All guides

The mole map, limiting reagents, and the cascading errors that ruin a synthesis calc — with three worked problems.

It is not the smallest number of moles — it is the reagent that runs out first at the reaction ratio. The three-column method that never fails.

Theoretical yield is a ceiling, actual yield is the receipt, and the gap between them is where the chemistry actually happened.

Molarity is one of six ways to say 'how concentrated'. Mass percent, molality, ppm, mole fraction — each has a job.

Four variables, one line — until temperature drops or pressure climbs. Boyle, Charles, Avogadro, and the van der Waals correction that patches the damage.

Split the equation in two, balance atoms, balance charge with electrons, add. A seven-step algorithm that never fails, in acid or in base.

Vapour-pressure lowering, boiling-point elevation, freezing-point depression, osmotic pressure — four properties, one common cause: lowered solvent chemical potential.

Substrate, nucleophile, leaving group, solvent, temperature — a five-way decision tree that predicts which mechanism wins.

Four mechanisms compete on the same substrate. Sort reagents on two axes, substrates on one, and the answer falls out.

Alkenes are electron-rich; electrophiles love them. Markovnikov, anti-Markovnikov exceptions, and cation rearrangements that flip the product.

The proton NMR spectrum is a compressed structure drawing. Three independent axes identify a molecule from scratch.

Six π electrons, one flat ring, one enormous energy discount. The four criteria for aromaticity and how they control reactivity.

Half of organic chemistry is one polarised π bond. Aldehyde and ketone additions, acyl-derivative substitutions, and the reactivity ladder.

Diene plus dienophile equals cyclohexene in one concerted step. FMO theory, endo rule, and the stereo constraints that make it a synthesis workhorse.

The three families that cover 90 percent of solubility questions, the classic exceptions, and how to spot them at a glance.

Move from 'insoluble' to a real molar solubility, then correct for the common-ion effect, pH, and selective precipitation.

d-orbital splitting, Δo, high-spin vs low-spin, and how one diagram predicts a complex's color, magnetic moment, and geometry.

Transition metals like to have 18 valence electrons. Count them right and half of organometallic reactivity falls out.

Bond order, magnetism, and bond length fall out of one MO diagram. Build it once for the first row and every diatomic follows.

One line shows every oxidation state and every E° between them. Read forward for stability, backward for disproportionation, both for oxidiser strength.

Every molecule belongs to a point group. The five symmetry elements identify it; the group then predicts polarity, chirality, and spectral activity.

Boltzmann's S = k ln W, worked out on a microstate count you can do by hand. Why 'disorder' is a lossy metaphor.

Universe's entropy proxy, max non-PV work, distance from equilibrium — three framings of ΔG that each earn their keep.

Rate laws come from mechanism, not the balanced equation. Elementary steps, RDS, steady-state, integrated rate laws — and when to trust them.

Arrhenius fits the rate; Eyring names the reason. ΔH‡ and ΔS‡ split 'why so slow' into an enthalpic hill and an entropic bottleneck.

One diagram encodes every phase transition a pure substance can undergo. The three lines are Clapeyron; the intersections carry the physics.

Two energy levels, one temperature — one exponential fixes the ratio. IR intensities, NMR sensitivity, and the molecular meaning of T all follow.

One particle, one 1D box, one exact solution. Quantised energies, zero-point energy, and a working model for the absorption of conjugated polyenes.

Concentration limits, scattering, stray light, chemical speciation — the five ways the A = εbc line stops being a line.

Build a regression that survives an audit: LOD, LOQ, confidence interval, residual plot, and when to switch to standard addition.

Buffer plateaus, equivalence points, and half-equivalence-point pH — the shape of the curve names the analyte and gives the pKa for free.

Retention, plate count, resolution, peak shape — the four numbers that grade any HPLC separation.

The molecular ion names the mass; the fragment pattern names the connectivity; the isotope satellites name the elements.

The 4000-1500 window names the functional groups; the fingerprint below 1500 confirms the identity. A four-question workflow reads any spectrum.

Every measurement is a random variable. Mean, standard deviation, standard error, confidence interval, t-test, and outlier rejection — in one workflow.

Michaelis-Menten in words. What Km and Vmax actually mean, and what kcat/Km tells you about a 'perfect' enzyme.

Each inhibition mode leaves a distinct Km/Vmax fingerprint. Match the pattern, extract Ki, watch for irreversibility.

Bicarbonate, phosphate, and protein buffers keep blood pH within 0.05 units. The 20:1 ratio, the open system, and the four ABG disturbances.

Hemoglobin binds four oxygens, and each binds easier than the last. The Hill equation, MWC states, and the Bohr effect.

ATP is not the fuel; ΔG is. Every step has a ΔG, and only the sum needs to be negative. How coupling and disequilibrium drive the pathway.

Four complexes drop electrons through a redox staircase to O₂; the released energy pumps protons; ATP synthase turns the gradient back into ATP.

Three transport modes set every ion gradient in every cell. Nernst equation, Na/K-ATPase, secondary active symporters and antiporters, and the physiology that rides them.