Comprehensive MCAT Quick-Reference

General Chemistry

Atomic Structure

• Rutherford (1911): nucleus surrounded by electrons; Bohr (1913): quantized circular orbits (farther $\Rightarrow$ higher E).
• Photon emitted when $n \downarrow$; absorbed when $n \uparrow$.
• Heisenberg Uncertainty: simultaneous exact $x$ & $p$ impossible.
• Hund: fill each degenerate orbital singly first.
• Pauli: paired e⁻ must have opposite spins.
• Aufbau: build from lowest E upward.
• Quantum #’s
  • $n$ (principal): shell, max e⁻ $=2n^2$.
  • $\ell$ (azimuthal): 3-D shape; s,p,d,f ($\ell=0,1,2,3$). Max e⁻ /subshell $=4\ell+2$.
  • $m_\ell$: orbital sub-type ($-\ell\,..\,+\ell$).
  • $m_s$: +½ or –½.
• Free radical = species w/ unpaired e⁻.
• Diamagnetic: all paired $\Rightarrow$ repel B-field; Paramagnetic: ≥1 unpaired $\Rightarrow$ attracted.
• Constants: $h=6.626\times10^{-34}\,\text{J·s}$, $c=3.0\times10^{8}\,\text{m·s}^{-1}$, $N_A=6.022\times10^{23}\,\text{mol}^{-1}$.
• Light: $E=hf=hc/\lambda$.

Periodic Table Trends

• $Z_{\text{eff}}$ ↑ left→right; atomic size ↓ left→right & ↑ top→bottom.
• Ionization Energy, Electron Affinity, Electronegativity: all ↑ up & right (F highest EN = 3.98).
• Noble gases: no EA, EN≈0 (except Kr, Xe).
• Cations < neutrals < anions (size).

Bonding & Geometry (VSEPR)

• Hybrid counts = steric #.
• Key shapes, bond angles: linear $sp$ $180°$; trigonal planar $sp^2$ $120°$; tetrahedral $sp^3$ $109.5°$; trig.-bipyram $sp^3d$ $90/120°$; octahedral $sp^3d^2$ $90°$.
• Bond order ↑ ⇒ length ↓, energy ↑, strength ↑.
• $\Delta EN$
• IMFs: London < dipole-dipole < H-bond (O-H, N-H, F-H).
• Formal charge $=\text{valence}-\text{dots}-\text{sticks}$.

Stoichiometry & Reaction Types

• Combustion: hydrocarbon + $O<em>2$ ⇒ $CO</em>2$ + $H_2O$.
• Single vs Double displacement; Neutralization (acid+base→salt+$H_2O$).
• Equivalents: $n=\frac{mass}{g\,equiv.wt}$; $N=n/L$.
• Ion nomenclature: Fe²⁺ iron(II)/ferrous; polyatomic ending ‑ate>-ite (more vs less O). Hyper-/hypo- prefixes for extremes.

Chemical Kinetics

• Rate Law: $rate=k[A]^m[B]^n$ (experimentally determined!).
• Arrhenius $k=Ae^{-E_a/RT}$; ↑T or ↑A ⇒ ↑k.
• Rate orders: 0th $t<em>{1/2}= [A]</em>0 /(2k)$ M/s, 1st $t<em>{1/2}=\ln2/k$ s, 2nd $t</em>{1/2}=1/(k[A]_0)$ 1/(M·s).
• Catalysts lower $E_a$, don’t affect Keq.

Equilibrium & Le Châtelier

• $K_{eq}=\frac{[C]^c[D]^d}{[A]^a[B]^b}$ (no solids/liquids).
• If Q<K shift → products (ΔG<0).
• Bicarbonate buffer: $CO<em>2+H</em>2O⇌H<em>2CO</em>3⇌H^++HCO_3^-$; hyperventilation ↓[CO₂] ↑pH.
• Kinetic vs Thermodynamic product: low-T, fast vs high-T, more stable.

Thermochemistry

• $\Delta H,\,\Delta S$ state functions. $\Delta G=\Delta H-T\Delta S$.
• Phase change enthalpies additive (Hess). $\Delta H<em>{rxn}=\Sigma\Delta H</em>f^{prod}-\Sigma\Delta H_f^{react}$.
• Gibbs & equilibrium: $\Delta G^°=-RT\ln K_{eq}$; $\Delta G=\Delta G^°+RT\ln Q$.

Gas Laws

• Ideal Gas: $PV=nRT$; STP 1 mol gas = 22.4 L.
• Combined $P<em>1V</em>1/T<em>1=P</em>2V<em>2/T</em>2$.
• Graham: $r\propto1/\sqrt{M}$ diffusion/effusion.
• Real gases deviate: low T, high P.

Solutions & Colligative Props

• $K_{sp}$ vs IP determines saturation. Common ion ↓solubility.
• Raoult: $P<em>A=X</em>A P<em>A^°$; Boil-point elevation $\Delta T</em>b=iK<em>b m$; Freeze depression analog $\Delta T</em>f=iK_f m$.
• Osmotic $\Pi=iMRT$.

Acids–Bases

• $pH=-\log[H^+]$; $K_w=10^{-14}$.
• $pK<em>a+pK</em>b=14$ conjugate pairs.
• Henderson-Hasselbalch: $pH=pK_a+\log([A^-]/[HA])$ (buffers max within ±1).
• Titration equivalence: $N<em>aV</em>a=N<em>bV</em>b$.

Redox & Electrochemistry

• Ox# bookkeeping: free element 0, group 1 +1, F –1, O –2 etc.
• Galvanic: spontaneous (+E°cell, –ΔG); anode– (oxidation), cathode+.
• Electrolytic: non-spont (–E°cell), anode+, cathode–.
• Nernst: $E=E^°-\frac{0.0592}{n}\log Q$ at 298 K.

Organic Chemistry

Nomenclature & Isomers

• IUPAC: parent chain incl highest priority FG; number to give FG lowest #; prefix substituents alphabetically.
• Conformational (chair: axial vs eq); Configurational: enantiomers (optically active unless racemic, meso). $R/S$ (CIP), $E/Z$.

Bonding & Resonance

• Hybridization $sp,sp^2,sp^3$ 25/33/50% s-char respectively; multiple bonds restrict rotation; conjugation stabilizes via resonance.

Reaction Principles

• Nucleophiles: e-rich (lone pairs, π); strength ↑ with ¯EN, ¯sterics, ↑¬charge.
• Electrophiles: e-poor (carbocations, carbonyl C).
• Sn1 (2-step, tertiary, racemic) vs Sn2 (backside, inversion, primary preferred).
• Oxidation increases bonds to O, reduction increases bonds to H.

Spectroscopy

• IR key peaks: O–H broad 3000-3300 cm⁻¹; N–H sharp 3300; C=O sharp 1700.
• ¹H-NMR: deshield downfield. Splitting n+1 rule. Common shifts: aldehyde ~10 ppm, COOH 12, aromatic 6-8, alkyl 0-3.

Biochemistry

Amino Acids & Proteins

• All chiral L (S) except cysteine (R) and glycine achiral.
• pI neutral AA $=\frac{pK<em>{COOH}+pK</em>{NH3}}{2}$; acidic use first two pKa, basic use last two.
• Levels: 1° sequence; 2° α-helix β-sheet (H-bond); 3° hydrophobic/acid-base/disulfide; 4° subunits.

Enzymes

• Lower $E_a$, no ΔG change. Kcat/Vmax definitions. Regulation by feedback, phosphorylation, zymogens.
• Inhibition summary: competitive ↑Km, same Vmax; non-competitive ↓Vmax same Km; uncompetitive ↓both.

Metabolism Overview

• Glycolysis (cytosol) net $+2\,ATP,+2\,NADH$; key enzymes hexokinase, PFK-1, pyruvate kinase.
• PDH: pyruvate → Acetyl-CoA + $NADH$.
• TCA (matrix): per acetyl-CoA: $3\,NADH,1\,FADH_2,1\,GTP$.
• ETC: complexes I-IV create proton gradient; ATP synthase chemiosmosis (≈32 ATP/glucose).
• Gluconeogenesis (liver): bypass enzymes PC/PEPCK, F-1,6-BPase, G-6-Pase.
• Glycogen regulation: synthase vs phosphorylase.
• PPP: G-6-PDH rate-limiting, makes $NADPH$ & ribose-5-P.
• β-Oxidation: fatty acyl-CoA (mito) → acetyl-CoA + $FADH_2+NADH$ per cycle.
• Fatty acid synthase (cytosol) needs NADPH, acetyl-CoA carboxylase (biotin, CO₂).
• Urea cycle disposes NH₃.

Hormone Highlights

• Peptide (fast, membrane), steroid (slow, nuclear), aa-derivative.
• Insulin (β-cells) ↓ glucose; glucagon (α) ↑; somatostatin (δ) inhibits both.
• Cortisol ↑ gluconeogenesis; catecholamines ↑ glycogenolysis.

Physics & Math Key Equations

• Kinematics $v=v<em>0+at$, $x=v</em>0t+\frac12 at^2$, $v^2=v_0^2+2ax$.
• Forces $F=ma$; grav $F=mg$; friction $f=\mu N$; centripetal $F=mv^2/r$.
• Work $W=Fd\cos\theta$; power $P=W/t$; KE $=\frac12 mv^2$.
• Ideal gas $PV=nRT$; Coulomb $F=kq<em>1q</em>2/r^2$; Ohm $V=IR$.
• Wave $v=f\lambda$; light Snell $n<em>1\sin\theta</em>1=n<em>2\sin\theta</em>2$.

Behavioral Sciences Snapshots

Learning & Memory

• Classical: associate stimuli; operant: consequences (reinforcement vs punishment).
• Memory types: sensory→STM→LTM (explicit vs implicit). LTP = mechanism.

Emotion Theories

• James-Lange: phys → emotion; Cannon-Bard: simultaneous; Schachter-Singer: phys + cognition.

Social Processes

• Deindividuation, bystander, groupthink/polarization; conformity vs obedience; biases (fundamental attribution, confirmation, self-serving).

Essential Constants

• $g=9.8\,\text{m/s}^2$; $R=0.0821\,L·atm/(mol·K)=8.314\,J/(mol·K)$.
• 1 atm = $760\,\text{torr}=101.3\,\text{kPa}$.