MCAT Chem/Phys cheat sheet

Ideal gas law: PV = nRT, with R = 0.0821 L·atm/(mol·K); at STP (0 °C, 1 atm) one mole of gas occupies 22.4 L, and density = PM/RT.

pH = −log[H3O+] and pOH = −log[OH−]; at 25 °C pH + pOH = 14; for a weak acid of concentration C, [H3O+] ≈ √(Ka·C) when dissociation is small.

Henderson–Hasselbalch: pH = pKa + log([A−]/[HA]); a buffer resists pH change most effectively within about ±1 pH unit of its pKa.

ΔG° = −RT ln K = ΔH° − TΔS°; a reaction is spontaneous as written when ΔG < 0, and at equilibrium ΔG = 0 with Q = K.

Le Châtelier's principle: raising pressure shifts a gas-phase equilibrium toward the side with fewer moles of gas; adding an inert gas at constant volume has no effect on the position of equilibrium.

Solubility product for A_aB_b is Ksp = [A]^a[B]^b; adding a common ion lowers solubility; colligative relations are ΔTb = iKb·m, ΔTf = −iKf·m, and π = iMRT.

Periodic trends: atomic radius decreases left to right across a period and increases down a group; ionization energy and electronegativity increase across a period and decrease down a group.

Rate law: rate = k[A]^m[B]^n; half-life is [A]0/(2k) for zero order and 0.693/k for first order; the Arrhenius equation k = A·e^(−Ea/RT) shows rate rises with temperature.

Calorimetry: q = mcΔT and qreaction = −qcalorimeter; at constant pressure ΔH = qp, and at constant volume ΔU = qv.

Approximate side-chain pKa values: Asp and Glu ~4, His ~6, Cys ~8, Tyr ~10, Lys ~10.5, Arg ~12.5; the peptide bond is an amide and has no acidic proton.

Amino acid charge rule: at pH below the pI the molecule is protonated and net positive; at pH above the pI it is deprotonated and net negative; at the pI net charge is zero.

Michaelis–Menten: v = Vmax[S]/(Km + [S]); Km equals the substrate concentration at half-maximal velocity, and on a Lineweaver–Burk plot the y-intercept is 1/Vmax and the x-intercept is −1/Km.

Competitive inhibition raises apparent Km with unchanged Vmax; noncompetitive inhibition lowers Vmax with unchanged Km; uncompetitive inhibition lowers both Vmax and Km.

Glycolysis converts one glucose to two pyruvate with a net yield of 2 ATP and 2 NADH; the committed, rate-limiting step is catalyzed by phosphofructokinase-1.

Per acetyl-CoA, the TCA cycle yields 3 NADH, 1 FADH2, 1 GTP, and 2 CO2; oxidative phosphorylation yields roughly 2.5 ATP per NADH and 1.5 ATP per FADH2.

β-oxidation of a saturated fatty acid with n carbons yields n/2 acetyl-CoA, (n/2 − 1) NADH, and (n/2 − 1) FADH2 before the acetyl-CoA enters the TCA cycle.

Protein structure levels: primary is amino acid sequence; secondary is α-helix and β-sheet stabilized by backbone hydrogen bonds; tertiary is the overall 3-D fold; quaternary is the assembly of multiple subunits.

Hemoglobin binds O2 cooperatively, giving a sigmoidal dissociation curve that is right-shifted by H+, CO2, and 2,3-BPG; myoglobin binds noncooperatively with a hyperbolic curve.

Constant-acceleration kinematics: v = v0 + at, x = x0 + v0t + ½at², and v² = v0² + 2aΔx; projectile horizontal velocity is constant while vertical acceleration is −g.

Newton's second law: ΣF = ma; static friction satisfies f ≤ μsN; on a frictionless incline the component of gravity along the plane is mg·sinθ.

Work–energy theorem: Wnet = Fd·cosθ = ΔKE; mechanical energy (KE + PE) is conserved only when nonconservative work is zero.

Momentum and impulse: p = mv and J = FΔt = Δp; momentum is conserved in all collisions of an isolated system, but kinetic energy is conserved only in elastic collisions.

Circular motion: centripetal acceleration a_c = v²/r and force F_c = mv²/r; period T = 2πr/v.

Fluids: P = P0 + ρgh; buoyant force equals the weight of displaced fluid, ρfluid·Vdisplaced·g; continuity gives A1v1 = A2v2, and Bernoulli gives P + ½ρv² + ρgh = constant.

Circuits: V = IR; resistors add in series and add as reciprocals in parallel; P = IV = I²R = V²/R; capacitors add in parallel and add as reciprocals in series.

Waves and optics: v = fλ; Snell's law n1·sinθ1 = n2·sinθ2; total internal reflection occurs when light travels from higher to lower n and the incident angle exceeds θc, where sinθc = n2/n1.

Thermodynamics: first law ΔU = Q − W; heat-engine efficiency e = W/QH; the entropy of the universe increases in every spontaneous process.

Hybridization from electron groups: four groups give sp3 and 109.5°, three give sp2 and 120°, two give sp and 180°; a lone pair counts as one group.

Hückel aromaticity: the ring must be cyclic, planar, fully conjugated, and contain 4n + 2 π electrons; 4n π electrons give antiaromatic behavior.

SN2 is a concerted backside displacement with inversion of configuration, favored by methyl or primary substrates, strong nucleophiles, and polar aprotic solvents.

SN1 proceeds through a carbocation and gives racemization, favored by tertiary substrates and polar protic solvents; E1 shares the carbocation intermediate and is favored by heat.

E2 requires an anti-periplanar β-hydrogen and a strong base; bulky bases favor Hofmann (less substituted) alkene products.

Acidity trends: resonance stabilization and electronegative atoms increase acidity, alkyl groups decrease it; typical pKa values are ~5 for carboxylic acids, ~16 for alcohols, and ~38 for amines.

IR absorptions: broad O–H at 3200–3600 cm−1, N–H near 3300 cm−1, strong C=O near 1700 cm−1, sp3 C–H just below 3000 cm−1, and sp2 C–H just above 3000 cm−1.

1H NMR: signal count equals the number of distinct proton environments; integration gives relative proton counts; n equivalent neighbors split a signal into n + 1 peaks; higher ppm means more deshielded.

Stereochemistry: assign R/S by CIP priority; swapping two groups inverts configuration; a meso compound contains stereocenters but is achiral because of internal symmetry.

Central dogma: DNA is transcribed to RNA by RNA polymerase and translated to protein by ribosomes; DNA replication is semiconservative and new strands grow 5′ to 3′.

Mitosis produces two genetically identical diploid cells; meiosis uses one replication and two divisions to produce four haploid, genetically distinct gametes.

Mendelian ratios: a monohybrid cross of heterozygotes gives a 3:1 phenotype ratio and 1:2:1 genotype ratio; a dihybrid cross of unlinked genes gives 9:3:3:1.

Membrane transport: simple and facilitated diffusion follow the concentration gradient without ATP; primary active transport uses ATP, and the Na+/K+ ATPase moves 3 Na+ out and 2 K+ in per ATP.

Prokaryotes lack membrane-bound organelles and have 70S ribosomes; eukaryotes have 80S ribosomes, membrane-bound organelles, and mitochondria and chloroplasts that carry their own DNA.

Peptide hormones bind cell-surface receptors and signal through second messengers; steroid hormones are lipid-soluble, enter the cell, and bind intracellular receptors that alter transcription.

Hardy–Weinberg equilibrium requires no mutation, no migration, no selection, infinite population size, and random mating; genotype frequencies are p² + 2pq + q² = 1.

Cell-cycle checkpoints occur at G1/S and G2/M; p53 responds to DNA damage by halting the cycle or triggering apoptosis, which is programmed cell death.