The 189 formulas, reactions and facts the paper tests

The mole

n = m/M = N/N_A = V/V_m

N_A = 6.022 × 10²³ mol⁻¹

V_m = 22.4 L at 273 K and 1 atm; 22.7 L at 273.15 K and 1 bar

Note:If the stem names no molar volume, try both: the intended one gives round numbers.

Counting atoms and electrons

atoms = n × N_A × atoms per formula unit electrons = n × N_A × electrons per molecule

H₂O has 3 atoms; C₁₂H₂₂O₁₁ has 45

CH₄ has 10 electrons; N₂ has 14

Note:Molecules are not atoms: multiply by the atoms in one formula unit.

Percentage and empirical formula

%X = (atoms of X × A_X / M) × 100 MF = (M / EF mass) × EF

Combustion: C is 12/44 of the CO₂ mass; H is 2/18 of the H₂O mass

Clear fractions: 1.5 → ×2, 1.33 → ×3, 1.25 → ×4

Note:Do not round 1.5 away; double every ratio instead.

Formula from combustion volumes

CxHy + (x + y/4) O₂ → x CO₂ + (y/2) H₂O

x = V(CO₂) / V(hydrocarbon)

Cooling removes the water; KOH absorbs CO₂; what remains is unused O₂

Limiting reagent and yield

limiting reagent = smallest n / coefficient % yield = actual / theoretical × 100

For aA → bB: n_B = n_A × b/a

Purity: use only the pure mass

Note:The test is moles over coefficient, not the fewest moles.

Gas laws

PV = nRT M = dRT/P p_i = x_i·P

R = 0.0821 L atm K⁻¹ mol⁻¹ = 0.083 L bar K⁻¹ mol⁻¹ = 8.314 J K⁻¹ mol⁻¹

T in kelvin; x_i = mole fraction

Note:Mass fraction is not mole fraction: turn each gas into moles first.

Molarity, dilution and mixing

M = n / V(L) M₁V₁ = M₂V₂ M_mix = (M₁V₁ + M₂V₂) / (V₁ + V₂)

Millimoles = M × V(mL)

CuSO₄·5H₂O is 249.5 g mol⁻¹: keep the water of crystallisation

Note:Water added is not the final volume.

Molality, mole fraction and ppm

m = n_solute / kg solvent M = 10 × (% w/w) × d / M_B ppm = (mass solute / mass solution) × 10⁶

d = density in g mL⁻¹; M_B = molar mass of solute

In water: x_solute = m / (m + 55.5)

Note:Molarity and normality change with temperature; molality, mole fraction and ppm do not.

Redox half-reactions

MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O

Neutral or basic: MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻

Oxidation numbers in a species add up to its charge

Note:The medium sets the product of permanganate.

Titrations and the n-factor

M₁n₁V₁ = M₂n₂V₂

Redox n: MnO₄⁻ 5 in acid, 3 in neutral or basic · Cr₂O₇²⁻ 6 · Fe²⁺ 1 · C₂O₄²⁻ 2 · FeC₂O₄ 3

Acid-base n: H₂SO₄ 2 · H₃PO₄ 3 when fully neutralised · Ca(OH)₂ 2

Note:Count every oxidisable part: in FeC₂O₄ both iron and oxalate lose electrons.

First law

ΔU = q + w

q > 0 when heat is absorbed; w > 0 when work is done ON the system

Adiabatic: q = 0, so ΔU = w

Note:Over a cycle ΔU = 0, so q = −w.

Work against a constant pressure

w = −p_ext·(V₂ − V₁)

Free expansion: p_ext = 0, so w = 0

1 L bar = 100 J · 1 L atm = 101.3 J

Note:Expansion work is negative; compression work is positive.

Reversible isothermal work

w = −2.303·nRT·log(V₂/V₁) = −2.303·nRT·log(p₁/p₂)

Isothermal ideal gas: ΔU = 0, ΔH = 0, q = −w

Reversible adiabatic: w = ΔU = nC_v·ΔT

Note:The log form needs the 2.303; the ln form does not.

Heat capacity and calorimetry

q_V = nC_v·ΔT = ΔU q_p = nC_p·ΔT = ΔH C_p − C_v = R

Monatomic ideal gas: C_v = 3R/2, C_p = 5R/2

Bomb calorimeter: Δ_cU = −C_cal·ΔT / n

Note:A bomb calorimeter measures ΔU, not ΔH.

ΔH and ΔU

ΔH = ΔU + Δn_g·RT

Δn_g = gas moles of products − gas moles of reactants

R = 8.314 × 10⁻³ kJ K⁻¹ mol⁻¹ beside ΔH in kJ

Note:Liquid water does not count in Δn_g; water vapour does.

Hess's law

Δ_rH° = Σν·Δ_fH°(products) − Σν·Δ_fH°(reactants)

Δ_fH° = 0 for an element in its reference state

From combustion: Δ_rH = ΣΔ_cH(reactants) − ΣΔ_cH(products)

Reverse an equation: −ΔH; multiply it by k: k·ΔH

Note:Combustion runs reactants minus products, the reverse of formation.

Neutralisation and phase change

H⁺ + OH⁻ → H₂O Δ_neutH = −57.1 kJ mol⁻¹ ΔT = q / (m·c)

Moles of water = the smaller of mol H⁺ and mol OH⁻; m = total mass of the mixture

Δ_subH = Δ_fusH + Δ_vapH at the same temperature

Note:A weak acid or base releases less: part of the heat ionises it.

Bond enthalpy

Δ_rH = ΣBE(bonds broken) − ΣBE(bonds formed)

All species gaseous; count every bond (C₂H₆: 6 C–H and 1 C–C)

Average bond enthalpy = atomisation enthalpy / number of bonds

Note:Broken minus formed: the reverse of the formation rule.

Gibbs energy and spontaneity

ΔG = ΔH − TΔS ΔG = 0 at T = ΔH/ΔS

ΔH > 0, ΔS > 0: spontaneous above ΔH/ΔS; ΔH < 0, ΔS < 0: below it

Δ_rS° = ΣνS°(products) − ΣνS°(reactants)

Phase change: ΔS = ΔH_trans / T_trans

Note:Put ΔS in kJ K⁻¹ before using it with ΔH in kJ.

Gibbs energy and K

ΔG° = −2.303·RT·log K log K = −ΔH°/(2.303R)·(1/T) + ΔS°/(2.303R)

ΔG° < 0 ⇒ K > 1; ΔG° = 0 ⇒ K = 1

Slope of log K against 1/T = −ΔH°/2.303R

Note:A positive ΔG° means K < 1, not no reaction.

Rate of reaction

r = −(1/a)·d[A]/dt = (1/c)·d[C]/dt

For aA + bB → cC + dD

Rate of Y = (y/x) × rate of X

Note:The rate of reaction is the per-coefficient value, not one species' rate.

Rate law and order

r₂/r₁ = ([A]₂/[A]₁)^m · ([B]₂/[B]₁)^n

m = log(r₂/r₁) / log([A]₂/[A]₁) with [B] fixed

Orders come from experiment, not from the balanced equation

Unit of k

unit of k = (mol L⁻¹)^(1 − n) s⁻¹

Zero order mol L⁻¹ s⁻¹ · first s⁻¹ · second L mol⁻¹ s⁻¹

Note:Molecularity is 1, 2 or 3, never zero or a fraction.

First order

k = (2.303/t)·log([A]₀/[A]) t½ = 0.693/k

[A] = what remains

log 2 = 0.301 · log 3 = 0.477 · log 5 = 0.699

Note:Use what remains, not what has reacted.

First-order landmarks

t(75%) = 2·t½ t(87.5%) = 3·t½ t(90%) = 3.32·t½ t(99%) = 2·t(90%)

After n half-lives, (½)ⁿ remains

[A] = [A]₀·e^(−kt): it never reaches zero

First order from gas pressure

A(g) → B(g) + C(g): k = (2.303/t)·log(p_i / (2p_i − P_t))

p_i = initial pressure; P_t = total pressure at time t

For this reaction P_∞ = 2p_i

Note:Never put the total pressure itself into the log.

Radioactive decay

N = N₀·e^(−λt) = N₀·(½)^(t/t½) λ = 0.693/t½

Activity is proportional to N

λ does not change with temperature or pressure

Zero order and half-life

[A] = [A]₀ − kt t½ = [A]₀/2k t(complete) = [A]₀/k

For order n: t½ ∝ [A]₀^(1 − n)

[A] against t is a straight line of slope −k

Note:Falling to a quarter takes 1.5 half-lives, not 2.

Arrhenius equation

k = A·e^(−Eₐ/RT) log(k₂/k₁) = Eₐ/(2.303R)·(1/T₁ − 1/T₂)

Slope of ln k against 1/T = −Eₐ/R; of log k = −Eₐ/2.303R

2.303R = 19.15 J K⁻¹ mol⁻¹

Note:Temperatures in kelvin.

Mechanisms and catalysts

ΔH = Eₐ(forward) − Eₐ(backward) k = k₁k₂/k₃ ⇒ Eₐ = Eₐ₁ + Eₐ₂ − Eₐ₃

Rate law = the slow step's rate law

Catalyst: k_cat / k_uncat = e^(ΔEₐ/RT)

Note:A catalyst lowers both barriers equally; ΔH, ΔG and K do not change.

Equilibrium constant

K_c = [C]^c[D]^d / [A]^a[B]^b

Pure solids and liquids are left out

Q has the same form at any moment: Q < K forward, Q > K backward

Note:Equal rates at equilibrium, not equal amounts.

Reversing, scaling and adding

reverse: 1/K multiply by n: Kⁿ add: K₁·K₂ subtract: K₁/K₂

Halving the equation gives √K

Note:Scaling is a power, not a factor.

Kp and Kc

K_p = K_c·(RT)^Δn

Δn = gas moles of products − gas moles of reactants

R = 0.0821 L atm K⁻¹ mol⁻¹ for K_p in atm

Note:Count gases only; Δn = 0 gives K_p = K_c.

Degree of dissociation

A ⇌ B + C: K_p = α²P / (1 − α²) A ⇌ 2B: K_p = 4α²P / (1 − α²)

α = degree of dissociation; P = total pressure

p_i = x_i·P; an inert gas counts in P, not in K

Note:When products have more gas moles, raising P lowers α.

K, ΔG° and temperature

ΔG° = −2.303·RT·log K log(K₂/K₁) = ΔH°/(2.303R)·(1/T₁ − 1/T₂)

Only temperature changes K

Heating an exothermic reaction lowers K

Note:Concentration, pressure, inert gas and a catalyst move the mixture, never K.

pH of strong acids and bases

pH = −log[H⁺] pH + pOH = 14 (25 °C) mixture: [H⁺] = (n_H⁺ − n_OH⁻) / V_total

H₂SO₄ gives 2 H⁺; Ca(OH)₂ and Ba(OH)₂ give 2 OH⁻

Diluting a strong acid n times raises its pH by log n

Note:A very dilute acid never crosses pH 7: water's own H⁺ counts.

Weak acids and bases

[H⁺] = √(K_a·C) pH = ½(pK_a − log C) α = √(K_a/C)

Weak base: [OH⁻] = √(K_b·C)

Diprotic H₂X: [X²⁻] ≈ K_a2

Note:Take the square root.

Buffers

pH = pK_a + log([salt]/[acid]) pOH = pK_b + log([salt]/[base])

Part-neutralised: pH = pK_a + log(n_b / (n_a − n_b))

Half-neutralised: pH = pK_a

Note:Strong reagent equal to or more than the weak one leaves no buffer.

Salt hydrolysis

WA + SB: pH = 7 + ½pK_a + ½log C SA + WB: pH = 7 − ½pK_b − ½log C WA + WB: pH = 7 + ½(pK_a − pK_b)

C = concentration of the hydrolysing ion

Phenolphthalein for weak acid with strong base; methyl orange for strong acid with weak base

Solubility product

AB: s² AB₂: 4s³ AB₃: 27s⁴ A₂B₃: 108s⁵ common ion: s = K_sp / Cⁿ

s = molar solubility; n = count of the common ion in the formula

Q > K_sp: precipitate, with concentrations after mixing

Note:Across salt types compare s, not K_sp.

Photon energy

E = hν = hc/λ = hc·ν̄ c = νλ

h = 6.626 × 10⁻³⁴ J s

E (eV) = 1240 / λ (nm)

Note:With ν̄ in cm⁻¹, use c = 3 × 10¹⁰ cm s⁻¹.

Photoelectric effect

hν = hν₀ + ½mv² λ₀ = hc / W₀

W₀ = hν₀ = work function

1 eV = 1.602 × 10⁻¹⁹ J

Note:Intensity changes the current, not the kinetic energy.

Bohr model

r = 52.9·n²/Z pm E = −13.6·Z²/n² eV v = 2.18 × 10⁶·Z/n m s⁻¹

KE = −E; PE = 2E

Ionisation energy from n = 1: 13.6·Z² eV

Note:The first excited state is n = 2.

Rydberg equation

ν̄ = 1/λ = R·Z²·(1/n₁² − 1/n₂²)

R = 1.097 × 10⁷ m⁻¹ = 109677 cm⁻¹; n₁ < n₂

ΔE = 13.6·Z²·(1/n₁² − 1/n₂²) eV

Note:First line: lowest energy, longest wavelength. Series limit: n₂ = ∞.

Spectral series and line counts

lines = Δn(Δn + 1)/2 Lyman n₁ = 1 (UV) · Balmer 2 (visible) · Paschen 3 · Brackett 4 · Pfund 5 (IR)

Δn = n₂ − n₁, for many atoms

One electron: at most n₂ − n₁ lines

de Broglie wavelength

λ = h/mv = h/√(2mK) = h/√(2mqV)

K = kinetic energy; q, V = charge and accelerating potential

In the n-th Bohr orbit: 2πr = nλ, so λ = 2πn·a₀/Z

Note:Work in kg and J.

Uncertainty principle

Δx·Δp ≥ h/4π Δv = h / (4πm·Δx)

Δp = m·Δv

If Δx = Δp, then Δp = √(h/4π)

Note:Δx = Δp is not Δx = Δv.

Quantum numbers

l = 0 … n − 1 m_l = −l … +l shell: n² orbitals, 2n² electrons subshell: 2(2l + 1) electrons

Orbital angular momentum L = √(l(l + 1))·h/2π

Pauli: no two electrons share all four quantum numbers

Note:Angular momentum uses l, not n; it is zero for every s orbital.

Nodes

radial nodes = n − l − 1 angular nodes = l total = n − 1

Peaks in 4πr²ψ² = n − l

A boundary surface encloses about 90 per cent of the probability

Orbital energy and filling

lower (n + l) fills first; a tie goes to the lower n Cr [Ar]3d⁵4s¹ · Cu [Ar]3d¹⁰4s¹

One-electron species: energy depends on n only (2s = 2p)

Hund: spread out with parallel spins before pairing

Note:Cations lose the highest-n electrons first: 4s before 3d.

Cell potential

E°cell = E°cathode − E°anode

Both are reduction potentials

Anode: oxidation, negative, left · Cathode: reduction, positive, right

Note:E° is intensive: doubling a half-reaction does not double it.

Nernst equation (298 K)

E = E° − (0.059/n)·log Q

Q = products over reactants; solids count as 1

Concentration cell: E = (0.059/n)·log(c_cathode / c_anode)

Note:Keep the powers from the balanced equation in Q.

Electrodes that depend on pH

E(H⁺/H₂) = −0.059·pH − (0.059/2)·log p_H₂

Oxygen electrode: E = 1.23 − 0.059·pH

MnO₄⁻/Mn²⁺ carries [H⁺]⁸ in the log; Cr₂O₇²⁻/Cr³⁺ carries [H⁺]¹⁴

Gibbs energy and K

ΔG° = −nFE° log K = nE° / 0.059

F = 96500 C mol⁻¹

Maximum electrical work = nFE

Note:The most negative ΔG° goes with the largest nE°, not the largest E°.

Combining electrode potentials

n₃E°₃ = n₁E°₁ ± n₂E°₂

E°(Fe³⁺/Fe²⁺) = 3E°(Fe³⁺/Fe) − 2E°(Fe²⁺/Fe)

E°(X⁻/MX/M) = E°(M⁺/M) + 0.059·log K_sp

Note:Never subtract two half-reaction potentials directly to get a third.

Conductivity

κ = G*/R Λm = 1000·κ / c

G* = l/A, the cell constant (cm⁻¹)

Λm in S cm² mol⁻¹ with κ in S cm⁻¹ and c in mol L⁻¹

1 S cm² mol⁻¹ = 10⁻⁴ S m² mol⁻¹

Note:On dilution κ falls and Λm rises.

Kohlrausch's law

Λ°m = ν₊λ°₊ + ν₋λ°₋

Λ°m(CH₃COOH) = Λ°m(CH₃COONa) + Λ°m(HCl) − Λ°m(NaCl)

Strong electrolytes: Λm = Λ°m − A·√c

Note:A weak electrolyte's Λ°m comes only from Kohlrausch's law, not by extrapolation.

Degree of dissociation and solubility

α = Λm / Λ°m K_a = cα² / (1 − α) s = 1000·κ / Λ°m

s = solubility of a sparingly soluble salt, mol L⁻¹

Then K_sp = s² for a 1 : 1 salt

Faraday's laws

m = M·I·t / (n·F) Q = I·t

n: Ag⁺ 1 · Cu²⁺ 2 · Al³⁺ 3 · O₂ 4 · H₂ and Cl₂ 2

Cells in series: masses in the ratio of M/n

Note:Time in seconds; oxygen needs four electrons.

Products of electrolysis

brine: Cl₂ at the anode, H₂ + OH⁻ at the cathode aq. CuSO₄, Pt: Cu and O₂ aq. CuSO₄, Cu: Cu deposits, the Cu anode dissolves

Na⁺, K⁺, Mg²⁺ and Al³⁺ are never deposited from water

Dilute H₂SO₄ gives O₂; concentrated H₂SO₄ gives S₂O₈²⁻

Henry's law

p = K_H·x

p = partial pressure of the gas; x = its mole fraction in solution

Moles in 1 L of water ≈ 55.56·x

Note:A larger K_H means a less soluble gas; K_H rises with temperature.

Raoult's law, two volatile liquids

P = x_A·p°_A + x_B·p°_B

p_A = x_A·p°_A

The higher p° belongs to the more volatile liquid

Vapour composition

y_A = x_A·p°_A / P 1/P = y_A/p°_A + y_B/p°_B

y = mole fraction in the vapour

Note:The vapour is richer in the more volatile liquid.

Deviations from Raoult's law

positive: ΔH_mix > 0, ΔV_mix > 0, minimum-boiling azeotrope negative: ΔH_mix < 0, ΔV_mix < 0, maximum-boiling azeotrope

Positive: ethanol + water, acetone + CS₂

Negative: chloroform + acetone, HNO₃ + water

Note:A new hydrogen bond between the two liquids means a negative deviation.

Relative lowering of vapour pressure

(p° − p)/p° = x₂ = n₂/(n₁ + n₂) ≈ n₂/n₁

x₂ = mole fraction of the solute

Electrolyte: use i·n₂

Note:The solute's mole fraction, not the solvent's.

Elevation and depression

ΔT_b = i·K_b·m ΔT_f = i·K_f·m M₂ = 1000·K·w₂ / (ΔT·W₁)

m = molality; W₁ = grams of solvent

Water: K_b = 0.52, K_f = 1.86 K kg mol⁻¹

Note:Only the solvent freezes out.

The solvent constants

K_b = R·T_b²·M₁ / (1000·Δ_vapH) K_f = R·T_f²·M₁ / (1000·Δ_fusH)

M₁ in g mol⁻¹; ΔH in J mol⁻¹

Note:For water K_f is larger than K_b.

Osmotic pressure

π = iCRT M = wRT / (πV) π = hρg

C in mol per litre of solution

R = 0.083 L bar K⁻¹ mol⁻¹ = 0.0821 L atm K⁻¹ mol⁻¹

Note:Isotonic means equal i·C, not equal C.

Van 't Hoff factor, dissociation

i = 1 + (n − 1)α α = (i − 1)/(n − 1)

n = ions per formula unit

i = normal molar mass / observed molar mass

Note:Divide by n − 1, not by n.

Van 't Hoff factor, association

i = 1 − (1 − 1/n)α dimer: i = 1 − α/2

Complete dimerisation gives i = ½ (acetic or benzoic acid in benzene)

Note:Association raises the apparent molar mass.

Making alkanes

Wurtz: 2RX + 2Na (dry ether) → R–R Kolbe: electrolysis of RCOONa → R–R + CO₂ soda lime: RCOONa + NaOH (CaO, Δ) → RH + Na₂CO₃

Wurtz and Kolbe double the chain; soda lime removes one carbon

RMgX + H₂O → RH; with D₂O → RD

Note:Two different halides in a Wurtz reaction give three alkanes.

Conformations

ethane: staggered (60°) most stable, eclipsed (0°) least n-butane: anti < gauche < eclipsed < fully eclipsed

Butane order is increasing energy

Conformers interconvert at room temperature and cannot be separated

Free-radical halogenation

Cl₂ (hν) → 2Cl· structural products = sets of non-equivalent H

H reactivity 3° > 2° > 1°; Br· is far more selective than Cl·

A chiral product counts twice when stereoisomers are asked for

Adding HX and water

RCH=CH₂ + HBr → RCHBrCH₃ RCH=CH₂ + HBr (peroxide) → RCH₂CH₂Br

Markovnikov through the more stable carbocation; check for a hydride or methyl shift

H₂O/H⁺: Markovnikov, may rearrange · Hg(OAc)₂ then NaBH₄: Markovnikov, no shift · B₂H₆ then H₂O₂/OH⁻: anti-Markovnikov

Note:The peroxide effect works with HBr only.

Bromine and permanganate

Br₂ in CCl₄: anti addition cold dilute KMnO₄: syn-diol hot KMnO₄: =CH₂ → CO₂, =CHR → RCOOH, =CR₂ → R₂C=O

trans-But-2-ene + Br₂ → meso; cis → racemic

Cl₂ with light, or NBS: allylic substitution, C=C kept

Ozonolysis

R₂C=CHR′ + O₃, then Zn/H₂O → R₂C=O + R′CHO

=CH₂ gives HCHO

A ring alkene gives one dicarbonyl chain

Note:Without Zn the aldehydes are oxidised to acids.

Alkynes

RC≡CH + NaNH₂ → RC≡C⁻Na⁺ + NH₃ H₂, Lindlar → cis-alkene Na in liquid NH₃ → trans-alkene H₂O, HgSO₄/H₂SO₄ → RCOCH₃

Only a terminal alkyne has the acidic H: white precipitate with ammoniacal AgNO₃

Ethyne alone hydrates to ethanal

Note:Alcoholic KOH stops at the vinyl halide; NaNH₂ finishes the alkyne.

Aromaticity

aromatic: planar, cyclic, conjugated, (4n + 2) π electrons antiaromatic: planar, cyclic, 4n

Aromatic ions: cyclopentadienyl anion, tropylium cation, cyclopropenyl cation

Cyclooctatetraene is non-aromatic: it is tub-shaped

Note:Count only π electrons in the ring, not an exocyclic C=O.

Electrophilic substitution

o/p: –NH₂ –OH –OCH₃ –NHCOCH₃ –R –X m: –NO₂ –CN –CHO –COR –COOH –SO₃H

Electrophiles: NO₂⁺ (HNO₃ + H₂SO₄) · Cl⁺ (Cl₂ + AlCl₃) · SO₃ · R⁺ and RCO⁺ (AlCl₃)

Halogens deactivate yet direct ortho and para

Note:Friedel–Crafts fails on rings carrying –NO₂ or –NH₂.

Side-chain oxidation and Friedel–Crafts

C₆H₅–CH₂R + KMnO₄/KOH (Δ), then H₃O⁺ → C₆H₅COOH

Needs a benzylic H: a tert-butyl group is not oxidised

Alkylation can rearrange and repeat; acylation does neither

Note:Do any Friedel–Crafts step before adding a strong deactivator.

Basicity of aliphatic amines

methyl: (CH₃)₂NH > CH₃NH₂ > (CH₃)₃N > NH₃ ethyl: (C₂H₅)₂NH > (C₂H₅)₃N > C₂H₅NH₂ > NH₃

In water; in the gas phase 3° > 2° > 1° > NH₃

pK_a(BH⁺) + pK_b(B) = 14

Note:Tertiary is not the strongest base in water.

Basicity of aryl amines

pK_b: C₆H₅CH₂NH₂ 4.70 < C₆H₅N(CH₃)₂ 8.92 < C₆H₅NHCH₃ 9.30 < C₆H₅NH₂ 9.38

Smaller pK_b, stronger base; para donors raise basicity, acceptors lower it

Pyridine is weak; pyrrole is almost non-basic

Note:Benzylamine behaves as an aliphatic amine.

Amines by reduction

ArNO₂ + Sn/HCl or Fe/HCl → ArNH₂ RCN + LiAlH₄ → RCH₂NH₂ RCONH₂ + LiAlH₄ → RCH₂NH₂

The nitrile route adds one carbon to the halide RX

SnCl₂/HCl on a nitrile gives an aldehyde, not an amine

Ammonolysis and Gabriel synthesis

RX + NH₃ → RNH₂ → R₂NH → R₃N → R₄N⁺X⁻ Gabriel: phthalimide + KOH, then RX, then NaOH(aq) → RNH₂

Excess NH₃ favours the primary amine

Gabriel makes primary alkyl amines only, never aryl amines

Hofmann bromamide degradation

RCONH₂ + Br₂ + 4NaOH → RNH₂ + Na₂CO₃ + 2NaBr + 2H₂O

One carbon fewer, through the isocyanate R–N=C=O

Benzamide gives aniline

Note:Only an unsubstituted amide RCONH₂ reacts.

Acylation

RNH₂ + (CH₃CO)₂O → RNHCOCH₃ + CH₃COOH

Each acetyl group adds 42 g mol⁻¹

Schotten–Baumann: C₆H₅COCl in aqueous NaOH

Note:The more nucleophilic group is acylated first.

Carbylamine, Hinsberg and nitrous acid

RNH₂ + CHCl₃ + 3KOH (Δ) → R–NC + 3KCl + 3H₂O

Hinsberg (C₆H₅SO₂Cl): 1° product dissolves in alkali · 2° insoluble · 3° no reaction

HNO₂, cold: 1° aliphatic → N₂ + ROH · 2° → yellow N-nitrosamine

Note:The carbylamine test is positive for primary aromatic amines too.

Ring substitution of aniline

Br₂ water → 2,4,6-tribromoaniline HNO₃/H₂SO₄ (288 K) → para and meta nitroaniline, little ortho

Protect by acetylation, substitute, then hydrolyse

The meta product comes from the anilinium ion; Friedel–Crafts fails because N binds AlCl₃

Note:NH₂ is not a meta director.

Diazonium salts

ArNH₂ + NaNO₂ + 2HCl (273–278 K) → ArN₂⁺Cl⁻ + NaCl + 2H₂O

CuCl/HCl → ArCl · CuBr/HBr → ArBr · CuCN/KCN → ArCN · KI → ArI · HBF₄, Δ → ArF · warm H₂O → ArOH

H₃PO₂ or ethanol → ArH

Note:Electron-withdrawing groups destabilise the diazonium salt.

Coupling and azo dyes

ArN₂⁺ + phenol (mild OH⁻) → p-hydroxyazobenzene (orange) ArN₂⁺ + aniline (mild H⁺) → p-aminoazobenzene (yellow)

β-Naphthol in NaOH → orange-red dye: the test for a primary aromatic amine

Coupling goes para; ortho if para is blocked

Note:Coupling keeps both nitrogens.

Named routes to carbonyls

Rosenmund: RCOCl + H₂ (Pd–BaSO₄) → RCHO Stephen: RCN + SnCl₂/HCl, then H₃O⁺ → RCHO Etard: toluene + CrO₂Cl₂, then H₃O⁺ → C₆H₅CHO

Gattermann–Koch: benzene + CO + HCl (AlCl₃, CuCl) → C₆H₅CHO

PCC stops a 1° alcohol at the aldehyde; DIBAL-H takes an ester or nitrile to RCHO

Note:The Stephen reduction needs the water step.

Nucleophilic addition

reactivity: HCHO > RCHO > RCOR′ and RCHO > ArCHO R₂C=O + HCN (OH⁻) → R₂C(OH)CN

Electron-withdrawing ring groups raise reactivity; donors lower it

Cyanohydrin + H₃O⁺ → 2-hydroxy acid; + LiAlH₄ → amino alcohol

Note:Cyanide adds to both faces, so the product is racemic.

Carbonyl derivatives

R₂C=O + H₂N–Z → R₂C=N–Z + H₂O (weak acid, pH about 4 to 5)

NH₂OH → oxime · NH₂NH₂ → hydrazone · 2,4-DNP → orange precipitate · NH₂NHCONH₂ → semicarbazone

Two R′OH, dry HCl → acetal: stable to base, hydrolysed by acid

Note:Semicarbazide bonds through the NH₂ of its NH–NH₂ end.

Grignard reagents

HCHO → 1° · RCHO → 2° · R₂CO → 3° alcohol RCN + R′MgX, then H₃O⁺ → RCOR′ RMgX + CO₂, then H₃O⁺ → RCOOH

An ester uses two equivalents and gives a 3° alcohol

Each acidic H uses up one more equivalent

Note:Carbon dioxide adds one carbon.

Reductions

Clemmensen: Zn–Hg/conc. HCl, C=O → CH₂ Wolff–Kishner: NH₂NH₂, KOH, glycol, heat, C=O → CH₂

LiAlH₄: aldehyde, ketone, acid, ester → alcohol; amide, nitrile → amine

NaBH₄: aldehydes and ketones only

Note:An acid-sensitive molecule needs Wolff–Kishner; a base-sensitive one needs Clemmensen.

Identification tests

Tollens' → silver mirror · Fehling's → red Cu₂O · 2,4-DNP → yellow-orange precipitate · I₂/NaOH → yellow CHI₃

Tollens': every aldehyde, HCOOH, α-hydroxy ketones · Fehling's: aliphatic aldehydes only

Iodoform: CH₃CO– or CH₃CH(OH)– joined to H or C

Note:Acetic acid and its esters fail the iodoform test.

Aldol condensation

2RCH₂CHO (dil. OH⁻) → RCH₂CH(OH)CH(R)CHO → (Δ, −H₂O) RCH₂CH=C(R)CHO

Needs an α-H; the new C–C joins the α-carbon to the carbonyl carbon

Crossed: products = (partners with an α-H) × (all partners)

Claisen–Schmidt: ArCHO + ketone with α-H, NaOH → α,β-unsaturated ketone

Note:Intramolecular aldol closes a five- or six-membered ring.

Cannizzaro reaction

2ArCHO (conc. OH⁻) → ArCOO⁻ + ArCH₂OH HCHO + ArCHO → HCOO⁻ + ArCH₂OH

Needs no α-H: HCHO, ArCHO, R₃CCHO

Crossed: HCHO is the one oxidised

Note:Concentrated alkali, not dilute.

Acid strength

pKa: CF₃COOH 0.23 < CCl₃COOH 0.65 < ClCH₂COOH 2.86 < HCOOH 3.75 < C₆H₅COOH 4.19 < CH₃COOH 4.76

−I groups strengthen: more of them, and nearer the COOH, is stronger

Acids release CO₂ from NaHCO₃; phenols do not, except picric acid

Reactions of carboxylic acids

HVZ: RCH₂COOH + X₂/red P → RCH(X)COOH RCOOH + SOCl₂ → RCOCl soda lime: RCOONa → RH

Hydrolysis rate: acid chloride > anhydride > ester > amide

LiAlH₄ or B₂H₆ → RCH₂OH; NaBH₄ does not reduce COOH

Note:COOH directs meta, and benzoic acid gives no Friedel–Crafts reaction.

Halides from alcohols

ROH + SOCl₂ → RCl + SO₂ + HCl ROH + HX: 3° > 2° > 1°

1° and 2° need ZnCl₂ (Lucas reagent); also PCl₅, PCl₃, PBr₃

Alkene + HX: Markovnikov; HBr with peroxide: anti-Markovnikov

Note:Phenol does not give an aryl halide with HX.

Halide exchange

Finkelstein: RCl/RBr + NaI (dry acetone) → RI Swarts: RCl/RBr + AgF, Hg₂F₂, CoF₂ or SbF₃ → RF

Swarts makes freons such as CCl₂F₂ from CCl₄

Note:Finkelstein runs because NaCl and NaBr precipitate in acetone.

Aryl halides from diazonium salts

Sandmeyer: ArN₂⁺ + Cu₂Cl₂/HCl → ArCl · Cu₂Br₂/HBr → ArBr · CuCN/KCN → ArCN Gattermann: Cu powder + HX → ArX KI → ArI

Iodide needs no copper

Note:Gattermann gives chlorides and bromides, not cyanides.

SN1 and SN2

SN2: rate = k[RX][Nu⁻], inversion SN1: rate = k[RX], racemisation

SN2: CH₃X > 1° > 2° > 3°; polar aprotic solvent

SN1: 3° > 2° > 1° > CH₃X; benzylic and allylic fast; polar protic solvent

Note:SN1 can rearrange; SN2 never does.

Leaving groups and nucleophiles

leaving group: I > Br > Cl > F protic: I⁻ > Br⁻ > Cl⁻ > F⁻ aprotic: F⁻ > Cl⁻ > Br⁻ > I⁻

Same donor atom: follow basicity (RO⁻ > C₆H₅O⁻ > CH₃COO⁻)

A bulky base such as (CH₃)₃CO⁻ is a poor nucleophile

Which halides ionise

alcoholic AgNO₃: 3°, benzylic, allylic at once · 1° slowly · vinylic, aryl, bridgehead never

SN1 order of cations: (C₆H₅)₃C⁺ > (C₆H₅)₂CH⁺ > C₆H₅CH₂⁺

A halide whose cation is aromatic ionises easily (tropylium)

Reagent to product

KCN → R–CN · AgCN → R–NC · KNO₂ → R–O–N=O · AgNO₂ → R–NO₂

KCN and KNO₂ are ionic; AgCN and AgNO₂ are covalent

Aq. KOH → ROH · NaOR′ → ROR′ · NH₃ → amines · LiAlH₄ → RH

Elimination

R–CH₂–CH₂–X + KOH (alcoholic, Δ) → R–CH=CH₂ + KX + H₂O

Aqueous KOH substitutes; alcoholic KOH eliminates

Zaitsev: the more substituted alkene is major; a bulky base gives the less substituted one

Note:No β-hydrogen, no elimination.

Substitution on haloarenes

C₆H₅Cl + NaOH (623 K, 300 atm), then H⁺ → C₆H₅OH

Nitro groups ortho or para to Cl make it far easier

Electrophiles go ortho and para to the halogen, para major

Note:A meta nitro group barely helps.

Reactions with metals

RX + Mg (dry ether) → RMgX Wurtz: 2RX + 2Na → R–R Wurtz–Fittig: ArX + RX + 2Na → Ar–R Fittig: 2ArX + 2Na → Ar–Ar

RMgX + H₂O → RH; with D₂O → RD

A 1,3-dihalide with Na or Zn gives cyclopropane

Making alcohols

RMgX + HCHO → 1° · RCHO → 2° · R₂CO → 3° alcohol (then H₃O⁺)

Acid hydration: Markovnikov, can rearrange; hydroboration: anti-Markovnikov, no shift

NaBH₄ reduces aldehydes and ketones, not acids; LiAlH₄ reduces acids

Boiling points

alkane < ether < aldehyde, ketone < alcohol < carboxylic acid

At similar molar mass; branching lowers the boiling point

Note:o-Nitrophenol is chelated: it boils lower and is steam volatile.

Acidity

pKa: p-nitrophenol 7.1 < o-nitrophenol 7.2 < m-nitrophenol 8.3 < phenol 10.0 < p-cresol 10.2 < ethanol 15.9

Alcohols: CH₃OH > 1° > 2° > 3°

−I and −R groups strengthen a phenol; +I and +R weaken it

Note:Methoxy weakens phenol at para but strengthens it at meta.

Screens for O–H compounds

Na: every O–H · NaOH: phenols and acids · NaHCO₃: acids and picric acid · neutral FeCl₃: violet with phenol

Active H: ROH + CH₃MgI → CH₄; mol CH₄ = mol O–H

Note:Benzyl alcohol is not a phenol.

Lucas test and oxidation

Lucas (conc. HCl + ZnCl₂): 3° turbid at once · 2° in about five minutes · 1° none at room temperature

Oxidation: 1° → aldehyde (PCC) or acid (KMnO₄, K₂Cr₂O₇); 2° → ketone; 3° resists

Hot Cu at 573 K: 1° → aldehyde, 2° → ketone, 3° → alkene

Note:Acetylation adds 42 g mol⁻¹ for each OH.

Acid dehydration

ROH + H⁺ → ROH₂⁺ → R⁺ (shift if better) → most substituted alkene

Ease: 3° > 2° > 1°; a 1° alcohol needs conc. H₂SO₄ at 443 K

At 413 K a 1° alcohol gives the ether instead

Note:Check for a hydride or methyl shift before drawing the alkene.

Making phenol

cumene + O₂, then H⁺ → phenol + propanone C₆H₅Cl + NaOH (623 K, 300 atm) → phenol C₆H₅N₂⁺Cl⁻ + warm H₂O → phenol

Benzenesulphonic acid fused with NaOH, then H⁺, also gives phenol

Named reactions of phenol

Reimer–Tiemann: phenol + CHCl₃/aq. NaOH → salicylaldehyde Kolbe: sodium phenoxide + CO₂ (400 K, 4–7 atm) → salicylic acid

Reimer–Tiemann electrophile: :CCl₂; ortho major

Zn dust → benzene · Na₂Cr₂O₇/H₂SO₄ → benzoquinone · acetylating salicylic acid → aspirin

Note:Chloroform gives the aldehyde; carbon dioxide gives the acid.

Ring substitution of phenol

bromine water → 2,4,6-tribromophenol (white) Br₂ in CS₂, 273 K → p-bromophenol dil. HNO₃ → o- + p-nitrophenol conc. HNO₃ → picric acid

No FeBr₃ needed: the OH activates the ring

Steam distillation carries off o-nitrophenol

Note:Picric acid is a trinitrophenol, not TNT.

Making and cleaving ethers

Williamson: RO⁻Na⁺ + R′X → ROR′ (R′ = CH₃ or 1°) ArOCH₃ + HI → ArOH + CH₃I R₃C–O–CH₃ + HI → R₃C–I + CH₃OH

Aryl ethers: phenoxide + alkyl halide, never aryl halide + alkoxide

Primary groups: I goes to the smaller one (SN2); a tertiary group takes the I (SN1)

Note:A tertiary halide with an alkoxide gives an alkene, not an ether.

Seniority of functional groups

–COOH > –SO₃H > –COOR > –COCl > –CONH₂ > –CN > –CHO > >C=O > –OH > –NH₂ > C=C, C≡C

The senior group takes the suffix and the lowest locant

–X, –NO₂ and –OR are always prefixes

Note:–CHO outranks the ketone, and –CN sits between the amide and the aldehyde.

Numbering the parent chain

principal group → multiple bonds → all prefixes (lowest set) → alphabetical order

Compare locant sets term by term: 2,3,6 beats 2,4,5

di-, tri-, tetra- are ignored when alphabetising

Note:An ene–yne tie goes to the double bond; in a ring the OH carbon is C-1.

Degree of unsaturation

DoU = (2C + 2 + N − H − X) / 2

Each ring or C=C counts 1, a C≡C 2, a benzene ring 4

X = halogen atoms, counted like H

Note:Alkane isomers: C₄H₁₀ 2, C₅H₁₂ 3, C₆H₁₄ 5, C₇H₁₆ 9.

Counting stereoisomers

N ≤ 2ⁿ n = chiral centres + stereogenic C=C bonds

cis–trans needs abC=Ccd with a ≠ b and c ≠ d

Chiral carbon: four different groups; D counts as different from H

Note:Identical halves give a meso form: tartaric acid has 3 stereoisomers, not 4.

Electronic effects and acid strength

RSO₃H > RCOOH > phenol > H₂O > ROH > RC≡CH

−I: –NO₂ > –CN > –COOH > –F > –Cl > –Br > –I; alkyl groups are +I

+R: –OH, –OR, –NH₂, –X −R: –NO₂, –CN, –CHO, –COOH, >C=O

C–H acidity: sp > sp² > sp³

Note:Conjugate bases run the other way, so RO⁻ is a stronger base than OH⁻.

Stability of reaction intermediates

carbocation and radical: 3° > 2° > 1° > CH₃ carbanion: CH₃⁻ > 1° > 2° > 3°

Carbocation sp², planar, 6 e⁻ · carbanion sp³, pyramidal · radical 7 e⁻

Resonance beats hyperconjugation: Ph₃C⁺ > Ph₂CH⁺ > PhCH₂⁺

Hyperconjugating H = number of α-H (CH₃⁺ has none)

Note:The more stable the cation, the LOWER its hydride affinity.

Choosing a purification method

simple: b.p. far apart · fractional: b.p. close · reduced pressure: decomposes at its b.p. · steam: steam volatile, immiscible with water

Sublimation: solid → vapour directly (camphor, naphthalene from NaCl)

o-Nitrophenol is steam volatile (intramolecular H-bond); p-nitrophenol is not

Note:Glycerol from spent lye: reduced pressure. An azeotrope cannot be split by fractional distillation.

Retardation factor

Rf = distance moved by the spot / distance moved by the solvent front

Both measured from the base line; Rf < 1, no unit

Column and TLC work by adsorption; paper by partition (water in the pores is the stationary phase)

Note:More polar on silica → lower Rf → elutes later from a column.

Lassaigne's test

N: Prussian blue Fe₄[Fe(CN)₆]₃ · S: violet with nitroprusside, black PbS · N + S: blood red [Fe(SCN)]²⁺ · Cl, Br, I: AgCl white, AgBr pale yellow, AgI yellow

Boil with dilute HNO₃ before adding AgNO₃, never HCl

P: yellow ammonium phosphomolybdate

Note:NaCN needs carbon: hydrazine and hydroxylamine give no Prussian blue.

Quantitative estimation

Kjeldahl %N = 1.4·M·V·b / m %C = (12/44)·m(CO₂)/m × 100 %H = (2/18)·m(H₂O)/m × 100 %X = (X/AgX)·m(AgX)/m × 100 %S = (32/233)·m(BaSO₄)/m × 100 %P = (62/222)·m(Mg₂P₂O₇)/m × 100

b = basicity of the acid (2 for H₂SO₄); V in mL, m in g

Dumas: subtract the aqueous tension, reduce to STP, %N = (28/22400)·V(mL)/m × 100

AgCl 143.5, AgBr 188, AgI 235; oxygen by difference

Note:Kjeldahl fails for nitro, azo and ring nitrogen; Mg₂P₂O₇ carries two P, so 62/222.

Werner's theory and ionisable ions

mol AgCl = mol complex × Cl⁻ outside [ ] x + Σ ligand charges = charge on the complex ion

Primary valency = oxidation state; secondary valency = coordination number

CoCl₃·xNH₃, x = 6, 5, 4, 3 → 3, 2, 1, 0 mol AgCl

Note:The ions per formula unit set the conductivity and i in ΔTf = i·Kf·m.

Denticity and ligand types

mono: NH₃, H₂O, Cl⁻, CO · bi: en, C₂O₄²⁻, dmgH⁻ · hexa: EDTA⁴⁻ · ambidentate: NO₂⁻, SCN⁻, CN⁻

Chelating: two atoms bind at once; ambidentate: one of two atoms binds

PPh₃ is a σ-donor and π-acceptor; N(CH₃)₃ only a σ-donor

Note:Oxalate chelates; it is not ambidentate.

Names and d-electron count

d count = group number − oxidation state

Anionic ligands end in -ido (chlorido, cyanido, oxido); an anionic complex ends in -ate (ferrate, cuprate, argentate)

Ligands alphabetical; bis-, tris- for ligands that already carry a number

Note:In nitroprusside, NO is counted as NO⁺.

Structural isomerism

linkage (–NO₂ / –ONO) · ionisation ([Co(NH₃)₅SO₄]Br / [Co(NH₃)₅Br]SO₄) · coordination (metals swap ligands) · hydrate ([Cr(H₂O)₆]Cl₃ / [Cr(H₂O)₅Cl]Cl₂·H₂O)

Ionisation pair: one gives AgBr, the other BaSO₄

Hydrate pair: AgNO₃ precipitates 3 and 2 Cl⁻

Note:Coordination isomerism needs two DIFFERENT metals.

Geometrical and optical isomers

square planar MA₂B₂ 2 · MABCD 3 octahedral MA₄B₂ 2 · MA₃B₃ 2 (fac, mer) · M(AA)₂B₂ 2 geometrical, 3 stereo · M(AA)₃ 0 geometrical, 2 optical

Tetrahedral complexes have no geometrical isomers

Stereoisomers = achiral forms + 2 × chiral forms

Note:Square planar complexes are never optically active.

Valence bond theory

d⁴–d⁷, strong field: d²sp³, inner orbital, low spin · weak field: sp³d², outer orbital, high spin

Octahedral Ni²⁺ (d⁸) is always sp³d² with 2 unpaired

Four-coordinate d⁸: CN⁻ → dsp², square planar, 0 unpaired; Cl⁻ → sp³, tetrahedral, 2 unpaired

Note:Ni(CO)₄ is Ni(0), d¹⁰, sp³, diamagnetic; Pt²⁺ and Pd²⁺ are always square planar.

Spectrochemical series

I⁻ < Br⁻ < SCN⁻ < Cl⁻ < S²⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < EDTA⁴⁻ < NH₃ < en < CN⁻ < CO

Higher metal charge, and 3d < 4d < 5d, raise Δo

Stronger field → larger Δ → shorter λ absorbed: Δ = hc/λ

Note:S-bonded SCN⁻ is weak; N-bonded NCS⁻ sits above water.

Crystal field splitting and CFSE

octahedral: eg +0.6Δo, t₂g −0.4Δo · tetrahedral: t₂ +0.4Δt, e −0.6Δt · Δt = (4/9)Δo CFSE = (−0.4·n(t₂g) + 0.6·n(eg))Δo

Δo > P → low spin; Δo < P → high spin; a choice only for d⁴ to d⁷

High-spin d³ and d⁸ −1.2Δo; low-spin d⁶ −2.4Δo; tetrahedral is always high spin, filling e first

Note:CFSE is not Δo: for d¹ the CFSE is −0.4Δo, but the light absorbed matches Δo.

Magnetic moment of complexes

μ = √(n(n + 2)) BM: [Fe(CN)₆]³⁻ 1 unpaired, 1.73 · [Fe(H₂O)₆]³⁺ 5 unpaired, 5.92

Diamagnetic: d⁰, d¹⁰, low-spin d⁶ ([Fe(CN)₆]⁴⁻, [Co(NH₃)₆]³⁺), square planar d⁸

Any odd d count is paramagnetic

Note:Cu²⁺ in any complex is 1.73 BM; Cu⁺ (d¹⁰) is zero.

Metal carbonyls, stability and uses

σ: C lone pair → metal · π: filled metal d → CO π* ⇒ M–C stronger, C–O weaker

Co₂(CO)₈: 2 bridging CO, one Co–Co bond · Mn₂(CO)₁₀: no bridging CO, one Mn–Mn bond

βn = K₁K₂…Kn; chelates are more stable: [Co(en)₃]²⁺ > [Co(NH₃)₆]²⁺

Chlorophyll Mg · haemoglobin Fe · vitamin B₁₂ Co · cisplatin Pt · Wilkinson's Rh

Note:π-acceptor ligands such as CO stabilise the zero oxidation state.

Configurations and ionisation

Cr [Ar]3d⁵4s¹ · Cu [Ar]3d¹⁰4s¹ d count of M²⁺ and above = Z − 18 − n

Ions lose 4s before 3d: Mn⁺ is 3d⁵4s¹, Cr⁺ is 3d⁵

4d: Nb 4d⁴5s¹, Mo 4d⁵5s¹, Ru 4d⁷5s¹, Rh 4d⁸5s¹, Pd 4d¹⁰5s⁰, Ag 4d¹⁰5s¹

IE₂ high for Cr and Cu (Cr⁺ 3d⁵, Cu⁺ 3d¹⁰); IE₃ high for Mn (Mn²⁺ 3d⁵)

Note:Atomisation enthalpy peaks at V, dips at Mn and is lowest at Zn.

Oxidation states of the 3d metals

most states: Mn (+2 to +7) · only one: Sc (+3)

Down a d-group the HIGHER state is more stable: CrO₃ is the strongest oxidant of Cr, Mo, W(VI)

Mn reaches +7 only in Mn₂O₇; its highest fluoride is MnF₄

Note:The opposite of the p-block, where the lower state wins down a group.

Electrode potentials

M³⁺/M²⁺: Mn +1.57, Co +1.97 V (strong oxidants) · Ti, V, Cr negative (M²⁺ liberates H₂)

Cu²⁺/Cu +0.34 V: the only positive M²⁺/M, so Cu gives no H₂ with dilute acid

Fe³⁺/Fe²⁺ is only +0.77 V because Fe³⁺ is already d⁵

Note:2Cu⁺ → Cu²⁺ + Cu: Cu²⁺ wins on its MORE negative hydration enthalpy.

Spin-only magnetic moment

μ = √(n(n + 2)) BM n = 1→1.73 · 2→2.83 · 3→3.87 · 4→4.90 · 5→5.92 · 7→7.94

n = unpaired electrons; free ion dˣ: n = x up to d⁵, 10 − x from d⁶

Note:Mn²⁺ is 3d⁵ (5.92 BM), not 3d³4s²; Cu²⁺ (d⁹) has one unpaired electron.

Colours of aqueous ions

Ti³⁺ purple · V³⁺ green · Cr³⁺ violet · Mn²⁺ pink · Fe²⁺ green · Fe³⁺ yellow · Co²⁺ pink · Ni²⁺ green · Cu²⁺ blue

Colourless: d⁰ (Sc³⁺, Ti⁴⁺) and d¹⁰ (Zn²⁺, Cu⁺)

MnO₄⁻ purple, Cr₂O₇²⁻ orange, CrO₄²⁻ yellow: d⁰, charge transfer, diamagnetic

Note:Anhydrous CuSO₄ is white; CuSO₄·5H₂O is blue.

Transition metal oxides

one metal: higher oxidation state → more covalent, more acidic

V₂O₃ basic, V₂O₄ less basic, V₂O₅ amphoteric · CrO basic, Cr₂O₃ amphoteric, CrO₃ acidic · MnO basic, Mn₂O₇ acidic

Mn₂O₇: two tetrahedra sharing one O, a covalent green oil

Note:Fe₃O₄, Mn₃O₄ and Co₃O₄ are mixed (+2 and +3); Fe₂O₃ is not.

Potassium dichromate

Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O 2CrO₄²⁻ + 2H⁺ ⇌ Cr₂O₇²⁻ + H₂O

n-factor 6 in acid; Cr stays +6 between chromate and dichromate

Chromyl chloride CrO₂Cl₂ (orange-red) → yellow Na₂CrO₄ → blue CrO₅, Cr +6 with two peroxo groups

Note:K₂Cr₂O₇ is a primary standard; Na₂Cr₂O₇ is hygroscopic.

Potassium permanganate

acid: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O neutral or faintly alkaline: MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻

Manganate MnO₄²⁻: green, +6, d¹, 1.73 BM · permanganate MnO₄⁻: purple, +7, d⁰

3MnO₄²⁻ + 4H⁺ → 2MnO₄⁻ + MnO₂ + 2H₂O

Note:Titrate in dilute H₂SO₄, never HCl: permanganate oxidises chloride.

Lanthanoids and actinoids

Ln³⁺: 4f electrons = Z − 57 Ce⁴⁺ (4f⁰), Tb⁴⁺ (4f⁷) oxidants · Eu²⁺ (4f⁷), Yb²⁺ (4f¹⁴) reductants

5d¹ in the atom: Ce 4f¹5d¹6s², Gd 4f⁷5d¹6s², Lu 4f¹⁴5d¹6s²

Actinoids: all radioactive, up to +7 (Np); the actinoid contraction is larger per element

Note:Gd³⁺ is 4f⁷ (7.94 BM); Cm has eight unpaired electrons, Am seven.

Cation groups and confirmatory tests

I dil. HCl (Pb²⁺) · II H₂S in dil. HCl (Pb²⁺, Cu²⁺, Cd²⁺, As³⁺) · III NH₄OH + NH₄Cl (Fe³⁺, Al³⁺, Cr³⁺) · IV H₂S in NH₄OH (Zn²⁺, Mn²⁺, Co²⁺, Ni²⁺) · V (NH₄)₂CO₃ (Ba²⁺, Sr²⁺, Ca²⁺) · VI Mg²⁺

Cu²⁺ + K₄[Fe(CN)₆] chocolate-brown · Fe³⁺ Prussian blue, blood red with SCN⁻ · Ni²⁺ + dmg red

Brown ring [Fe(H₂O)₅(NO)]²⁺: Fe is +1

Note:Nessler's reagent K₂[HgI₄] gives a brown precipitate with NH₄⁺ and contains no N.

Lone pairs and formal charge

lone pairs = (valence e⁻ − 2 × bonds) / 2 FC = V − L − S/2

V = valence e⁻ of the free atom, L = its lone-pair e⁻, S = its bonding e⁻

Add one e⁻ per negative charge, remove one per positive

Note:Read whether the question counts the whole molecule or the central atom only.

Octet rule exceptions

incomplete: BeF₂ (4), BF₃, AlCl₃ (6) · odd electron: NO, NO₂, ClO₂ · expanded: PCl₅, SF₄ (10), SF₆, H₂SO₄, SO₃ (12), IF₇ (14)

Only period 3 and heavier atoms expand the octet

Lewis acid strength: BI₃ > BBr₃ > BCl₃ > BF₃ (back-bonding in BF₃)

Note:PCl₅ has no lone pair on P, so it is not a Lewis base.

Born–Haber cycle

ΔfH = ΔsubH + ΔiH + ½ΔdissH + ΔegH + ΔlatticeH

Lattice step for ions coming together: negative

|ΔlatticeH| ∝ z⁺z⁻ / (r⁺ + r⁻)

Note:Half the X–X bond enthalpy, not all of it.

Fajans' rules

more covalent: smaller cation · higher cation charge · larger anion · 18-electron cation

LiCl > NaCl > KCl · AlCl₃ > MgCl₂ > NaCl · CaI₂ > CaF₂ · CuCl > NaCl

Note:A bigger cation means LESS covalent; a bigger anion means MORE.

Resonance bond order and bond length

bond order = total bonds to the equivalent atoms / number of them: O₃ 1.5 · CO₃²⁻, NO₃⁻ 4/3 · RCOO⁻ 1.5

Same two atoms: higher bond order → shorter bond

PCl₅: axial 219 pm > equatorial 204 pm

Note:C≡N (116 pm) is shorter than C=O (122 pm): compare orders only for the same pair of atoms.

Bond angles

lp–lp > lp–bp > bp–bp CH₄ 109.5° · NH₃ 107° · H₂O 104.5° · NF₃ 102°

OF₂ 103° < H₂O 104.5° < Cl₂O ≈ 111°

Down a group the angle closes: H₂S 92°, PH₃ 93.5°

Note:SO₂ (sp², ≈ 119°) is bent at a wider angle than H₂O.

Steric number and hybridisation

SN = ½(V + M − c + a): 2 sp · 3 sp² · 4 sp³ · 5 sp³d · 6 sp³d² · 7 sp³d³

V = valence e⁻ of the centre, M = H or halogen atoms, c = + charge, a = − charge; O adds nothing

Lone pairs on the centre = SN − atoms bonded to it

Note:π bonds add no hybrid orbital: SO₃ is sp², BrF₅ is sp³d².

Shapes with lone pairs

SN 5: AX₄E see-saw · AX₃E₂ T-shape · AX₂E₃ linear SN 6: AX₅E square pyramidal · AX₄E₂ square planar

Lone pairs sit equatorial in a trigonal bipyramid, trans in an octahedron

SF₄ see-saw · ClF₃ T-shape · XeF₂, I₃⁻ linear · BrF₅ square pyramid · XeF₄ square planar

Note:Charge changes the shape: I₃⁻ linear, I₃⁺ bent; NO₂⁺ linear, NO₂⁻ bent.

MO bond order

bond order = ½(Nb − Na): B₂ 1 · C₂ 2 · N₂ 3 · O₂ 2 · F₂ 1 · O₂⁺ 2.5 · O₂⁻ 1.5 · O₂²⁻ 1

Up to 14 e⁻: π2p below σ2p; from O₂ on, σ2p below π2p

14 e⁻ (N₂, CO, CN⁻, NO⁺) all have bond order 3

Paramagnetic: B₂, O₂, O₂⁺, O₂⁻, NO, N₂²⁻

Note:Bond order zero (He₂, Be₂) means no molecule; He₂⁺ (0.5) exists.

Dipole moment and hydrogen bonding

μ = q × d 1 D = 10⁻¹⁸ esu cm = 3.336 × 10⁻³⁰ C m

Zero: CO₂, BF₃, CCl₄, XeF₂, XeF₄, PCl₅, SF₆, p-dichlorobenzene

NH₃ 1.47 D > NF₃ 0.23 D: the lone-pair moment adds in NH₃, opposes in NF₃

Note:o-Nitrophenol: intramolecular H-bond, lower b.p., steam volatile; the para isomer bonds between molecules.

Colour tests

Fehling's red Cu₂O · Tollens' silver mirror · Seliwanoff's cherry red (ketoses) · iodine blue-black (starch) · biuret violet (two or more peptide bonds) · ninhydrin purple (amino acids)

Every monosaccharide is reducing, fructose included (enediol to glucose)

Note:Seliwanoff's and the iodine test use no copper.

Reactions of glucose

HI → n-hexane · Br₂ water → gluconic acid · HNO₃ → saccharic acid · (CH₃CO)₂O → pentaacetate · NH₂OH → oxime

Straight chain, one CHO and five OH

No Schiff's test, no NaHSO₃ adduct: the evidence for the ring

Note:Bromine water oxidises only the CHO; nitric acid also oxidises the CH₂OH.

Anomers, epimers and rings

α-D-glucose: m.p. 419 K, +111° · β-D-glucose: m.p. 423 K, +19° · equilibrium +52.5°

Anomers differ at C-1; glucose and galactose are C-4 epimers, glucose and mannose C-2 epimers

Glucose forms a pyranose, fructose a furanose

Note:D or L comes from the last stereocentre's OH, not from the sign of rotation.

Glycosidic linkages

sucrose α1–β2 (non-reducing) · maltose α1–4 · lactose β1–4 · amylose α1–4 · amylopectin, glycogen α1–4 + α1–6 · cellulose β1–4

Invert sugar: glucose +52.5°, fructose −92.4°, so the mixture is laevorotatory

Lactose: C-1 of galactose to C-4 of glucose

Note:Only sucrose joins two anomeric carbons; amylose is the water-soluble fraction of starch.

Amino acids

essential: V L I R K T M F W H

Acidic: D, E · basic: K, R, H · sulphur: C, M

D Asp, E Glu, N Asn, Q Gln, K Lys, R Arg, F Phe, W Trp, Y Tyr

Note:Tyrosine and proline are non-essential; threonine and isoleucine have two stereocentres.

Peptides and protein structure

peptide bonds = n − 1 · sequences n! (no repeats), kⁿ (repeats allowed) · M_min = M × 100/p

1° sequence (peptide bonds) · 2° α-helix, β-sheet (H-bonds) · 3° overall fold · 4° subunit packing

Fibrous (keratin, collagen, myosin) insoluble; globular (insulin, albumin) soluble

Note:Denaturation destroys the 2° and 3° structure; the primary structure stays.

Enzymes

invertase: sucrose → glucose + fructose · diastase: starch → maltose · maltase: maltose → glucose · zymase: glucose → ethanol + CO₂ · urease: urea → NH₃ + CO₂

Pepsin: proteins → peptides; trypsin: → amino acids

Almost all enzymes are globular proteins, each highly specific

Note:Diastase stops at maltose; maltase takes it on to glucose.

Vitamins and deficiency diseases

A xerophthalmia · B1 beri-beri · B2 cheilosis · B6 convulsions · B12 pernicious anaemia · C scurvy · D rickets · E fragile red cells · K longer clotting time

B1 thiamine, B2 riboflavin, B6 pyridoxine, B12 cyanocobalamin

Stored: A, D, E, K and B12

Note:B12 is water soluble but is still stored.

Nucleic acids

DNA: A, G, C, T + β-D-2-deoxyribose · RNA: A, G, C, U + β-D-ribose

Purines A, G (two rings); pyrimidines C, T, U (one ring)

Nucleoside = base + sugar; nucleotide adds phosphate at C-5′; phosphodiester link C-5′ to C-3′

Note:DNA carries the message; the proteins are made by RNA.

Base pairing

H-bonds = 2 × n(A–T) + 3 × n(G–C)

A pairs with T (U in RNA), G with C

Antiparallel strands: write the complement 3′ → 5′

Note:Count one strand only; counting both doubles the answer.

Periods and the periodic law

elements per period = 2 × orbitals filled: 2, 8, 8, 18, 18, 32, 32

Modern law: properties are a periodic function of atomic number (Moseley)

Mendeleev used atomic weight and predicted eka-aluminium (Ga), eka-silicon (Ge)

Names for Z above 100

0 nil · 1 un · 2 bi · 3 tri · 4 quad · 5 pent · 6 hex · 7 sept · 8 oct · 9 enn + ium

Drop a doubled letter: enn + nil = ennil; bi or tri + ium = bium, trium

113 to 118: Nh, Fl, Mc, Lv, Ts, Og

Placing an element

s: group = ns e⁻ · d: group = (n − 1)d + ns e⁻ · p: group = 10 + ns + np e⁻ Z = e⁻ + q

Period = highest n; block = subshell of the last electron

q = charge with its sign: X²⁻ with 10 e⁻ has Z = 8

Note:Diagonal pairs: Li–Mg, Be–Al, B–Si.

Atomic and ionic radii

N³⁻ > O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺ P³⁻ > S²⁻ > Cl⁻ > K⁺ > Ca²⁺

Isoelectronic: the radius falls as Z rises (10 and 18 electrons above)

Falls across a period, rises down a group; cation < atom < anion

Covalent radius = half the X–X bond length

Note:Down a group beats across a period: Be (111 pm) is smaller than Mg (160 pm).

First ionization enthalpy across a period

Li < B < Be < C < O < N < F < Ne Na < Al < Mg < Si < S < P < Cl < Ar

Group 2 > group 13: an s electron is held better than a p

Group 15 > group 16: half-filled np³

Note:Down groups 13 and 14: B > Tl > Ga > Al > In and C > Si > Ge > Pb > Sn.

Successive ionization enthalpies

IE₁ < IE₂ < IE₃ … a big jump after IE(k) → k valence electrons E = (m/M)·(IE₁ + IE₂ + …)

IE₂ compares the cations: Na > Mg; C < N < F < O

Note:IE₂ of Mg must be positive and larger than its IE₁ (737 kJ/mol).

Electron gain enthalpy

by magnitude: Cl > F > Br > I > At S > Se > Te > Po > O

Positive (endothermic): noble gases, Be, N; Ne +116 the most positive, He +48

Electron affinity has the opposite sign to ΔegH

Note:Cl (−349 kJ/mol) is the most negative of all elements, not F.

Electronegativity and metallic character

Pauling: F 4.0 > O 3.5 > N = Cl 3.0 rises across a period, falls down a group

Not a constant: it changes with the bonded atom and the oxidation state

Metallic character: down and to the left; metalloids B, Si, Ge, As, Sb, Te

Note:Mg (1.2) is below Al (1.5); Bi and Pb are metals.

Nature of oxides

neutral: CO, NO, N₂O · amphoteric: Al₂O₃, BeO, ZnO, SnO, SnO₂, PbO, PbO₂, Cr₂O₃, As₂O₃, V₂O₅

Period 3: Na₂O strongly basic → Al₂O₃ amphoteric → Cl₂O₇ strongly acidic

Higher oxidation state of one element → more acidic oxide

Note:GeO is acidic, not amphoteric; NO is neutral, not amphoteric.

Group 13 trends

atomic radius: B < Ga < Al < In < Tl IE₁: In < Al < Ga < Tl < B

M³⁺ radius rises steadily; electronegativity dips at Al

m.p.: B > Al > Tl > In > Ga (Ga liquid from 303 to 2676 K)

Note:Inert pair: Tl⁺ is more stable than Tl³⁺, so TlI₃ is Tl⁺[I₃]⁻.

Borax and boric acid

borax Na₂[B₄O₅(OH)₄]·8H₂O B(OH)₃ + 2H₂O → [B(OH)₄]⁻ + H₃O⁺

Boric acid: weak, monobasic Lewis acid; H-bonded layers

Borax bead: Na₂B₄O₇ → 2NaBO₂ + B₂O₃; Cu blue-green (oxidising), Co blue

Note:Borax in water is alkaline: NaOH + H₃BO₃.

Diborane and borazine

B₂H₆: 4 terminal 2c–2e B–H + 2 bridging 3c–2e B–H–B; B ≈ sp³, non-planar

Borazine B₃N₃H₆: planar ring, B sp², all B–N bonds equal

Lewis acid strength: BF₃ < BCl₃ < BBr₃ < BI₃ (back-bonding strongest in BF₃)

Note:Boron's maximum covalency is 4: BF₆³⁻ does not exist.

Group 14: inert pair and oxides

Sn⁴⁺ more stable than Sn²⁺ (SnCl₂ reduces) · Pb²⁺ more stable than Pb⁴⁺ (PbO₂ oxidises)

CO₂, SiO₂, GeO₂ acidic; SnO, SnO₂, PbO, PbO₂ amphoteric; CO neutral

C₆₀: 20 six-membered + 12 five-membered rings, every C sp²

Note:[SiF₆]²⁻ exists; [SiCl₆]²⁻ does not.

Group 15 hydrides

stability and basicity: NH₃ > PH₃ > AsH₃ > SbH₃ > BiH₃ reducing power: the reverse

b.p.: PH₃ < AsH₃ < NH₃ < SbH₃

Bond angle: NH₃ 107.8° down to SbH₃ 91.3°

Note:The N–N single bond is weaker but shorter than P–P.

Oxides of nitrogen

N₂O +1 · NO +2 · N₂O₃ +3 · NO₂ +4 · N₂O₄ +4 · N₂O₅ +5

Neutral: N₂O, NO; the rest acidic

N–N bond in N₂O, N₂O₃, N₂O₄; an N–O–N bridge only in N₂O₅

Note:The brown ring is [Fe(H₂O)₅(NO)]²⁺: NO, not NO₂.

Reactions of phosphorus

P₄ + 3NaOH + 3H₂O → PH₃ + 3NaH₂PO₂ PCl₃ + 3H₂O → H₃PO₃ + 3HCl PCl₅ + 4H₂O → H₃PO₄ + 5HCl

P₄ + 8SOCl₂ → 4PCl₃ + 4SO₂ + 2S₂Cl₂

Red P: white P heated at 573 K in an inert atmosphere

Phosphorus oxoacids

basicity = number of P–OH: H₃PO₂ 1 · H₃PO₃ 2 · H₃PO₄ 3 · H₄P₂O₇ 4

P–H bonds = non-ionisable H; a P–H bond makes the acid reducing

P: H₃PO₂ +1, H₃PO₃ +3, H₄P₂O₆ +4, H₃PO₄ and H₄P₂O₇ +5

Note:P–O–P bridges: H₄P₂O₇ one, (HPO₃)₃ three, P₄O₁₀ six.

Group 16 and the sulphur oxoacids

H₂SO₃ +4 · H₂SO₄ +6 · H₂S₂O₇ +6 (S–O–S) · H₂S₂O₈ +6 (O–O peroxo) · H₂S₂O₆ +5 (S–S)

Hydride acid strength: H₂O < H₂S < H₂Se < H₂Te

O is −1 in H₂O₂, +1 in O₂F₂, +2 in OF₂

Note:Rhombic sulphur is stable below 369 K, monoclinic above; ozone has six lone pairs.

Halogens and noble gases

bond enthalpy: Cl₂ > Br₂ > F₂ > I₂ ΔegH (magnitude): Cl > F > Br > I oxidising power: F₂ > Cl₂ > Br₂ > I₂

HX b.p.: HCl < HBr < HI < HF; m.p.: HCl < HBr < HF < HI

Cl₂ + cold dilute OH⁻ → Cl⁻ + ClO⁻; hot concentrated → Cl⁻ + ClO₃⁻

XeF₂ linear · XeF₄ square planar · XeF₆ distorted octahedral

Note:F₂ does not disproportionate, and neither does a +7 oxoanion (ClO₄⁻).