Chemistry — Complete Formula Sheet

$n_{\text{solute}}$: Moles of solute (mol) · $w_B$: Mass of solute (g) · $M_B$: Molar mass of solute (g/mol) · $V$: Volume of solution (L or mL as noted)

Moles of solute per litre of SOLUTION. Temperature-dependent because volume changes.

Moles of solute per kg of SOLVENT. Temperature-independent — preferred for colligative properties.

Ratio of moles of one component to total moles. Dimensionless. Sum of all mole fractions = 1.

Relative lowering of vapour pressure equals mole fraction of solute. Used to find molar mass of unknown solute.

Total pressure over an ideal binary solution equals sum of partial pressures. Ideal solution obeys this at all compositions.

$\Delta T_b$: T_b(solution) − T_b(pure solvent) in K · $K_b$: Molal elevation constant (K·kg/mol) · $m$: Molality of solute (mol/kg) · $i$: Van't Hoff factor (=1 for non-electrolyte)

Kb = molal elevation constant (ebullioscopic). For water Kb = 0.52 K·kg/mol.

Kf = molal depression constant (cryoscopic). For water Kf = 1.86 K·kg/mol.

Pressure required to prevent osmosis. C = molar concentration (mol/L). Use for determining molar mass of macromolecules.

$i$: Van't Hoff factor (dimensionless) · $n$: Number of particles produced per formula unit · $\alpha$: Degree of dissociation (0 to 1)

For dissociation into n ions with degree α, i = 1+(n−1)α. For association of n molecules into one, i = 1−(n−1)α/n. Non-electrolyte i = 1.

Partial pressure of a gas above solution ∝ its mole fraction in solution. K_H = Henry's constant (larger K_H ⇒ lower solubility).

$E_{cell}^{\circ }$: Standard cell potential (V) · $E_{cathode}^{\circ }$: SRP of the cathode (reduction site) · $E_{anode}^{\circ }$: SRP of the anode (oxidation site)

Both electrode potentials as reduction potentials (SRP). Positive E°(cell) ⇒ spontaneous reaction.

Gives cell potential at non-standard concentrations. Q is reaction quotient.

Numerical version. Learn this 298 K form for quick calculation. n = number of electrons transferred.

$n$: Moles of electrons transferred · $F$: Faraday's constant = 96500 C/mol · $K_c$: Equilibrium constant of cell reaction

Links thermodynamics with electrochemistry. F = 96500 C/mol. Also gives equilibrium constant K_c of cell reaction.

$\kappa$: Specific conductivity (S·cm⁻¹) · $G$: Conductance = 1/R (siemens, S) · $l/A$: Cell constant (cm⁻¹)

κ = specific conductivity (S/cm). G = conductance (S). l/A = cell constant (cm⁻¹). ρ = resistivity.

${\Lambda }_m$: Molar conductivity (S·cm²·mol⁻¹) · $c$: Molar concentration (mol/L)

c = molarity (mol/L). Units of Λm: S·cm²·mol⁻¹. Increases as dilution increases (fewer inter-ionic interactions).

Limiting molar conductivity = sum of contributions from cation and anion. Used to find Λ°m of weak electrolytes indirectly.

Λ_m at concentration c divided by limiting Λ°m. Substitute into Ostwald's dilution law to find K_a.

$w$: Mass deposited (g) · $E$: Equivalent mass = molar mass / n · $I$: Current (A) · $t$: Time (s) · $F$: Faraday = 96500 C/mol

Mass deposited (w) ∝ charge (Q). Z = electrochemical equivalent. E = M/n (equivalent mass).

Same quantity of charge through different electrolytes ⇒ masses deposited are in the ratio of their equivalent masses.

$[A],[B]$: Molar concentrations (mol/L) · $a,b$: Stoichiometric coefficients · $t$: Time (s)

For aA → bB, rate expressed with negative sign for reactants (disappearing) and positive for products, divided by stoichiometric coefficients.

Powers m, n are EXPERIMENTAL (not stoichiometric). Overall order = m + n. Units of k depend on total order.

$[A{]}_t$: Concentration at time t · $[A{]}_0$: Initial concentration · $k$: Zero-order rate constant

Concentration decreases LINEARLY with time. Half-life ∝ [A]₀. Rate independent of [A]. Units of k: mol L⁻¹ s⁻¹.

Working equation for most numericals. Also written as ln([A]₀/[A]_t) = kt or [A]_t = [A]₀ e^(−kt). Units of k: s⁻¹.

INDEPENDENT of initial concentration. Fundamental property of first-order kinetics (used in radioactive decay).

Depends INVERSELY on initial concentration. Units of k: L mol⁻¹ s⁻¹.

$A$: Frequency factor (same units as k) · $E_a$: Activation energy (J/mol) · $R$: 8.314 J·mol⁻¹·K⁻¹ · $T$: Absolute temperature (K)

Rate constant rises exponentially with temperature. A = frequency factor (collisions per second, correct orientation). E_a = activation energy.

Direct application: given k at two temperatures, find Ea, or vice versa.

For a 10 °C rise in temperature the rate typically 2-3 fold. Used in qualitative reasoning.

$n$: Principal quantum number of the outermost shell (4, 5 or 6)

Holds for the 3d, 4d and 5d series; Pd (4d¹⁰ 5s⁰) is the notable exception. The (n−1)d and ns energies are very close, so electrons shift between them easily.

Half-filled (d⁵) and completely filled (d¹⁰) sets are extra stable, so one 4s electron moves into 3d. Writing 3d⁴4s² or 3d⁹4s² is marked wrong.

On ionisation the 4s electrons leave first, then 3d. Shortcut for the 3d series: M²⁺ = [Ar]3dⁿ with n = Z − 20, and M³⁺ has n = Z − 21.

Up to Mn every 3d and 4s electron can be used. After Mn the d electrons pair up and high states become rare (Zn shows only +2). Oxygen stabilises high states better than fluorine: Mn's highest fluoride is MnF₄ but its highest oxide is Mn₂O₇.

Cr²⁺ and Mn³⁺ are both d⁴. Cr²⁺ is reducing (d⁴ → d³, half-filled t₂g); Mn³⁺ is oxidising (d⁴ → stable d⁵). Cu is the only 3d metal with positive E°(M²⁺/M) (+0.34 V), so it does not liberate H₂ from dilute acids.

$\mu$: Spin-only magnetic moment (Bohr magneton, BM) · $n$: Number of unpaired electrons (no unit)

n is the number of UNPAIRED electrons, not the total number of d electrons. n ≥ 1 ⇒ paramagnetic; n = 0 ⇒ diamagnetic.

Reverse use: from a given μ, solve n(n+2) = μ² for a whole number n. Unpaired electrons for free ions: d¹–d⁵ → 1–5; d⁶, d⁷, d⁸, d⁹ → 4, 3, 2, 1. (NCERT Table 4.7 prints 2.84 for n = 2; √8 = 2.828 rounds to 2.83.)

Colour comes from d–d transitions: an electron absorbs visible light to jump to a higher d level and the complementary colour is seen. MnO₄⁻ and Cr₂O₇²⁻ are d⁰ — their colour is due to charge transfer, not d–d transitions.

Chromite ore is fused with sodium carbonate in free access of air. Cr is oxidised from +3 to +6 (yellow sodium chromate).

The chromate solution is acidified with H₂SO₄ to give orange sodium dichromate. KCl is then added: K₂Cr₂O₇ is less soluble than Na₂Cr₂O₇, so orange crystals separate.

Acid shifts it right (yellow → orange); alkali shifts it back: Cr₂O₇²⁻ + 2OH⁻ → 2CrO₄²⁻ + H₂O. Cr is +6 in both ions — this is not a redox change. Dichromate is two tetrahedra sharing one O (Cr–O–Cr angle 126°).

Orange → green (Cr³⁺). Six electrons per dichromate ion, so it oxidises 6 Fe²⁺, 6 I⁻ (to 3 I₂), 3 Sn²⁺ or 3 H₂S (to 3 S).

1 mol Cr₂O₇²⁻ oxidises 6 mol Fe²⁺ — the basis of estimating iron(II) by titration. Check: total charge is +24 on each side.

MnO₂ is fused with KOH and an oxidising agent (air or KNO₃) to give dark green K₂MnO₄, which disproportionates in neutral or acidic solution to purple permanganate. Commercially, manganate is oxidised to permanganate electrolytically in alkaline solution.

Purple → colourless; 5 electrons per MnO₄⁻. Example: 2MnO₄⁻ + 16H⁺ + 5C₂O₄²⁻ → 2Mn²⁺ + 10CO₂ + 8H₂O. Acidify with dilute H₂SO₄, not HCl (HCl would be oxidised to Cl₂).

Only 3 electrons; brown MnO₂ forms. Example: 2MnO₄⁻ + H₂O + I⁻ → 2MnO₂ + 2OH⁻ + IO₃⁻ (iodide goes to iodate, not to I₂).

+3 is characteristic. Ce⁴⁺ (4f⁰) is a strong oxidant (E° Ce⁴⁺/Ce³⁺ = +1.74 V) and returns to +3; Eu²⁺ (4f⁷) and Yb²⁺ (4f¹⁴) are reductants — again empty, half-filled and full subshells explain them.

Steady decrease in atomic and ionic radii from La to Lu. Key consequence: 4d and 5d elements of the same group have almost equal radii (Zr 160 pm, Hf 159 pm).

General pattern; thorium (6d² 7s², no 5f electron) is a known exception. Actinoids show more oxidation states than lanthanoids because 5f, 6d and 7s levels are close in energy (Th +4, Pa +5, U +6, Np +7). Actinoid contraction from element to element is greater than lanthanoid contraction because 5f electrons shield even more poorly. All actinoids are radioactive.

Primary valency = charge on metal, satisfied by anions in the ionisation sphere. Secondary valency = number of ligand-metal bonds inside coordination sphere.

${\text{OS}}_M$: Oxidation state of the central metal · $\text{ligand charge}$: Formal charge on each coordinated ligand

Solve for OS_M knowing overall charge and each ligand's charge. NH₃, H₂O, CO, en = 0; Cl⁻, CN⁻, OH⁻ = −1; O²⁻, ox²⁻ = −2.

Monodentate contributes 1, bidentate 2, EDTA⁴⁻ (hexadentate) 6 per molecule. Common CNs: 2, 4, 6.

$n$: Number of unpaired electrons · $\mu$: Magnetic moment (Bohr magnetons, BM)

n = number of unpaired electrons in the metal ion's d-orbitals. BM = Bohr Magneton.

In an octahedral field, five d-orbitals split into lower t₂g (3) and upper eg (2). Splitting energy Δ_o (also written 10Dq).

$n_{t_{2g}}$: Electrons in t₂g set · $n_{e_g}$: Electrons in eg set · ${\Delta }_o$: Octahedral crystal field splitting (units of energy) · $P$: Pairing energy (added for each extra pair)

Sum of contributions from t₂g and eg electrons. Include pairing energy P if number of pairs in complex exceeds that in free ion.

Weak-field ligands (small Δ) leave electrons unpaired (high-spin). Strong-field ligands (large Δ) force pairing (low-spin).

Tetrahedral splitting is smaller and INVERTED (e below t₂). All tetrahedral complexes are high-spin because Δ_t < P.

Anionic complex ends in '-ate' (ferrate, cuprate, argentate). Use bis/tris for ligands whose names already contain di/tri (e.g. bis(ethylenediamine)).

Sidgwick's rule: stable complex often has EAN equal to the next noble gas. E.g. [Fe(CN)₆]⁴⁻: EAN = 26 − 2 + 12 = 36 (Kr).

$k$: Second-order rate constant (L mol⁻¹ s⁻¹) · $[R\text{-}X]$: Substrate concentration · $[{\text{Nu}}^{-}]$: Nucleophile concentration

Second-order overall. Concerted single-step mechanism with a transition state — no intermediate.

First-order overall. Two-step mechanism via carbocation intermediate. Independent of [Nu⁻].

Concerted anti-periplanar removal of H and X. Follows Saytzeff's rule — more substituted alkene is major product.

Ionisation to carbocation (slow) then β-H loss (fast). Competes with SN1 in the same conditions.

Fewer alkyl groups on carbon ⇒ easier back-side attack. Bulky 3° halides are unreactive to SN2.

More alkyl groups stabilise the carbocation intermediate (hyperconjugation + inductive effect).

Halide exchange in dry acetone. NaCl/NaBr precipitate out, driving equilibrium to R-I.

Preparation of alkyl fluoride from alkyl bromide/chloride using AgF, Hg₂F₂, CoF₂, or SbF₃.

Coupling of two alkyl halides via Na. Only works well for identical R groups (symmetric alkanes).

Couples an aryl halide with an alkyl halide to give an alkylarene.

Diazonium salt → aryl halide via Cu(I) halide. For Ar-I, KI alone works (no Cu needed).

Markovnikov addition: OH goes to the carbon with fewer H atoms. Mechanism: protonation gives the more stable carbocation, water attacks, H⁺ is lost.

Net anti-Markovnikov addition of water — a terminal alkene gives a 1° alcohol. Boron adds to the less substituted carbon; H₂O₂ in aqueous NaOH then replaces B by OH.

Aldehydes → 1° alcohols, ketones → 2° alcohols. Use H₂ with Pt, Pd or Ni, or NaBH₄ / LiAlH₄. Carboxylic acids need LiAlH₄ (NaBH₄ does not reduce –COOH).

Methanal (HCHO) gives a 1° alcohol, any other aldehyde a 2° alcohol, and a ketone a 3° alcohol. The R′ group forms a new C–C bond to the carbonyl carbon.

Cumene (isopropylbenzene) is air-oxidised to cumene hydroperoxide, which dilute acid splits into phenol and acetone. This is the industrial route; acetone is a valuable by-product.

The diazonium salt is made ice-cold, then hydrolysed by warming with water or dilute acid.

Shows the acidic O–H. Acid strength of alcohols: 1° > 2° > 3° (alkyl groups push electron density onto O and destabilise the alkoxide). Alcohols are weaker acids than water.

Phenoxide is resonance-stabilised (charge spread into the ring); ethoxide is not. –NO₂ (electron-withdrawing) raises acidity, most at o/p (pKa o 7.2, m 8.3, p 7.1); –CH₃ (electron-releasing) lowers it. Phenol reacts with aqueous NaOH; ethanol does not.

Lucas reagent = conc. HCl + anhydrous ZnCl₂. The insoluble alkyl chloride makes the mixture turbid: 3° — immediately; 2° — after a few minutes; 1° — no turbidity at room temperature. Order follows carbocation stability.

Ease of dehydration: 3° > 2° > 1°. Milder conditions work for 2° (85% H₃PO₄, 440 K) and 3° alcohols (20% H₃PO₄, 358 K).

1° alcohol → aldehyde with PCC (pyridinium chlorochromate) or anhydrous CrO₃; acidified KMnO₄ takes it all the way to the carboxylic acid. 2° → ketone. 3° alcohols resist oxidation; strong oxidants at high temperature break C–C bonds.

Alcohol vapour over Cu at 573 K: 1° → aldehyde, 2° → ketone, but a 3° alcohol is dehydrated to an alkene. Another way to tell the three classes apart.

–OH strongly activates the ring, so bromine water gives a white precipitate of 2,4,6-tribromophenol. For monobromination use Br₂ in CS₂ or CHCl₃ at low temperature → o- and p-bromophenol (p major).

Separate by steam distillation: o-nitrophenol is steam-volatile (intramolecular H-bond); p-nitrophenol is not (intermolecular H-bonds associate the molecules). Conc. HNO₃ gives 2,4,6-trinitrophenol (picric acid).

Phenoxide (phenol + NaOH) is even more reactive than phenol, so the weak electrophile CO₂ substitutes, mainly at the ortho position. Product: 2-hydroxybenzoic acid.

Introduces –CHO at the ortho position. The intermediate (a substituted benzal chloride, –CHCl₂) is hydrolysed by the alkali. Do not confuse with Kolbe, which gives –COOH.

Alcohols and phenols react with acids, acid anhydrides or acid chlorides. Water is removed (or pyridine added with acid chlorides) to push the reaction forward. Acetylation of salicylic acid with acetic anhydride gives aspirin.

SN2 attack of an alkoxide on an alkyl halide. Use a PRIMARY (or methyl) halide. The alkoxide is also a strong base, so with 2° halides elimination competes, and a 3° halide gives only the alkene. Sodium phenoxide + R–X gives alkyl aryl ethers.

Same reagent as ethene formation but a lower temperature (413 K ether, 443 K alkene). Suitable only for unhindered 1° alcohols giving symmetrical ethers; 2° and 3° alcohols give alkenes.

Reactivity HI > HBr > HCl. With 1°/2° groups the smaller alkyl becomes the iodide (SN2); with a 3° group the 3° iodide forms (SN1). Alkyl aryl ethers always give phenol + alkyl halide, since the O–aryl bond is stronger.

BaSO₄ poisons the Pd catalyst so the aldehyde is not reduced further to an alcohol. Gives aldehydes, not ketones.

Nitrile → imine → aldehyde on hydrolysis. Alternatively DIBAL-H reduces nitriles (and esters) to aldehydes: R–CN → (i) AlH(i-Bu)₂, (ii) H₂O → R–CHO.

Chromyl chloride converts the –CH₃ of toluene into a chromium complex that hydrolyses to benzaldehyde, so oxidation stops at the aldehyde. Strong oxidants like KMnO₄ would give benzoic acid.

Puts –CHO directly on the benzene ring using carbon monoxide and HCl.

CH₃COCl gives acetophenone. Ketones also come from a nitrile + Grignard reagent followed by hydrolysis, e.g. CH₃CH₂CN + C₆H₅MgBr → propiophenone (C₆H₅COCH₂CH₃).

Base generates CN⁻, the real nucleophile. Reactivity: HCHO > CH₃CHO > CH₃COCH₃ (ketones have two electron-releasing groups and more crowding). Aromatic aldehydes are less reactive than aliphatic ones because of resonance.

Z = –OH (oxime), –NH₂ (hydrazone), –NHC₆H₅ (phenylhydrazone), –NHCONH₂ (semicarbazone). 2,4-DNP gives coloured 2,4-dinitrophenylhydrazones, a test for C=O. Acid-catalysed and reversible.

C=O → CH₂ in acidic conditions. Suitable for compounds that are stable to acid.

C=O → CH₂ in basic conditions, through the hydrazone. Suitable for compounds that are sensitive to acid.

All aldehydes, aliphatic and aromatic, reduce Tollens' reagent (ammoniacal AgNO₃) and give a silver mirror; ketones do not. The aldehyde is oxidised to the carboxylate.

Red-brown Cu₂O precipitate with aliphatic aldehydes. Aromatic aldehydes (benzaldehyde) and ketones do NOT respond. Fehling A = aqueous CuSO₄; Fehling B = alkaline sodium potassium tartrate.

Yellow CHI₃ precipitate shows a CH₃CO– group, or a CH₃CH(OH)– group (oxidised to CH₃CO– first). Positive: ethanal, ethanol, propanone, propan-2-ol. Negative: methanal, methanol, propanal, pentan-3-one. The acid formed has one carbon fewer.

Needs at least one α-H. Ethanal → 3-hydroxybutanal (aldol) → but-2-enal on heating. Propanone with Ba(OH)₂ → 4-hydroxy-4-methylpentan-2-one → 4-methylpent-3-en-2-one. Two different carbonyls that both have α-H (cross aldol) give a mixture of four products.

Only aldehydes with NO α-H. Disproportionation: one molecule is reduced to the alcohol, the other oxidised to the carboxylate. Also 2C₆H₅CHO + conc. NaOH → C₆H₅CH₂OH + C₆H₅COONa.

The whole side chain becomes –COOH whatever its length (ethylbenzene also gives benzoic acid). 1° and 2° alkyl groups are oxidised; a 3° alkyl group is not affected.

Dry ice (solid CO₂) is used. The acid has one carbon MORE than the alkyl halide. Nitriles also give acids on hydrolysis: R–CN → R–CONH₂ → R–COOH (H⁺ or OH⁻ catalyst).

Electron-withdrawing groups stabilise the carboxylate ion and raise acidity; electron-releasing alkyl groups lower it. pKa: HCOOH 3.75, C₆H₅COOH 4.19, CH₃COOH 4.76. More halogens, or a halogen closer to –COOH, means a stronger acid (CF₃COOH > CCl₃COOH > CHCl₂COOH).

SOCl₂ is preferred because both by-products are gases, so the acid chloride is easy to purify. Also: RCOOH + PCl₅ → RCOCl + POCl₃ + HCl, and 3RCOOH + PCl₃ → 3RCOCl + H₃PO₃.

Soda lime = NaOH + CaO (3 : 1). The alkane has one carbon fewer: CH₃COONa gives CH₄. (Kolbe electrolysis of the salt instead gives R–R.)

Halogenation at the α-carbon; the acid must have an α-H. α-Halo acids are useful starting materials for other substitutions.

Iron scrap + HCl is preferred: the FeCl₂ formed hydrolyses and releases HCl, so only a little acid is needed to start the reaction. In acid the amine is present as its salt; NaOH sets free the amine.

Gives a mixture of 1°, 2° and 3° amines and a quaternary ammonium salt, because the amine formed is itself a nucleophile. A large excess of NH₃ favours the 1° amine. Halide reactivity: RI > RBr > RCl.

R–X → R–CN → R–CH₂NH₂ gives an amine with one carbon more than the alkyl halide (ascent of the series). Amide reduction keeps every carbon.

Gives pure 1° aliphatic amines only. Aniline and other aromatic 1° amines cannot be made, because aryl halides do not undergo nucleophilic substitution with the phthalimide anion. By-product: sodium phthalate.

The amine has ONE CARBON FEWER than the amide — the carbonyl carbon leaves as carbonate while R moves from C to N. Works for aryl amides too: benzamide → aniline.

$K_b$: Base dissociation constant of the amine in water · $\text{p}{K}_b$: Negative logarithm of K_b (smaller value = stronger base)

Larger K_b (smaller pK_b) ⇒ stronger base. pK_b of NH₃ = 4.75; simple alkylamines 3.0–4.2 (stronger than NH₃); aniline 9.38 (much weaker).

In the gas phase only the +I effect matters: 3° > 2° > 1° > NH₃. In water, solvation of the ammonium ion and steric hindrance also count, which changes the order.

In aniline the N lone pair is delocalised into the ring by resonance, so it is less available to accept a proton. Electron-releasing groups (–CH₃, –OCH₃) on the ring increase basicity; electron-withdrawing groups (–NO₂) decrease it.

Only 1° amines (aliphatic AND aromatic) give the foul-smelling isocyanide. 2° and 3° amines do not. Ethanolic KOH is used.

Aliphatic diazonium salts are unstable even in the cold; N₂ is given off quantitatively (used to estimate amino acids and proteins). Aromatic 1° amines instead give diazonium salts that are stable for a short time in solution at 273–278 K.

1° and 2° amines (which have N–H) react with acid chlorides, anhydrides or esters; 3° amines do not. Pyridine, a stronger base, removes HCl and pushes the reaction forward. With C₆H₅COCl it is called benzoylation.

1° amine → N-alkylbenzenesulphonamide, whose N–H is acidic, so it is SOLUBLE in alkali. 2° amine → N,N-dialkylbenzenesulphonamide with no N–H, INSOLUBLE in alkali. 3° amine → no reaction.

–NH₂ activates the ring so strongly that bromine water gives a white precipitate of 2,4,6-tribromoaniline at room temperature. For a monobromo product, acetylate first, brominate, then hydrolyse.

Direct nitration gives tarry oxidation products and a large amount of m-nitroaniline, because in strong acid aniline becomes the m-directing anilinium ion. Protecting –NH₂ as –NHCOCH₃ makes p-nitroaniline the major product.

Keep the mixture ice-cold (273–278 K). The salt decomposes when warmed, so it is used immediately rather than stored. Arenediazonium ions are stabilised by resonance with the ring; aliphatic ones are not.

Sandmeyer uses Cu(I) salts. Gattermann uses copper powder with the halogen acid: ArN₂⁺X⁻ + Cu/HX → ArX + N₂ + CuX. Sandmeyer usually gives the better yield.

Iodine is hard to introduce into benzene directly, so KI on the diazonium salt is the standard route to iodobenzene. Aryl fluorides come from heating the diazonium fluoroborate.

Hypophosphorous acid (or ethanol, which is oxidised to ethanal) replaces –N₂⁺ by H — useful to remove an –NH₂ group that was only there to direct substitution. Warming with water gives phenol.

The diazonium ion is a weak electrophile that attacks the para position of phenol (mildly alkaline), giving orange p-hydroxyazobenzene. With aniline (mildly acidic) it gives yellow p-aminoazobenzene. Here the N₂ is retained.

Open-chain form has 5 –OH groups and one –CHO. Cyclic (pyranose) form is 6-membered ring — α and β anomers differ at C-1.

Sucrose is dextrorotatory but the product mixture is levorotatory (fructose has larger −ve rotation) — hence 'invert sugar'.

Reducing sugars have a FREE hemiacetal/hemiketal (open-chain aldehyde/ketone available). Detected by Tollens', Fehling's, Benedict's test.

Condensation of –COOH of one amino acid with –NH₂ of next. The C–N amide bond is planar and partially double-bond (resonance).

At isoelectric pH the amino acid exists as a dipolar ion. Solid amino acids have high m.p. and are crystalline because of ionic zwitterion form.

Purines (A, G) pair with pyrimidines (T, C). Two H-bonds in A=T pair, three in G≡C pair.

20 standard α-amino acids in proteins. Except glycine (R = H), all α-carbons are chiral ⇒ optically active. All natural amino acids are L-series (S-configuration except cysteine).

$v$: Reaction velocity · $v_{\max }$: Maximum velocity (at saturating [S]) · $[S]$: Substrate concentration · $K_m$: Michaelis constant

Basic enzyme kinetics. Km = [S] at which v = v_max/2; small Km ⇒ high affinity.

α-linkage: digestible by humans (starch, glycogen). β-linkage: indigestible fibre (cellulose).