (H⁺). A proton donor.

   • Base: A species that accepts a hydrogen ion (H⁺). A proton acceptor.

   • Key: This definition created the concept of conjugate acid-base pairs.

3. Lewis (The Most General, The "Electron" Definition):

   • Acid: An electron-pair acceptor. (Thinks: "Loves" electrons, has an empty orbital. e.g., BF₃).

   • Base: An electron-pair donor. (Thinks: "Lends" electrons, has a lone pair. e.g., NH₃).

   • This is the broadest definition and is key for organic chemistry and complex ion formation.

The Nested Relationship: All Arrhenius acids/bases are Brønsted–Lowry. All Brønsted–Lowry acids/bases are Lewis. The reverse is NOT true. A Lewis acid like BF₃ is not a Brønsted–Lowry acid because it doesn't donate a proton.

Amphoteric Species

• Amphoteric: A species that can act as either an acid OR a base, depending on its environment.

• Amphiprotic: A specific type of amphoteric species that can either donate or accept a proton (H⁺). All amphiprotic species are amphoteric, but not all amphoteric species are amphiprotic (a Lewis acid/base that doesn't transfer protons, like a metal oxide, is only amphoteric).

• Classic Example: Water (H₂O)

  • As a base: H₂O + H⁺ → H₃O⁺ (hydronium ion)

  • As an acid: H₂O → H⁺ + OH⁻ (hydroxide ion)

• Polyvalent (Polyprotic) Intermediates: The partially deprotonated forms of polyprotic acids are also amphiprotic (e.g., HCO₃⁻ can donate a proton to become CO₃²⁻ or accept one to become H₂CO₃).

Key Properties

• Water Autoionization: Water spontaneously splits into ions to a tiny extent. 2H₂O ⇌ H₃O⁺ + OH⁻

  • Kw (Ion Product Constant): Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴ at 298 K.

  • Kw is an equilibrium constant and only changes with temperature.

• pH and pOH:

  • pH = –log[H⁺] (Strictly [H₃O⁺])

  • pOH = –log[OH⁻]

  • The Golden Relationship (at 298 K): pH + pOH = 14

• The p-Scale Approximation Trick: p-value ≈ m – 0.n . If [H⁺] = n × 10⁻ᵐ, the pH is approximately (m – 1).(10 – n). Example: [H⁺] = 3 × 10⁻⁸ gives pH ≈ (8 – 1).(10 – 3) = 7.7. (True value is 7.52, a good estimate).

Strong vs. Weak

• Strong Acids/Bases: Dissociate completely. Have a very large or undefined Ka/Kb. Their conjugates are extremely weak (inert) and don't re-react.

• Weak Acids/Bases: Dissociate only partially. Have a small Ka or Kb (equilibrium lies far left). Their conjugates are weak but not inert, and can react.

Acid/Base Dissociation Constants

• Acid: Ka = [H₃O⁺][A⁻] / [HA]

• Base: Kb = [HB⁺][OH⁻] / [B]

• Conjugate Pair Relationship: For a conjugate pair at 298 K, Ka × Kb = Kw = 10⁻¹⁴. The stronger the acid, the weaker its conjugate base.

• Neutralization: Acid + Base → Salt + (sometimes) Water.

Polyvalence and Normality (The "n" Factor Revisited)

• Polyvalent (Polyprotic) Acid/Base: Can donate or accept more than one proton (e.g., H₂SO₄ has 2 protons, Ca(OH)₂ has 2 hydroxides).

• Equivalent: 1 mole of the "species of interest" (H⁺ or OH⁻).

• Normality (N): N = Molarity (M) × n, where n is the number of H⁺ or OH⁻ per formula unit. A 1 M H₂SO₄ solution is 2 N.

• Equivalence Point Calculation: N_a V_a = N_b V_b . This is a direct way to solve titrations, especially with polyvalent species.

Titration and Titration Curves

A titration reveals the pKa of the unknown species and its concentration.

• Titrant: The known solution, added from a buret.

• Titrand (Analyte): The unknown solution, in the flask.

• Half-Equivalence Point: The midpoint of the flat "buffering" region. Exactly HALF of the acid/base has been neutralized.

  • Key Feature: [HA] = [A⁻], so pH = pKa. This is where a buffer is at its most effective.

• Equivalence Point: The point where the number of equivalents of titrant added exactly equals the number of equivalents of titrand present. Steepest slope on the curve.

  • Strong Acid + Strong Base: pH = 7.

  • Weak Acid + Strong Base: pH > 7 (conjugate base is formed, making the solution basic).

  • Weak Base + Strong Acid: pH < 7 (conjugate acid is formed, making the solution acidic).

  • Weak Acid + Weak Base: pH depends on relative strengths (this is a faint, hard-to-detect endpoint).

• Indicator: A weak acid/base whose protonated and deprotonated forms have different colors. Choose an indicator whose pKa is close to the expected equivalence point pH. The color change is the endpoint.

• Polyvalent Titrations: Have multiple buffering regions and equivalence points, one for each proton removed (e.g., H₃PO₄ has three equivalence points).

Buffers

A buffer is a solution that resists dramatic changes in pH when small amounts of acid or base are added. It's made of a weak acid AND its conjugate salt (or a weak base and its conjugate salt) in roughly equal concentrations.

• Mechanism: The weak acid neutralizes added base; the conjugate base neutralizes added acid.

• Buffering Capacity: The ability to resist pH change. It is maximal within ±1 pH unit of the pKa of the weak acid component.

• The Henderson–Hasselbalch Equation (The Buffer Equation):

  • For an acid buffer: pH = pKa + log([A⁻]/[HA])

  • For a base buffer: pOH = pKb + log([HB⁺]/[B])

  • Optimal Buffering: When [A⁻] = [HA], the log term is zero, and pH = pKa.

Key Equations Summary

• Water Autoionization: Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴ at 298 K

• pH/pOH Definition: pH = –log[H⁺], pOH = –log[OH⁻]

• pH + pOH: pH + pOH = 14 at 298 K

• Acid Dissociation: Ka = [H₃O⁺][A⁻] / [HA]

• Base Dissociation: Kb = [HB⁺][OH⁻] / [B]

• Conjugate Pair: Ka × Kb = Kw = 10⁻¹⁴

• Titration Equivalence: NaVa = NbVb

• Henderson–Hasselbalch (Acid): pH = pKa + log([A⁻]/[HA])

• Henderson–Hasselbalch (Base): pOH = pKb + log([HB⁺]/[B])

Oxidation–Reduction (Redox) Reactions

Redox reactions are all about the movement of electrons. They are always paired: you can't have one without the other.

• The Core Definitions (LEO GER):

  • Oxidation Is Loss of electrons. (A substance becomes more positive).

  • Reduction Is Gain of electrons. (A substance becomes more negative).

• The Agents (Think of them as causing the opposite action):

  • Oxidizing Agent: The substance that causes another to be oxidized. It accepts those lost electrons and is itself reduced.

  • Reducing Agent: The substance that causes another to be reduced. It donates electrons and is itself oxidized.

• Common Agents to Recognize:

  • Oxidizing Agents: Often contain oxygen or highly electronegative elements (O₂, F₂, Cl₂, MnO₄⁻, Cr₂O₇²⁻).

  • Reducing Agents: Often contain metals (Na, Zn) or hydrides (H⁻).

Oxidation Numbers

Oxidation numbers are the "accounting" charges assigned to atoms to track electron flow. They don't always represent real ionic charges.

The Hierarchy of Rules (Apply in order; the top rule wins if there's a conflict):

1. Free Element/Diatomic: The oxidation number is always 0. (e.g., Na, Cl₂, O₂, P₄).

2. Monatomic Ion: The oxidation number equals its ionic charge. (e.g., Na⁺ = +1, Cl⁻ = -1).

3. Group IA Metals (Li, Na, K, etc.): Always +1 in a compound.

4. Group IIA Metals (Mg, Ca, etc.): Always +2 in a compound.

5. Hydrogen: Usually +1. The EXCEPTION is when bonded to a less electronegative metal (a metal hydride like NaH), where it is -1.

6. Oxygen: Usually -2. Two EXCEPTIONS:

   • Peroxides (contains O₂²⁻): Oxygen is -1 (e.g., H₂O₂).

   • Bonded to Fluorine (a more electronegative element): Oxygen is +2 (e.g., OF₂).

7. Group VIIA Halogens (F, Cl, Br, I): Usually -1, unless bonded to a more electronegative element (F is always -1).

8. The Sum Rule: The sum of all oxidation numbers in a neutral compound is 0. For a polyatomic ion, the sum equals the overall charge of the ion.

Balancing Redox Reactions

Simple inspection often fails for redox reactions. This systematic method works for both acidic and basic solutions.

1. Separate: Write the two unbalanced half-reactions: one for oxidation, one for reduction.

2. Balance Main Atoms: Balance all atoms EXCEPT H and O.

3. Balance O and H (Depends on Solution):

   • In Acidic Solution: Balance O by adding H₂O. Balance H by adding H⁺.

   • In Basic Solution: Balance O by adding OH⁻. Balance H by adding H₂O. (A trick: balance it as if it's acidic first, then add enough OH⁻ to both sides to neutralize all H⁺ into H₂O).

4. Balance Charge: Add electrons (e⁻) to the more positive side of each half-reaction to make the charges equal on both sides.

5. Equalize Electrons: Multiply each half-reaction by a whole number so that the number of electrons lost in the oxidation half-reaction equals the number gained in the reduction half-reaction.

6. Add and Cancel: Add the two half-reactions together. Cancel out electrons and any other identical species (H₂O, H⁺, OH⁻) that appear on both sides of the arrow.

7. Final Check: Confirm that both mass (atoms) and total charge are balanced.

Net Ionic Equations

• Complete Ionic Equation: Write all soluble, strong electrolytes (aqueous salts, strong acids/bases) as their dissociated ions. Solids, liquids, gases, and weak electrolytes stay written as a formula unit.

• Spectator Ions: Ions that appear unchanged on both the reactant and product sides of the complete ionic equation. They don't participate in the chemical change.

• Net Ionic Equation: Remove the spectator ions. This reveals the actual chemical reaction.

  • For a reaction with no aqueous ionic species, the net ionic equation is the same as the molecular equation.

  • For double-displacement reactions where no precipitate, gas, or liquid water forms, all ions are spectators, and there is no net ionic reaction.

Special Redox Reactions

• Disproportionation (Dismutation) Reactions: A special redox reaction where one element is both oxidized AND reduced. It starts with one oxidation state and ends up forming products in at least two different oxidation states.

  • Classic Example: Hydrogen peroxide decomposition (2H₂O₂ → 2H₂O + O₂). The oxygen in H₂O₂ (oxidation state -1) is both reduced to H₂O (-2) and oxidized to O₂ (0).