MCAT Chemical and Physical Foundations of Biological Systems (C/P) — Study Guide

PowerExams original content. Maps to AAMC Foundational Concepts 4 and 5 (content categories 4A–5E). Quantitative work on the MCAT is calculator-free: lean on estimation, scientific notation, logs, and ratios.

Foundational Concept 4

Complex living organisms transport materials, sense their environment, process signals, and respond to changes using processes that can be understood in terms of physical principles.

4A — Translational Motion, Forces, Work, Energy, and Equilibrium

High-yield ideas. Kinematics describes motion (displacement, velocity, acceleration) without reference to cause; dynamics adds Newton's laws. A body is in translational equilibrium when ΣF = 0 and in rotational equilibrium when Στ = 0. Energy is conserved in an isolated system; non-conservative forces (friction, drag) convert mechanical energy to heat. Simple harmonic motion (SHM) describes any restoring force proportional to displacement (springs, pendula, and—approximately—molecular bonds).

Key equations.

Kinematics (constant a): v = v₀ + at, x = v₀t + ½at², v² = v₀² + 2aΔx
Newton's second law: F = ma
Work: W = Fd·cosθ; Kinetic energy: KE = ½mv²; Gravitational PE: PE = mgh
Work–energy theorem: W_net = ΔKE
Torque: τ = rF·sinθ; Equilibrium: ΣF = 0, Στ = 0
SHM: T_spring = 2π√(m/k), T_pendulum = 2π√(L/g)

Worked example 1 — projectile time. A ball is dropped from rest off a 45 m cliff (g ≈ 10 m/s²). Time to land? Use h = ½gt² → 45 = ½(10)t² → t² = 9 → t = 3 s. Impact speed = gt = 30 m/s.

Worked example 2 — torque balance. A 2 m uniform plank pivots at its center. A 30 N weight hangs 0.8 m left of the pivot. How far right must a 40 N weight hang for balance? Set torques equal: 30(0.8) = 40(d) → 24 = 40d → d = 0.6 m.

4B — Fluids: Circulation, Gas Movement, and Exchange

High-yield ideas. Fluid statics: pressure rises with depth (P = ρgh); buoyant force equals the weight of displaced fluid (Archimedes). Fluid dynamics for ideal fluids: the continuity equation conserves volume flow rate (A₁v₁ = A₂v₂), so a narrower vessel speeds flow; Bernoulli trades pressure for kinetic energy. Real (viscous) flow through a tube follows Poiseuille's law, where radius dominates (r⁴). Gases obey the ideal gas law; in a mixture each gas exerts its partial pressure (Dalton).

Key equations.

Static pressure: P = P₀ + ρgh; Buoyancy: F_b = ρ_fluid·V_displaced·g
Continuity: A₁v₁ = A₂v₂
Bernoulli: P + ½ρv² + ρgh = constant
Poiseuille: Q = πr⁴ΔP / (8ηL)
Ideal gas: PV = nRT (R = 0.0821 L·atm/mol·K); Partial pressure: P_i = x_i·P_total

Worked example 1 — continuity. Blood flows at 0.4 m/s in a vessel of cross-section 6 cm². It enters a constriction of 2 cm². New speed? A₁v₁ = A₂v₂ → 6(0.4) = 2(v₂) → v₂ = 1.2 m/s (3× faster, area cut to one-third).

Worked example 2 — Poiseuille radius. If a vessel's radius doubles at constant driving pressure, flow rate increases by 2⁴ = 16×. A modest vasodilation has an outsized effect on perfusion.

4C — Electrochemistry and Electrical Circuits

High-yield ideas. Coulomb's law governs electrostatic force; like charges repel. Electric field points away from positive charge; potential is energy per charge. In circuits, Ohm's law relates V, I, R. Series resistors add; parallel resistors combine reciprocally and lower total resistance. Capacitors store charge (Q = CV). Electrochemical cells: galvanic (spontaneous, E°cell > 0) generate current; electrolytic (non-spontaneous) consume it. Oxidation occurs at the anode, reduction at the cathode (mnemonic: "an ox, red cat").

Key equations.

Coulomb: F = kq₁q₂/r² (k = 9×10⁹ N·m²/C²)
Ohm: V = IR; Power: P = IV = I²R = V²/R
Series: R_eq = R₁ + R₂ + …; Parallel: 1/R_eq = 1/R₁ + 1/R₂ + …
Capacitor: Q = CV; Energy: U = ½CV²
Cell potential: E°cell = E°cathode − E°anode; ΔG° = −nFE°cell
Nernst (298 K): E = E° − (0.059/n)·log Q

Worked example 1 — parallel resistors. Two 6 Ω resistors in parallel: 1/R = 1/6 + 1/6 = 2/6 → R = 3 Ω. Two equal parallel resistors always give half the single value.

Worked example 2 — ΔG from cell potential. A cell has E°cell = +0.50 V and transfers n = 2 electrons (F ≈ 96,500 C/mol). ΔG° = −nFE° = −(2)(96,500)(0.50) ≈ −96,500 J ≈ −96.5 kJ. Negative ΔG° confirms spontaneity.

4D — How Light and Sound Interact with Matter

High-yield ideas. Sound is a longitudinal pressure wave needing a medium; speed rises in stiffer/denser-bonded media (solids > liquids > gases). The Doppler effect shifts perceived frequency when source and observer move relatively (approaching = higher pitch). Light is electromagnetic and travels in vacuum at c. Geometric optics: reflection (θᵢ = θᵣ), refraction (Snell's law), and image formation by mirrors/lenses via the thin-lens equation. Sign conventions: converging lens/concave mirror have positive focal length.

Key equations.

Wave: v = fλ; Period: T = 1/f
Snell's law: n₁sinθ₁ = n₂sinθ₂; Index: n = c/v
Thin lens/mirror: 1/f = 1/d_o + 1/d_i; Magnification: m = −d_i/d_o
Power of lens: P = 1/f (diopters, f in meters)
Doppler (qualitative): approaching raises f, receding lowers f

Worked example 1 — Snell's law. Light passes from air (n = 1.0) into water (n ≈ 1.33) at 30° incidence. 1.0·sin30° = 1.33·sinθ₂ → sinθ₂ = 0.5/1.33 ≈ 0.376 → θ₂ ≈ 22°. The ray bends toward the normal entering the denser medium.

Worked example 2 — thin lens. An object sits 30 cm from a converging lens of f = 10 cm. 1/10 = 1/30 + 1/d_i → 1/d_i = 1/10 − 1/30 = 3/30 − 1/30 = 2/30 → d_i = 15 cm. Positive d_i means a real, inverted image; m = −15/30 = −0.5 (reduced).

4E — Atoms, Nuclear Decay, Electronic Structure, and Atomic Behavior

High-yield ideas. Electron configurations fill by the Aufbau principle, Hund's rule, and the Pauli exclusion principle; quantum numbers (n, l, mₗ, mₛ) label each electron. Periodic trends: atomic radius decreases left→right and increases down a group; ionization energy and electronegativity rise toward fluorine. Nuclear decay: alpha (loses ⁴₂He), beta-minus (neutron→proton + e⁻), gamma (energy only). Half-life governs exponential decay; binding energy per nucleon peaks near iron.

Key equations.

Quantum numbers: l = 0…(n−1), mₗ = −l…+l
Half-life decay: N = N₀·(½)^(t/t₁/₂)
Mass–energy: E = mc²
Photon energy: E = hf = hc/λ

Worked example 1 — half-life. A radioisotope has t₁/₂ = 8 days. What fraction remains after 24 days? 24/8 = 3 half-lives → (½)³ = 1/8 remains (12.5%).

Worked example 2 — periodic trend. Rank ionization energy: Na, Mg, Al. Trend rises left→right, but Al's 3p¹ electron is easier to remove than Mg's filled 3s², so order is Na < Al < Mg. (A classic exception to the smooth trend.)

Active recall — FC4.

Why does doubling a vessel's radius increase flow 16-fold rather than 4-fold, and which law explains it?
State the sign of ΔG° for a galvanic cell and the equation linking it to E°cell.
After 3 half-lives, what fraction of a sample remains, and is that fraction order-dependent on decay type?

Foundational Concept 5

The principles that govern chemical interactions and reactions form the basis for a broader understanding of the molecular dynamics of living systems.

5A — Water, Solutions, Solubility, Acids/Bases

High-yield ideas. Water's polarity and hydrogen bonding make it an excellent solvent for ionic and polar solutes ("like dissolves like"). pH = −log[H⁺]; pure water at 25 °C has Kw = 10⁻¹⁴, so pH 7 is neutral. Strong acids/bases dissociate completely; weak acids reach equilibrium described by Ka and pKa. The Henderson–Hasselbalch equation predicts buffer pH; buffering is strongest when pH = pKa (equal acid and conjugate base). Colligative properties (freezing-point depression, osmotic pressure) depend on particle count, not identity.

Key equations.

pH = −log[H⁺], pOH = −log[OH⁻], pH + pOH = 14
Ka·Kb = Kw = 10⁻¹⁴; pKa + pKb = 14
Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA])
Osmotic pressure: Π = iMRT; FP depression: ΔTf = i·Kf·m

Worked example 1 — pH of strong acid. 0.001 M HCl fully dissociates → [H⁺] = 10⁻³ → pH = 3. For 0.0005 M HCl, [H⁺] = 5×10⁻⁴, pH = 4 − log5 ≈ 4 − 0.7 = 3.3.

Worked example 2 — buffer. A buffer has [A⁻] = 0.1 M, [HA] = 0.01 M, pKa = 4.7. pH = 4.7 + log(0.1/0.01) = 4.7 + log10 = 4.7 + 1 = 5.7.

5B — Molecules and Intermolecular Interactions

High-yield ideas. Lewis structures and VSEPR predict geometry by minimizing electron-pair repulsion (e.g., 4 bonding pairs → tetrahedral, 109.5°). Molecular polarity arises from polar bonds in an asymmetric arrangement; symmetric molecules (CO₂, CCl₄) are nonpolar despite polar bonds. Intermolecular forces, weakest to strongest: London dispersion < dipole–dipole < hydrogen bonding < ion–dipole. Stronger IMFs raise boiling point. Stereochemistry: enantiomers are non-superimposable mirror images; diastereomers differ at some but not all stereocenters.

Key ideas/relationships.

VSEPR shapes: 2 e⁻ domains = linear; 3 = trigonal planar; 4 = tetrahedral
Boiling point ↑ with IMF strength and (for nonpolar) molar mass
n stereocenters → up to 2ⁿ stereoisomers
Chirality requires four different groups on a carbon

Worked example — IMF ranking. Order boiling points: CH₄, CH₃OH, CH₃CH₃. CH₃OH hydrogen-bonds (highest); CH₃CH₃ has more electrons/larger dispersion than CH₄. Order: CH₄ < CH₃CH₃ < CH₃OH.

5C — Separation and Purification

High-yield ideas. Separations exploit differences in physical properties. Chromatography partitions analytes between a mobile and stationary phase; in normal-phase TLC (polar plate), polar compounds travel less and have lower Rf. Distillation separates by boiling point. Liquid–liquid extraction separates by relative solubility between immiscible solvents (and can be tuned by protonating/deprotonating to switch a compound's solubility). Electrophoresis separates by charge and size; gel filtration (size-exclusion) elutes large molecules first.

Key ideas.

Rf = (distance traveled by spot) / (distance traveled by solvent front) (0 < Rf < 1)
Lower boiling point distills first
Size-exclusion: large molecules elute first (excluded from pores)
SDS-PAGE: migration distance ∝ inverse of molecular weight (small = farther)

Worked example — Rf. A spot moves 3.0 cm; the solvent front moves 6.0 cm. Rf = 3.0/6.0 = 0.50. On a polar (silica) plate, a more polar compound would show a smaller Rf.

5D — Structure, Function, and Reactivity of Biological Molecules

High-yield ideas. Functional groups dictate reactivity: alcohols, aldehydes/ketones (carbonyl), carboxylic acids and derivatives (acyl), amines. Nucleophilic substitution: SN2 is one-step, bimolecular, with inversion (favored by strong nucleophile, unhindered primary carbon); SN1 is two-step via a carbocation (favored by tertiary substrate, polar protic solvent). Biomolecules: amino acids link by peptide bonds; carbohydrates form glycosidic bonds; nucleotides carry phosphates; lipids store energy and form membranes. Spectroscopy IDs structure: IR detects functional groups (broad O–H ~3300, C=O ~1700 cm⁻¹), ¹H NMR counts proton environments, mass spec gives molecular weight.

Key ideas.

SN2: rate = k[substrate][nucleophile]; backside attack → inversion
SN1: rate = k[substrate]; planar carbocation → racemization
IR: O–H broad ~3200–3550, C=O sharp ~1700 cm⁻¹
Peptide bond = amide linking carboxyl of one residue to amine of next

Worked example — IR diagnosis. An unknown shows a strong absorption near 1715 cm⁻¹ and no broad band near 3300 cm⁻¹. This indicates a carbonyl (C=O) without O–H or N–H — consistent with a ketone or aldehyde, not a carboxylic acid or alcohol.

5E — Chemical Thermodynamics and Kinetics

High-yield ideas. Thermodynamics asks whether a reaction is favorable: ΔG = ΔH − TΔS. Negative ΔG = spontaneous (exergonic). ΔG° = −RT·lnK, so K > 1 when ΔG° < 0. Le Chatelier predicts how equilibrium shifts when stressed. Kinetics asks how fast: the rate law (rate = k[A]^m[B]^n) and reaction order come from experiment, not stoichiometry. Activation energy is the barrier; catalysts lower Ea (and raise k) without changing ΔG or K. The Arrhenius relationship shows rate rises with temperature.

Key equations.

ΔG = ΔH − TΔS; ΔG° = −RT·lnK
Rate law: rate = k[A]^m[B]^n; overall order = m + n
Integrated first-order: ln[A] = ln[A]₀ − kt; first-order half-life t₁/₂ = 0.693/k
Arrhenius: k = A·e^(−Ea/RT)

Worked example 1 — spontaneity sign analysis. A reaction has ΔH = +40 kJ/mol and ΔS = +0.1 kJ/(mol·K). At what temperature does it become spontaneous? Set ΔG = 0: T = ΔH/ΔS = 40/0.1 = 400 K. Above 400 K, TΔS exceeds ΔH and ΔG < 0.

Worked example 2 — rate order from data. Doubling [A] quadruples the rate while [B] is held constant → reaction is second order in A (2² = 4). If doubling [B] leaves the rate unchanged, it is zero order in B. Overall order = 2.

Active recall — FC5.

Write Henderson–Hasselbalch and state the [A⁻]/[HA] ratio at which pH = pKa.
Contrast SN1 and SN2 in rate law, stereochemical outcome, and favored substrate.
Does a catalyst change ΔG°, K, or Ea? For a reaction with ΔH > 0 and ΔS > 0, how does raising T affect spontaneity?