MCAT Chemistry

Atomic number (Z) vs mass number (A)

Z = number of protons (defines the element). A = protons + neutrons. Neutrons = A − Z.

Isotopes

Same element (same Z, same protons) but different number of neutrons, so different mass number A. Same chemical behaviour, different mass.

Atomic mass vs atomic weight

Atomic mass ≈ mass of one specific isotope (amu).

Atomic weight = weighted average of all naturally occurring isotopes (the value on the periodic table).

Bohr model — key idea

Electrons orbit the nucleus in fixed, quantised energy levels. Light is emitted/absorbed only when an electron jumps between levels; energy of photon = ΔE between shells.

Emission vs absorption spectrum

Absorption = electron jumps UP a level (absorbs a photon of specific energy). Emission = electron falls DOWN (emits a photon). Lines correspond to discrete ΔE values.

Quantum numbers — n

Principal quantum number (n = 1,2,3...). Sets the shell / energy level and size. Max electrons in a shell = 2n².

Quantum numbers — l

Azimuthal/angular momentum (l = 0 to n−1). Sets subshell/shape: l=0 s, l=1 p, l=2 d, l=3 f.

Quantum numbers — ml

Magnetic quantum number (ml = −l...0...+l). Specifies the orbital orientation. Number of orbitals in a subshell = 2l+1.

Quantum numbers — ms

Spin (ms = +½ or −½). Each orbital holds at most 2 electrons with opposite spins.

Pauli exclusion principle

No two electrons in an atom can have the same set of all four quantum numbers; an orbital holds max 2 electrons with opposite spin.

Hund's rule

Electrons fill degenerate (equal-energy) orbitals singly with parallel spins before pairing up — minimises repulsion.

Aufbau principle

Electrons fill lowest-energy orbitals first. Order: 1s 2s 2p 3s 3p 4s 3d 4p… (note 4s fills before 3d).

Paramagnetic vs diamagnetic

Paramagnetic = has unpaired electrons, attracted to a magnetic field. Diamagnetic = all electrons paired, slightly repelled.

Heisenberg uncertainty principle

You cannot simultaneously know an electron's exact position and momentum; the more precisely one is known, the less precisely the other.

Ground vs excited state

Ground state = electrons in lowest available energy configuration. Excited state = one or more electrons promoted to higher orbitals after absorbing energy.

Common stable-configuration exceptions (Cr, Cu)

Cr is [Ar]4s¹3d⁵ and Cu is [Ar]4s¹3d¹⁰ — a half-filled or fully-filled d subshell is extra stable, so one 4s electron shifts.

Valence electrons

Outermost-shell electrons involved in bonding. For main-group elements they equal the group number's ones digit (e.g. group 16 → 6 valence e⁻).

Effective nuclear charge (Zeff)

Net positive charge an electron actually feels = Z − shielding by inner electrons. Increases across a period → pulls electrons in tighter.

Atomic radius trend

Decreases left→right across a period (rising Zeff). Increases top→bottom down a group (more shells).

Ionization energy trend

Energy to remove an electron. Increases left→right and bottom→top (opposite of atomic radius).

Electron affinity trend

Energy released when an atom gains an electron; generally more negative toward the upper right. Many exceptions: noble gases are unfavourable, and Cl is actually more favourable (more negative) than F due to F's small size and electron–electron repulsion.

Electronegativity trend

Tendency to attract bonding electrons. Increases toward upper right; F is the most electronegative.

Cation vs anion size

Cations are SMALLER than the parent atom (lost a shell / higher Zeff per e⁻). Anions are LARGER (added e⁻, more repulsion).

Metallic character trend

Increases down and to the left. Metals lose electrons easily (low ionisation energy).

Groups to know

1 = alkali metals, 2 = alkaline earth, 17 = halogens, 18 = noble gases, plus transition metals (d-block). Halogens are highly reactive nonmetals; noble gases are inert.

Metalloids

Elements with intermediate properties along the staircase (e.g. B, Si, Ge, As, Sb, Te) — often semiconductors.

Successive ionization energies

Each successive electron is harder to remove. A huge jump occurs after the valence shell is emptied (removing a core electron).

Alpha decay (α)

Emits a ⁴₂He nucleus. Mass number −4, atomic number −2. Weakly penetrating (stopped by paper/skin).

Beta-minus decay (β⁻)

A neutron → proton + emitted electron. Atomic number +1, mass number unchanged.

Beta-plus / positron decay (β⁺)

A proton → neutron + emitted positron. Atomic number −1, mass number unchanged.

Electron capture

Nucleus captures an inner electron; a proton → neutron. Atomic number −1, mass number unchanged.

Gamma decay (γ)

Emission of a high-energy photon; no change in mass or atomic number. Most penetrating radiation.

Half-life (t½)

Time for half of a radioactive sample to decay. After n half-lives, fraction remaining = (1/2)ⁿ. First-order process.

Mass defect & binding energy

The nucleus weighs slightly less than its parts; the missing mass converted to binding energy via E = mc². Higher binding energy per nucleon = more stable.

Fission vs fusion

Fission = splitting a heavy nucleus into lighter ones.

Fusion = combining light nuclei into a heavier one.

Both release energy by increasing binding energy per nucleon.

Ionic vs covalent vs metallic

Ionic = electron transfer (metal + nonmetal). Covalent = electron sharing (nonmetals). Metallic = delocalised 'sea' of electrons.

Polar vs nonpolar covalent

Nonpolar: ΔEN ≈ 0–0.4 (shared evenly).

Polar: ΔEN ≈ 0.5–1.7 (partial charges). >~1.7 → largely ionic.

These ΔEN cutoffs are rough guidelines, not strict rules.

Octet rule & exceptions

Atoms tend toward 8 valence electrons. Exceptions: H/He (2), incomplete octets (B, Be), expanded octets (P, S, Cl and beyond, period 3+).

Formal charge

FC = (valence e⁻) − (nonbonding e⁻) − ½(bonding e⁻). Best Lewis structure minimises formal charges and puts negative FC on the most electronegative atom.

Resonance

When a molecule's bonding can be drawn multiple valid ways; the true structure is a delocalised hybrid (weighted average). Delocalisation = stability.

Sigma (σ) vs pi (π) bonds

σ = head-on overlap, free rotation, present in every bond. π = side-on p-orbital overlap, no rotation. Single = 1σ; double = 1σ+1π; triple = 1σ+2π.

Bond order vs length vs strength

Higher bond order (triple>double>single) → shorter and stronger bond. Resonance gives fractional bond orders.

VSEPR — premise

Electron domains (bonds + lone pairs) repel and arrange to maximise separation, setting molecular geometry.

VSEPR geometries

2 domains linear (180°); 3 trigonal planar (120°); 4 tetrahedral (109.5°); 5 trigonal bipyramidal; 6 octahedral (90°).

Lone pairs & bond angle

Lone pairs repel more than bonding pairs, compressing bond angles (e.g. H2O ~104.5°, NH3 ~107° vs ideal 109.5°).

Hybridisation from domains

2 domains = sp (linear); 3 = sp² (trig planar); 4 = sp³ (tetrahedral). Count electron domains on the central atom.

Molecular polarity

Polar if bond dipoles do NOT cancel (asymmetric, e.g. H2O, NH3). Nonpolar if symmetric dipoles cancel (e.g. CO2, CCl4).

Lewis acid vs base

Lewis acid = electron-pair acceptor (electrophile). Lewis base = electron-pair donor (nucleophile).

Coordinate (dative) bond

A covalent bond where both shared electrons come from the same atom (e.g. in NH4⁺ or metal complexes).

Ranking of intermolecular forces

Strongest→weakest: ion–dipole > hydrogen bonding > dipole–dipole > London dispersion (van der Waals).

London dispersion forces

Temporary induced dipoles present in ALL molecules; the only force in nonpolar molecules. Stronger with greater molar mass / surface area (more polarisable).

Hydrogen bonding requirement

An H bonded to F, O or N interacting with a lone pair on another F/O/N.

Explains water's high boiling point, surface tension, ice density.

FON - Full Of Nonsense

IMF effect on physical properties

Stronger IMFs → higher boiling/melting point, higher viscosity & surface tension, lower vapour pressure.

Why ice floats

Hydrogen bonding locks water into an open hexagonal lattice, making solid water LESS dense than liquid.

The mole & Avogadro's number

1 mole = 6.022×10²³ particles. Moles = mass / molar mass. The bridge between grams and number of particles.

Empirical vs molecular formula

Empirical = simplest whole-number ratio of atoms (e.g. CH2O). Molecular = actual numbers (e.g. C6H12O6). Molecular = (empirical) × n.

Limiting reagent

The reactant that runs out first and caps product yield. Convert all reactants to moles of product; the smallest amount is limiting.

Percent yield

% yield = (actual yield / theoretical yield) × 100. Theoretical yield is based on the limiting reagent.

Types of reactions

Combination, decomposition, single replacement, double replacement (metathesis), combustion, and acid–base neutralisation.

Net ionic equation

Shows only species that change; spectator ions (unchanged on both sides) are cancelled out.

Solubility rules (key ones)

Always soluble: group 1, NH4⁺, NO3⁻, most acetates.

Generally insoluble: most carbonates, phosphates, sulfides, hydroxides (except group 1/2).

Balancing — conservation of mass

Atoms of each element must be equal on both sides; adjust coefficients only, never subscripts.

Dilution equation

M1V1 = M2V2. Moles of solute stay constant when you add solvent; use it for any dilution.

Mass percent

% by mass = (mass of solute / mass of solution) × 100. Mass of solution = solute + solvent.

Parts per million (ppm)

ppm = mg of solute per L of dilute aqueous solution (since 1 L water ≈ 1 kg = 10⁶ mg, 1 mg/L ≈ 1 ppm).

Percent composition

% of an element = (mass of that element in 1 mol / molar mass of compound) × 100.

Molecular formula from empirical

Molecular formula = empirical formula × n, where n = (molecular molar mass / empirical formula mass), rounded to the nearest integer.

Titration mole ratios

At equivalence, moles acid H⁺ = moles base OH⁻. M_aV_a = M_bV_b ONLY holds for a 1:1 reaction; otherwise scale by the balanced-equation ratio.

Serial dilution

Each step multiplies the dilution factor; total dilution = product of all step factors (e.g. three 1:10 steps = 1:1000).

Ideal Gas Law

PV = nRT. Relates pressure, volume, moles, and temperature (T in Kelvin). R = 0.0821 L·atm/mol·K.

Kinetic molecular theory assumptions

Gas particles: have negligible volume, no intermolecular forces, undergo elastic collisions, and have average KE proportional to absolute temperature.

Boyle's law

At constant T, n: P ∝ 1/V (P1V1 = P2V2). Squeeze the volume → pressure rises.

Charles's law

At constant P, n: V ∝ T (V1/T1 = V2/T2). Heat a gas → it expands.

Avogadro's law

At constant T, P: V ∝ n. Equal volumes of gases hold equal numbers of molecules. 1 mol gas = 22.4 L at STP.

Dalton's law of partial pressures

Total pressure = sum of partial pressures. Partial pressure = mole fraction × total pressure.

Graham's law of effusion

Rate ∝ 1/√(molar mass).

Lighter gases effuse/diffuse faster.

(rate1/rate2 = √(M2/M1))

Real gas deviations

Real gases deviate from ideal at HIGH pressure and LOW temperature (molecular volume and IMFs matter). Van der Waals equation corrects for both.

Henry's law

Gas solubility in a liquid is proportional to its partial pressure above the liquid (more pressure → more dissolved gas).

Molarity

M = moles of solute / litres of solution. The most common MCAT concentration unit.

Molality

m = moles of solute / kg of solvent. Used for colligative properties (temperature-independent).

Solubility product (Ksp)

Equilibrium constant for a slightly soluble salt dissolving. Larger Ksp = more soluble. Pure solids/liquids excluded from the expression.

Common-ion effect

Adding an ion already present in a dissolved salt shifts equilibrium back (Le Châtelier), DECREASING solubility.

Solubility vs pH

Salts of weak acids/bases become more soluble in solutions that consume their ions (e.g. carbonates and hydroxides dissolve more in acid).

Colligative properties — definition

Depend on the NUMBER of dissolved particles, not their identity: vapour-pressure lowering, boiling-point elevation, freezing-point depression, osmotic pressure.

Van 't Hoff factor (i)

Number of particles a solute dissociates into (NaCl → i≈2, glucose → i=1). Multiplies colligative effects.

Boiling-point elevation / freezing-point depression

ΔTb = i·Kb·m (raises BP); ΔTf = i·Kf·m (lowers FP). Adding solute makes solutions boil higher and freeze lower.

Osmotic pressure

Π = iMRT. Pressure needed to stop solvent flowing across a semipermeable membrane toward higher solute concentration.

Electrolytes

Strong electrolytes fully dissociate (strong acids/bases, soluble salts) and conduct well; weak electrolytes partially dissociate.

'Like dissolves like'

Polar/ionic solutes dissolve in polar solvents; nonpolar solutes dissolve in nonpolar solvents.

Brønsted–Lowry definition

Acid = proton (H⁺) donor; base = proton acceptor.

Arrhenius vs Brønsted vs Lewis

Arrhenius: produces H⁺ / OH⁻ in water. Brønsted–Lowry: donates/accepts H⁺. Lewis: accepts/donates an electron pair (broadest).

Conjugate acid–base pair

Differ by one H⁺ (e.g. NH4⁺/NH3, CH3COOH/CH3COO⁻). A strong acid has a weak conjugate base, and vice versa.

Strong acids (memorise)

HCl, HBr, HI, HNO3, H2SO4, HClO4 (and HClO3). They dissociate completely. Mnemonic: 'So I Brought No Clean Clothes'. Note: H2SO4 is fully strong only for its first proton; the second (HSO4⁻) is weak.

Strong bases

Group 1 hydroxides (NaOH, KOH) and the heavier group 2 hydroxides (Ca(OH)2, Sr(OH)2, Ba(OH)2) dissociate completely. Mg(OH)2 is a strong base in principle but only sparingly soluble, so it produces little [OH⁻].

Kw and pH of water

Kw = [H⁺][OH⁻] = 1×10⁻¹⁴ at 25°C. Pure water: [H⁺]=[OH⁻]=10⁻⁷, pH=7 (neutral).

pH and pOH

pH = −log[H⁺]; pOH = −log[OH⁻]; pH + pOH = 14 (at 25°C). Each pH unit = 10× change in [H⁺].

Ka, Kb, pKa, pKb

Ka = acid dissociation constant (larger = stronger acid). pKa = −log Ka (smaller = stronger acid). pKa + pKb = 14 for a conjugate pair.

Hydrolysis of salts

Salt of strong acid + weak base → acidic solution.

Salt of weak acid + strong base → basic.

Salt of strong acid + strong base → neutral.

Amphoteric species

Can act as either acid or base (e.g. water, HCO3⁻, HSO4⁻, amino acids).

Polyprotic acids

Donate more than one H⁺ (e.g. H2SO4, H3PO4) in successive steps, each with its own Ka (Ka1 > Ka2 > Ka3).