JEE Challenger

Chemistry

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Formula Reference

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30 Chapters • 199 Formulas

Avogadro's Number

NA=6.022×1023 mol−1N_A = 6.022\times10^{23}\text{ mol}^{-1}

Number of entities in 1 mole

Moles from Mass

n=mass (g)molar mass (g/mol)n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}

Most fundamental mole calculation

Number of Particles

N=n×NAN = n \times N_A

Total particles in n moles

Percent Composition

%X=mass of X in 1 mol compoundmolar mass of compound×100\%X = \frac{\text{mass of X in 1 mol compound}}{\text{molar mass of compound}}\times100

Elemental percentage

Empirical Formula Multiplier

n=molecular massempirical formula massn = \frac{\text{molecular mass}}{\text{empirical formula mass}}

Integer that converts empirical to molecular formula

Molarity

M=nsoluteVsolution(L)M = \frac{n_{solute}}{V_{solution}(\text{L})}

Moles of solute per litre of solution

Molality

m=nsoluteWsolvent(kg)m = \frac{n_{solute}}{W_{solvent}(\text{kg})}

Independent of temperature; preferred for colligative properties

Mole Fraction

χA=nAnA+nB+...\chi_A = \frac{n_A}{n_A + n_B + ...}

Dimensionless; all mole fractions sum to 1

Normality

N=M×n-factorN = M \times n\text{-factor}

n-factor = valency / change in O.S. / H⁺ or OH⁻ per formula unit

Dilution Law

M1V1=M2V2M_1V_1 = M_2V_2

Moles of solute remain constant on dilution

Law of Conservation of Mass

∑mreactants=∑mproducts\sum m_{reactants} = \sum m_{products}

Mass is neither created nor destroyed

Bohr Radius (nth orbit)

rn=0.529n2Z A˚r_n = 0.529\frac{n^2}{Z}\text{ Å}

Å = 10⁻¹⁰ m; for hydrogen Z = 1

Energy of nth Orbit

En=−13.6 Z2n2 eVE_n = -\frac{13.6\,Z^2}{n^2}\text{ eV}

Negative sign indicates bound state

Velocity in nth Orbit

vn=2.18×106Zn m/sv_n = 2.18\times10^6\frac{Z}{n}\text{ m/s}

Decreases with n; increases with Z

Rydberg Formula

1λ=RHZ2 ⁣(1n12−1n22)\frac{1}{\lambda} = R_H Z^2\!\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)

R_H = 1.097 × 10⁷ m⁻¹; n₂ > n₁

de Broglie Wavelength

λ=hmv\lambda = \frac{h}{mv}

h = 6.626 × 10⁻³⁴ J·s

Heisenberg Uncertainty Principle

Δx⋅Δp≥h4π\Delta x\cdot\Delta p \geq \frac{h}{4\pi}

Cannot determine both position and momentum precisely

Number of Orbitals in Subshell

(2l+1)(2l+1)

l = 0(s): 1; l=1(p): 3; l=2(d): 5; l=3(f): 7

Max Electrons in Shell n

2n22n^2

K=2, L=8, M=18, N=32

Photon Energy (Planck)

E=hν=hcλE = h\nu = \frac{hc}{\lambda}

h = 6.626 × 10⁻³⁴ J·s; c = 3 × 10⁸ m/s

Effective Nuclear Charge

Z∗=Z−σZ^* = Z - \sigma

Z = atomic number; σ = shielding constant (Slater's rules)

Atomic Radius Trend

Across period: r↓,Down group: r↑\text{Across period: }r\downarrow,\quad\text{Down group: }r\uparrow

Due to increasing Z* across and addition of shells down

Ionisation Energy Trend

IE1<IE2<IE3<...\text{IE}_1 < \text{IE}_2 < \text{IE}_3 < ...

Successive IEs increase; large jump indicates noble gas config.

Electronegativity (Pauling Scale)

χA−χB=0.102Δ\chi_A - \chi_B = 0.102\sqrt{\Delta}

Δ = extra ionic resonance energy in kJ/mol

Group Number from Electron Configuration

Group=no. of valence electrons\text{Group} = \text{no. of valence electrons}

For s and p blocks

Period Number

Period=highest principal quantum number (n)\text{Period} = \text{highest principal quantum number (n)}

Number of occupied electron shells

Formal Charge

FC=V−N−B2FC = V - N - \frac{B}{2}

V = valence e⁻; N = non-bonding e⁻; B = bonding e⁻

Bond Order (MOT)

BO=Nb−Nab2BO = \frac{N_b - N_{ab}}{2}

N_b = bonding e⁻; N_ab = antibonding e⁻

Dipole Moment

μ=q×d\mu = q\times d

q = charge; d = bond length; unit: Debye (D) = 3.336 × 10⁻³⁰ C·m

Hybridisation Index

H=12(V+M−C+A)H = \frac{1}{2}(V + M - C + A)

V = valence e⁻; M = monovalent atoms; C = cation charge; A = anion charge

VSEPR — Total Electron Pairs

Total EP=Bonding Pairs (BP)+Lone Pairs (LP)\text{Total EP} = \text{Bonding Pairs (BP)} + \text{Lone Pairs (LP)}

Geometry: 2-linear, 3-trig. planar, 4-tetra, 5-tbp, 6-octahedral

Resonance Structures

Bond Order=total bondsno. of resonating bonds\text{Bond Order} = \frac{\text{total bonds}}{\text{no. of resonating bonds}}

Example: O₃ bond order = 1.5; benzene = 1.5

Lattice Energy (Born-Landé)

U=−NAMz+z−e24πϵ0r0 ⁣(1−1n)U = -\frac{N_A M z^+ z^- e^2}{4\pi\epsilon_0 r_0}\!\left(1-\frac{1}{n}\right)

M = Madelung constant; n = Born exponent (5–12)

Ideal Gas Law

PV=nRTPV = nRT

R = 8.314 J/mol·K = 0.0821 L·atm/mol·K

Combined Gas Law

P1V1T1=P2V2T2\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}

For fixed amount of ideal gas

Dalton's Law

Ptotal=P1+P2+...=∑χiPtotalP_{total} = P_1 + P_2 + ... = \sum\chi_i P_{total}

P_i = χ_i × P_total; partial pressure

Graham's Law of Diffusion

r1r2=M2M1=d2d11/2\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} = \frac{d_2}{d_1}^{1/2}

Lighter gases diffuse faster

Van der Waals Equation

(P+an2V2)(V−nb)=nRT\left(P+\frac{an^2}{V^2}\right)(V-nb) = nRT

a = attraction correction; b = volume correction

Compressibility Factor

Z=PVnRTZ = \frac{PV}{nRT}

Z=1 ideal; Z>1 repulsion dominant; Z<1 attraction dominant

RMS Speed

urms=3RTMu_{rms} = \sqrt{\frac{3RT}{M}}

M in kg/mol; largest of the three speeds

Most Probable Speed

ump=2RTMu_{mp} = \sqrt{\frac{2RT}{M}}

Speed at peak of Maxwell distribution; smallest

Average Speed

uavg=8RTπMu_{avg} = \sqrt{\frac{8RT}{\pi M}}

Between u_mp and u_rms

Van der Waals Constants

Tc=8a27Rb,Pc=a27b2,Vc=3nbT_c = \frac{8a}{27Rb},\quad P_c = \frac{a}{27b^2},\quad V_c = 3nb

Critical constants in terms of a, b

First Law

ΔU=q+w(q=heat absorbed,  w=work done on system)\Delta U = q + w \quad (q = \text{heat absorbed},\;w = \text{work done on system})

Energy conservation

Work by Gas (expansion)

wby=−PextΔVw_{by} = -P_{ext}\Delta V

Negative: gas expands and does work on surroundings

Enthalpy

H=U+PV,ΔH=ΔU+PΔV=ΔU+ΔngRTH = U + PV,\quad \Delta H = \Delta U + P\Delta V = \Delta U + \Delta n_g RT

Δn_g = moles of gaseous products − reactants

Hess's Law

ΔHrxn=∑ΔHf∘(products)−∑ΔHf∘(reactants)\Delta H_{rxn} = \sum\Delta H_f^\circ(\text{products}) - \sum\Delta H_f^\circ(\text{reactants})

Enthalpy is a state function; path-independent

Bond Enthalpy

ΔHrxn=∑BE(broken)−∑BE(formed)\Delta H_{rxn} = \sum BE(\text{broken}) - \sum BE(\text{formed})

Breaking is endothermic (+); formation is exothermic (−)

Gibbs Free Energy

ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S

Spontaneous if ΔG < 0 at constant T and P

Standard Free Energy & K

ΔG∘=−RTln⁡K=−2.303RTlog⁡K\Delta G^\circ = -RT\ln K = -2.303RT\log K

Links thermodynamics and equilibrium

Entropy Change

ΔS=qrevT\Delta S = \frac{q_{rev}}{T}

Reversible heat exchange per kelvin; increases with disorder

Kirchhoff's Law

ΔH2∘=ΔH1∘+ΔCP(T2−T1)\Delta H_2^\circ = \Delta H_1^\circ + \Delta C_P(T_2-T_1)

Temperature correction of enthalpy

Equilibrium Constant Kc

Kc=[C]c[D]d[A]a[B]bK_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}

For aA + bB ⇌ cC + dD; constant at fixed T

Kp and Kc

Kp=Kc(RT)ΔngK_p = K_c(RT)^{\Delta n_g}

Δn_g = moles of gaseous products − reactants

Reaction Quotient Q

Q<K⇒forward;Q>K⇒backwardQ < K\Rightarrow\text{forward};\quad Q > K\Rightarrow\text{backward}

Q = Kc expression at any moment, not equilibrium

Degree of Dissociation

α=moles dissociatedinitial moles\alpha = \frac{\text{moles dissociated}}{\text{initial moles}}

Range 0 to 1

Van't Hoff Equation

ln⁡K2K1=−ΔH∘R ⁣(1T2−1T1)\ln\frac{K_2}{K_1} = -\frac{\Delta H^\circ}{R}\!\left(\frac{1}{T_2}-\frac{1}{T_1}\right)

Effect of temperature on K

pH Definition

pH=−log⁡[H+]=−log⁡[H3O+]pH = -\log[H^+] = -\log[H_3O^+]

pH + pOH = 14 at 25°C

Ionic Product of Water

Kw=[H+][OH−]=10−14 at 25°CK_w = [H^+][OH^-] = 10^{-14}\text{ at 25°C}

pKw = 14

Weak Acid [H⁺]

[H+]=Ka⋅C[H^+] = \sqrt{K_a\cdot C}

Assuming α << 1; C = initial concentration

Henderson-Hasselbalch

pH=pKa+log⁡[A−][HA]pH = pK_a + \log\frac{[A^-]}{[HA]}

Buffer solution of weak acid and its conjugate base

Solubility Product (Ksp)

Ksp=[Mm+]m[Xn−]nK_{sp} = [M^{m+}]^m[X^{n-}]^n

For M_m X_n; precipitate forms if Q > K_sp

Oxidation State Rules

Sum of OS in compound=charge of species\text{Sum of OS in compound} = \text{charge of species}

OS of O usually −2; H usually +1

n-factor (Redox)

n=change in OSformula unitn = \frac{\text{change in OS}}{\text{formula unit}}

Used to find normality and equivalents

Equivalents (Redox)

equivalents=n×moles\text{equivalents} = n \times \text{moles}

Equivalents of oxidant = equivalents of reductant at equivalence

Half-Reaction Method

(Oxidation half)+(Reduction half)=balanced equation\text{(Oxidation half)} + \text{(Reduction half)} = \text{balanced equation}

Balance atoms, then balance charge with e⁻

Cell Potential

Ecell∘=Ecathode∘−Eanode∘E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}

Positive E° = spontaneous under standard conditions

H₂O₂ Oxidation State

OS of O in H2O2=−1\text{OS of O in H}_2\text{O}_2 = -1

Between −2 (water) and 0 (O₂); acts as both oxidant and reductant

H₂O₂ Normality

N=M×2N = M\times2

n-factor of H₂O₂ = 2 in most redox reactions

Strength of H₂O₂ (volume strength)

Volume strength=5.6×N=11.2×M\text{Volume strength} = 5.6\times N = 11.2\times M

Volume of O₂ (mL at STP) released by 1 mL of H₂O₂

Structure of Water

∠H-O-H=104.5°\angle H\text{-}O\text{-}H = 104.5°

Bent/V-shaped; sp³ hybridised O with 2 lone pairs

Hard Water Hardness

Temporary hardness: HCO3− salts; Permanent: Cl−,SO42− salts\text{Temporary hardness: HCO}_3^-\text{ salts; Permanent: Cl}^-,\text{SO}_4^{2-}\text{ salts}

Temporary removed by boiling; permanent by chemicals

Flame Test Colors

Li: crimson, Na: golden, K: lilac, Ca: brick red, Sr: crimson, Ba: apple green\text{Li: crimson, Na: golden, K: lilac, Ca: brick red, Sr: crimson, Ba: apple green}

Characteristic emission due to electronic transitions

Diagonal Relationship

Li∼Mg;Be∼Al;Na∼Ca\text{Li}\sim\text{Mg};\quad\text{Be}\sim\text{Al};\quad\text{Na}\sim\text{Ca}

Similar properties due to comparable charge/radius ratio

Hydration Enthalpy Order (Alkali)

Li+>Na+>K+>Rb+>Cs+\text{Li}^+ > \text{Na}^+ > \text{K}^+ > \text{Rb}^+ > \text{Cs}^+

Smaller ion → higher charge density → more hydration

Reaction with Water

2M+2H2O→2MOH+H2↑2M + 2H_2O \rightarrow 2MOH + H_2\uparrow

M = Group 1 alkali metals; reactivity increases down the group

Boron Family (Group 13)

Valence e−:ns2np1,usual OS: +3\text{Valence e}^-: ns^2np^1,\quad\text{usual OS: +3}

B is metalloid; Al, Ga, In, Tl are metals

Carbon Family (Group 14)

Valence e−:ns2np2,usual OS: +4, +2\text{Valence e}^-: ns^2np^2,\quad\text{usual OS: +4, +2}

C is unique: catenation, allotropes, tetravalency

Nitrogen Family (Group 15)

OS range: −3 to +5\text{OS range: }-3\text{ to }+5

N: −3(NH₃) to +5(HNO₃); P: −3 to +5

Oxygen Family (Group 16)

OS of O: 0 to −2 (usually −2)\text{OS of O: }0\text{ to }-2 \text{ (usually }-2\text{)}

Highest EN after F; S shows +4 and +6 also

Halogen Family (Group 17)

Oxidising power: F2>Cl2>Br2>I2\text{Oxidising power: }F_2 > Cl_2 > Br_2 > I_2

F₂ strongest oxidising agent; cannot be oxidised further

Noble Gases (Group 18)

Ionisation Energy: highest in period\text{Ionisation Energy: highest in period}

Xe forms compounds: XeF₂, XeF₄, XeO₃ etc.

Oxyacid Strength (Halogens)

HClO<HClO2<HClO3<HClO4\text{HClO} < \text{HClO}_2 < \text{HClO}_3 < \text{HClO}_4

More O atoms → more electron withdrawal → stronger acid

Degree of Unsaturation (DBE)

DBE=2C+2+N−H−X2DBE = \frac{2C+2+N-H-X}{2}

C = carbons, H = hydrogens, N = nitrogens, X = halogens; O and S ignored

Inductive Effect Order (−I)

−F>−Cl>−Br>−I>−OR>−OH>−NH2-F > -Cl > -Br > -I > -OR > -OH > -NH_2

Electron-withdrawing through σ-bonds

Resonance Effect (+M)

−OH, −NH2, −OR: lone pair into ring (+M)-OH,\,-NH_2,\,-OR:\text{ lone pair into ring (+M)}

+M groups increase electron density on ring

Resonance Effect (−M)

−NO2, −CHO, −COOH, −CN: withdraw by π (+)M)-NO_2,\,-CHO,\,-COOH,\,-CN:\text{ withdraw by }\pi\text{ (+)M)}

Electron-withdrawing via π system

Acidity (pKa)

More stable conjugate base=more acidic\text{More stable conjugate base} = \text{more acidic}

pKa: HF(3.2) > CH₃COOH(4.7) > HCN(9.2) > H₂O(15.7)

SN1 vs SN2

SN1: 3°>2°>1°, SN2: 1°>2°>3°\text{SN1: 3°>2°>1°, SN2: 1°>2°>3°}

SN1: carbocation stability; SN2: steric hindrance matters

Markovnikov's Rule

H adds to C with more H atoms (HX addition to alkenes)H\text{ adds to C with more H atoms (HX addition to alkenes)}

Carbocation stability: 3° > 2° > 1°

General Formula

Alkane: CnH2n+2,  Alkene: CnH2n,  Alkyne: CnH2n−2\text{Alkane: }C_nH_{2n+2},\;\text{Alkene: }C_nH_{2n},\;\text{Alkyne: }C_nH_{2n-2}

Each degree of unsaturation removes 2H

Combustion of Alkane

CnH2n+2+3n+12O2→nCO2+(n+1)H2OC_nH_{2n+2} + \frac{3n+1}{2}O_2 \rightarrow nCO_2 + (n+1)H_2O

Complete combustion in excess O₂

Ozonolysis (Alkene)

C=C+O3→Zn/H2Otwo carbonyl compounds\text{C=C} + O_3\xrightarrow{\text{Zn/H}_2\text{O}} \text{two carbonyl compounds}

Cleavage of C=C double bond; identifies position of double bond

Wurtz Reaction

2RX+2Na→dry etherR-R+2NaX2\text{RX} + 2\text{Na}\xrightarrow{\text{dry ether}} \text{R-R} + 2\text{NaX}

Coupling of alkyl halides; best for symmetric products

Aromaticity (Hückel)

4n+2 π electrons,n=0,1,2,...4n+2\text{ π electrons},\quad n = 0,1,2,...

Benzene: n=1 (6π); cyclopentadienyl anion: n=1 (6π)

Friedel-Crafts Alkylation

C6H6+RCl→AlCl3C6H5R+HCl\text{C}_6\text{H}_6 + \text{RCl}\xrightarrow{\text{AlCl}_3} \text{C}_6\text{H}_5\text{R} + \text{HCl}

Electrophilic aromatic substitution; Lewis acid catalyst

BOD

BOD=Biochemical Oxygen Demand\text{BOD} = \text{Biochemical Oxygen Demand}

Amount of O₂ needed by microbes to decompose organic matter in water; higher BOD = more polluted

Ozone Depletion

Cl∙+O3→ClO∙+O2\text{Cl}^\bullet + \text{O}_3 \rightarrow \text{ClO}^\bullet + \text{O}_2

CFC-derived Cl radicals destroy ozone catalytically

Photochemical Smog

NO2→hνNO+O∙,O∙+O2→O3\text{NO}_2 \xrightarrow{h\nu} \text{NO} + \text{O}^\bullet,\quad \text{O}^\bullet + \text{O}_2 \rightarrow \text{O}_3

Ozone formed at ground level (harmful); different from stratospheric ozone

Greenhouse Gases

CO2, CH4, N2O, CFCs, H2O vapour\text{CO}_2,\,\text{CH}_4,\,\text{N}_2\text{O},\,\text{CFCs},\,\text{H}_2\text{O vapour}

Absorb and re-emit IR radiation causing warming

pH of Acid Rain

pH<5.6\text{pH} < 5.6

CO₂ + H₂O → H₂CO₃; SO₂, NOx make it more acidic

Packing Efficiency — Simple Cubic

PE=43πr3a3×100=52.4%PE = \frac{\frac{4}{3}\pi r^3}{a^3}\times100 = 52.4\%

a = 2r; 1 atom per unit cell

Packing Efficiency — BCC

PE=68%PE = 68\%

a√3 = 4r; 2 atoms per unit cell

Packing Efficiency — FCC/HCP

PE=74%PE = 74\%

a√2 = 4r; 4 atoms per unit cell (FCC); most efficient

Number of Atoms per Unit Cell

Z=Ncorner×18+Nface×12+Nedge×14+Nbody×1Z = N_{corner}\times\frac{1}{8} + N_{face}\times\frac{1}{2} + N_{edge}\times\frac{1}{4} + N_{body}\times1

Contribution rule for different positions

Density of Crystal

ρ=Z×MNA×a3\rho = \frac{Z\times M}{N_A\times a^3}

Z = atoms/cell; M = molar mass; a = edge length

Schottky Defect

ns=N e−ΔHs/2RTn_s = N\,e^{-\Delta H_s/2RT}

Equal cation and anion vacancies; density decreases

Frenkel Defect

nF=NN′ e−ΔHF/2RTn_F = \sqrt{NN'}\,e^{-\Delta H_F/2RT}

Ion shifts to interstitial site; density unchanged

Raoult's Law

PA=χAPA∘P_A = \chi_A P_A^\circ

Partial vapour pressure of A = mole fraction × VP of pure A

Vapour Pressure Lowering

P∘−PsP∘=χsolute\frac{P^\circ - P_s}{P^\circ} = \chi_{solute}

Relative lowering of vapour pressure

Boiling Point Elevation

ΔTb=Kb⋅m\Delta T_b = K_b\cdot m

K_b for water = 0.52 K·kg/mol; m = molality

Freezing Point Depression

ΔTf=Kf⋅m\Delta T_f = K_f\cdot m

K_f for water = 1.86 K·kg/mol; m = molality

Osmotic Pressure

π=CRT=nRTV\pi = CRT = \frac{nRT}{V}

C = molarity; R = 0.0821 L·atm/mol·K; isotonic: π₁ = π₂

Van't Hoff Factor

i=observed colligative propertyideal colligative propertyi = \frac{\text{observed colligative property}}{\text{ideal colligative property}}

i > 1: dissociation; i < 1: association

Modified Colligative Property

ΔTb=iKbm,π=iCRT\Delta T_b = iK_b m,\quad\pi = iCRT

i accounts for electrolyte dissociation

Degree of Dissociation from i

α=i−1n−1\alpha = \frac{i-1}{n-1}

n = number of ions produced per formula unit

Henry's Law

p=KH⋅χp = K_H\cdot\chi

Solubility of gas ∝ partial pressure above solution; K_H varies with gas and T

Standard Cell Potential

Ecell∘=Ecathode∘−Eanode∘E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}

Positive E° = spontaneous (galvanic cell)

Nernst Equation (25°C)

Ecell=Ecell∘−0.0592nlog⁡QE_{cell} = E^\circ_{cell} - \frac{0.0592}{n}\log Q

n = electrons transferred; Q = reaction quotient

Gibbs Energy & Cell Potential

ΔG∘=−nFEcell∘\Delta G^\circ = -nFE^\circ_{cell}

F = 96485 C/mol (Faraday's constant)

Equilibrium from E°

log⁡K=nEcell∘0.0592at 25°C\log K = \frac{nE^\circ_{cell}}{0.0592}\quad\text{at 25°C}

Links thermodynamics, electrochemistry and equilibrium

Faraday's First Law

m=M⋅I⋅tn⋅Fm = \frac{M\cdot I\cdot t}{n\cdot F}

M = molar mass; n = n-factor; I = current (A); t = time (s)

Faraday's Second Law

m1m2=E1E2\frac{m_1}{m_2} = \frac{E_1}{E_2}

E = equivalent weight = M/n-factor

Molar Conductivity

Λm=κ×1000M\Lambda_m = \frac{\kappa\times1000}{M}

κ = specific conductance (S/cm); M = molarity

Kohlrausch's Law

Λm∞=ν+λ+∞+ν−λ−∞\Lambda_m^\infty = \nu_+\lambda_+^\infty + \nu_-\lambda_-^\infty

At infinite dilution; independent ionic contributions

α from Conductance

α=ΛmΛm∞\alpha = \frac{\Lambda_m}{\Lambda_m^\infty}

Degree of dissociation for weak electrolytes

Rate of Reaction

r=−1ad[A]dt=+1cd[C]dtr = -\frac{1}{a}\frac{d[A]}{dt} = +\frac{1}{c}\frac{d[C]}{dt}

For aA + bB → cC + dD; always positive

Rate Law

r=k[A]m[B]nr = k[A]^m[B]^n

m, n = orders; determined experimentally (not stoichiometry)

Units of k (nth order)

[k]=(mol/L)1−n⋅s−1[k] = (\text{mol/L})^{1-n}\cdot\text{s}^{-1}

Zero order: mol/L·s; First order: s⁻¹; Second order: L/mol·s

Zero Order: [A] vs t

[A]=[A]0−kt,t1/2=[A]02k[A] = [A]_0 - kt,\quad t_{1/2} = \frac{[A]_0}{2k}

Linear [A]–t graph; half-life depends on [A]₀

First Order: [A] vs t

[A]=[A]0e−kt,ln⁡[A]=ln⁡[A]0−kt[A] = [A]_0 e^{-kt},\quad\ln[A] = \ln[A]_0 - kt

Exponential decay; linear ln[A]–t graph

First Order Half-Life

t1/2=ln⁡2k=0.693kt_{1/2} = \frac{\ln2}{k} = \frac{0.693}{k}

Independent of [A]₀ — key identifier of first order

Arrhenius Equation

k=Ae−Ea/RTk = Ae^{-E_a/RT}

A = frequency factor; E_a = activation energy (J/mol)

Arrhenius: Two Temperatures

log⁡k2k1=Ea2.303R ⁣(1T1−1T2)\log\frac{k_2}{k_1} = \frac{E_a}{2.303R}\!\left(\frac{1}{T_1}-\frac{1}{T_2}\right)

Used to calculate E_a or predict k at new temperature

Freundlich Isotherm

xm=kP1/n(0<1n<1)\frac{x}{m} = kP^{1/n}\quad(0 < \tfrac{1}{n} < 1)

x/m = amount adsorbed per gram of adsorbent

Freundlich (log form)

log⁡xm=log⁡k+1nlog⁡P\log\frac{x}{m} = \log k + \frac{1}{n}\log P

Straight line graph; slope = 1/n, intercept = log k

Langmuir Isotherm

xm=aP1+bP\frac{x}{m} = \frac{aP}{1+bP}

Monolayer adsorption; a, b = Langmuir constants

Tyndall Effect

Colloid particle size: 1–1000 nm\text{Colloid particle size: 1–1000 nm}

Scattering of light by colloidal particles; not seen in true solutions

Coagulation (Hardy-Schulze Rule)

Higher charge of coagulating ion=greater coagulating power\text{Higher charge of coagulating ion} = \text{greater coagulating power}

Trivalent > divalent > monovalent

Ellingham Diagram Criterion

ΔG=ΔH−TΔS<0 for feasible reduction\Delta G = \Delta H - T\Delta S < 0\text{ for feasible reduction}

Lower ΔG°_formation means stronger reducing agent at that T

Flux Reactions

Basic flux (CaO) + acidic gangue (SiO2)→slag\text{Basic flux (CaO) + acidic gangue (SiO}_2\text{)} \rightarrow \text{slag}

Flux removes gangue as slag; acidic flux for basic gangue

van Arkel Method

TiI4→ΔTi (pure)+2I2\text{TiI}_4\xrightarrow{\Delta}\text{Ti (pure)} + 2\text{I}_2

Thermal decomposition for purification of Ti, Zr, Si

Zone Refining

k=cscl<1 (impurity concentrates in melt)k = \frac{c_s}{c_l} < 1\text{ (impurity concentrates in melt)}

k = distribution coefficient; impurity swept to one end

Bond Angle: NH₃ vs PH₃

∠H-N-H=107.8°  >  ∠H-P-H=93.5°\angle\text{H-N-H} = 107.8°\; > \;\angle\text{H-P-H} = 93.5°

N: large lone pair repulsion on small central atom

Acid Strength of Oxoacids (N)

HNO3>HNO2\text{HNO}_3 > \text{HNO}_2

+5 oxidation state → stronger acid; more O atoms

Thermal Stability of Hydrides (Group 15)

NH3>PH3>AsH3>SbH3\text{NH}_3 > \text{PH}_3 > \text{AsH}_3 > \text{SbH}_3

M-H bond strength decreases down group

Bleaching Power of Cl₂

Cl2+H2O→HCl+HOCl→O (nascent)\text{Cl}_2 + \text{H}_2\text{O} \rightarrow \text{HCl} + \text{HOCl}\xrightarrow{} \text{O (nascent)}

Nascent O bleaches; permanent bleaching

Bond Dissociation Energy (Halogens)

Cl2>Br2>F2>I2\text{Cl}_2 > \text{Br}_2 > \text{F}_2 > \text{I}_2

F₂ anomalously weak due to lone pair–lone pair repulsion

Xenon Fluorides Geometry

XeF2:linear,  XeF4:sq. planar,  XeF6:distorted octahedral\text{XeF}_2: \text{linear},\;\text{XeF}_4: \text{sq. planar},\;\text{XeF}_6: \text{distorted octahedral}

VSEPR determines geometry

Magnetic Moment

μ=n(n+2) BM\mu = \sqrt{n(n+2)}\text{ BM}

n = number of unpaired electrons; BM = Bohr Magnetons

Variable Oxidation States

Easy (n-1)d e− participation due to similar energy to ns\text{Easy (n-1)d e}^-\text{ participation due to similar energy to ns}

Ti: +2 to +4; Mn: +2 to +7; Cr: +2 to +6

Lanthanoid Contraction

Poor shielding by 4f e−⇒Z∗↑⇒r↓\text{Poor shielding by 4f e}^-\Rightarrow Z^*\uparrow\Rightarrow r\downarrow

Across lanthanoids, size decreases gradually but cumulatively

Catalytic Activity (d-block)

Variable OS+ability to adsorb reactants\text{Variable OS} + \text{ability to adsorb reactants}

Fe (Haber), Pt (Ostwald), V₂O₅ (Contact process)

Colour (d-block)

d−d transition absorbs visible light⇒complementary colour seend-d\text{ transition absorbs visible light}\Rightarrow\text{complementary colour seen}

Cu²⁺: blue; Cr³⁺: violet; Mn²⁺: pale pink; Zn²⁺: colourless

Coordination Number

CN=number of donor atoms directly bonded to metalCN = \text{number of donor atoms directly bonded to metal}

[Co(NH₃)₆]³⁺: CN=6; [PtCl₄]²⁻: CN=4

Werner's Primary & Secondary Valency

Primary: ionisable; Secondary: coordination sphere\text{Primary: ionisable; Secondary: coordination sphere}

[CoCl₃(NH₃)₃]: primary=3, secondary=6

Crystal Field Splitting (Octahedral)

Δo=E(eg)−E(t2g)\Delta_o = E(e_g) - E(t_{2g})

Strong field ligand: large Δ_o (low spin); weak field: small Δ_o (high spin)

CFSE (Octahedral, Strong Field)

CFSE=−0.4n1Δo+0.6n2ΔoCFSE = -0.4n_1\Delta_o + 0.6n_2\Delta_o

n₁ = electrons in t₂g; n₂ = electrons in e_g

Magnetic Moment

μspin−only=n(n+2) BM\mu_{spin-only} = \sqrt{n(n+2)}\text{ BM}

n = unpaired electrons in complex

Spectrochemical Series

I−<Br−<Cl−<F−<OH−<en<CN−<COI^- < Br^- < Cl^- < F^- < OH^- < en < CN^- < CO

Increasing field strength → increasing Δ

SN2 Rate

Rate=k[RX][Nu−]\text{Rate} = k[\text{RX}][\text{Nu}^-]

Bimolecular; inversion of configuration; 1° > 2° > 3°

SN1 Rate

Rate=k[RX]\text{Rate} = k[\text{RX}]

Unimolecular; racemisation; 3° > 2° > 1°

Reactivity Order (RX with SN2)

RI>RBr>RCl>RF\text{RI} > \text{RBr} > \text{RCl} > \text{RF}

C-I bond weakest; best leaving group

Elimination vs Substitution

Bulky base/high T: elimination (E2); small Nu/low T: substitution\text{Bulky base/high T: elimination (E2); small Nu/low T: substitution}

Hoffman elimination with bulky base; Zaitsev with non-bulky

Benzene Diazonium Salt Reactions

ArN2+Cl−→Ar-X, Ar-OH, Ar-CN, Ar-H...\text{ArN}_2^+\text{Cl}^- \rightarrow \text{Ar-X, Ar-OH, Ar-CN, Ar-H...}

Key synthetic intermediate in aromatic substitution

Lucas Test

3°: immediate cloudiness; 2°: slow; 1°: no reaction with ZnCl2/HCl\text{3°: immediate cloudiness; 2°: slow; 1°: no reaction with ZnCl}_2\text{/HCl}

Distinguishes primary, secondary, tertiary alcohols

Esterification

RCOOH + R’OH→H+,Δ−H2ORCOOR’\text{RCOOH + R'OH} \underset{-H_2O}{\xrightarrow{H^+,\Delta}} \text{RCOOR'}

Acid-catalysed; reversible

Iodoform Test

CH3CHO, CH3CO-R, C2H5OH→I2/NaOHCHI3\text{CH}_3\text{CHO, CH}_3\text{CO-R, C}_2\text{H}_5\text{OH}\xrightarrow{I_2/\text{NaOH}} \text{CHI}_3

Yellow precipitate: positive test for methyl ketone or ethanol

Phenol Acidity

pKa(phenol)≈10,  pKa(alcohol)≈16pK_a(\text{phenol}) \approx 10,\;pK_a(\text{alcohol}) \approx 16

Phenol more acidic due to resonance stabilisation of phenoxide

Kolbe's Reaction

C6H5OH+CO2→NaOH,Δ,Psalicylate\text{C}_6\text{H}_5\text{OH} + \text{CO}_2 \xrightarrow{\text{NaOH},\Delta, P} \text{salicylate}

Sodium phenoxide + CO₂ under pressure → sodium salicylate

Cleavage of Ethers (HI)

R-O-R’+HI→ΔROH + R’I\text{R-O-R'} + \text{HI}\xrightarrow{\Delta}\text{ROH + R'I}

Larger R group gets iodide; SN2 mechanism

Nucleophilic Addition (Aldehyde > Ketone)

Reactivity: HCHO > RCHO > RCOR’\text{Reactivity: HCHO > RCHO > RCOR'}

Steric and electronic factors: less alkyl = more reactive

Aldol Condensation

2CH3CHO→dil. OH−CH3CH(OH)CH2CHO2\text{CH}_3\text{CHO}\xrightarrow{\text{dil. OH}^-}\text{CH}_3\text{CH(OH)CH}_2\text{CHO}

α-H aldehyde/ketone; forms β-hydroxy carbonyl

Cannizzaro Reaction

2HCHO→conc. OH−CH3OH+HCOONa2\text{HCHO}\xrightarrow{\text{conc. OH}^-}\text{CH}_3\text{OH} + \text{HCOONa}

No α-H; disproportionation of aldehyde

Tollen's Test

RCHO+2[Ag(NH3)2]+→RCOOH+2Ag↓\text{RCHO} + 2[\text{Ag(NH}_3\text{)}_2]^+\rightarrow\text{RCOOH} + 2\text{Ag}\downarrow

Silver mirror test; only aldehydes (not ketones)

Fehling's Test

RCHO+2Cu2+→RCOOH+Cu2O↓(red)\text{RCHO} + 2\text{Cu}^{2+}\rightarrow\text{RCOOH} + \text{Cu}_2\text{O}\downarrow\text{(red)}

Aliphatic aldehydes only; ketones don't react

Carboxylic Acid pKa

Electron-withdrawing groups increase acidity (↓ pKa)\text{Electron-withdrawing groups increase acidity (↓ pKa)}

FCH₂COOH (2.59) < ClCH₂COOH (2.86) < CH₃COOH (4.74)

Hell-Volhard-Zelinsky

RCOOH+Cl2→PRCH(Cl)COOH\text{RCOOH} + Cl_2\xrightarrow{\text{P}}\text{RCH(Cl)COOH}

α-halogenation of carboxylic acids

Basicity Order (Aliphatic)

R2NH>RNH2>R3N>NH3 (aqueous)\text{R}_2\text{NH} > \text{RNH}_2 > \text{R}_3\text{N} > \text{NH}_3\text{ (aqueous)}

Steric vs. inductive; 2° amine most basic in water

Basicity: Aniline vs Alkyl Amine

Alkyl amine≫Aniline (aromatic)\text{Alkyl amine} \gg \text{Aniline (aromatic)}

Lone pair delocalisation in aniline reduces basicity

Substituted Aniline Basicity

o,p-withdrawing groups decrease; o,p-donating increase basicityo,p\text{-withdrawing groups decrease; o,p-donating increase basicity}

NO₂ group at ortho/para decreases basicity most

Diazonium Salt Formation

ArNH2+NaNO2+HCl→0-5°CArN2+Cl−\text{ArNH}_2 + \text{NaNO}_2 + \text{HCl}\xrightarrow{0\text{-}5°C}\text{ArN}_2^+\text{Cl}^-

Low temperature critical to prevent hydrolysis

Hoffmann Bromamide

RCONH2+Br2+4NaOH→RNH2+Na2CO3+2NaBr+2H2O\text{RCONH}_2 + \text{Br}_2 + 4\text{NaOH}\rightarrow\text{RNH}_2 + \text{Na}_2\text{CO}_3 + 2\text{NaBr} + 2\text{H}_2\text{O}

Carbon chain decreases by 1; primary amine product

Gabriel Phthalimide

Phthalimide→KOH, RX, H3O+RNH2\text{Phthalimide}\xrightarrow{\text{KOH, RX, H}_3\text{O}^+}\text{RNH}_2

Synthesis of primary amines without secondary/tertiary contamination

Glycosidic Bond

Monosaccharide+Monosaccharide→−H2ODisaccharide\text{Monosaccharide} + \text{Monosaccharide}\xrightarrow{-H_2O}\text{Disaccharide}

C1-OH of one sugar + OH of another; α- or β-linkage

Isoelectric Point

pI=pKa1+pKa22pI = \frac{pK_{a1} + pK_{a2}}{2}

pH at which amino acid has zero net charge; minimum solubility

Peptide Bond

-COOH+H2N-→-CO-NH-+H2O\text{-COOH} + \text{H}_2\text{N-}\rightarrow\text{-CO-NH-} + H_2O

Planar and rigid due to partial double bond character (resonance)

Mutarotation

α-D-glucose⇌Δopen chain⇌β-D-glucose\text{α-D-glucose}\underset{\Delta}{\rightleftharpoons}\text{open chain}\rightleftharpoons\text{β-D-glucose}

Change in optical rotation until equilibrium; characteristic of reducing sugars

Protein Structure Levels

1°: peptide bonds; 2°: H-bonds; 3°: S-S, H-bonds; 4°: subunit interactions1°\text{: peptide bonds; }2°\text{: H-bonds; }3°\text{: S-S, H-bonds; }4°\text{: subunit interactions}

Primary to quaternary structure

Degree of Polymerisation

n=MpolymerMmonomern = \frac{M_{polymer}}{M_{monomer}}

Number of monomer units in polymer chain

Addition Polymerisation

nCH2 ⁣= ⁣CH2→(−CH2-CH2-)nn\text{CH}_2\!=\!\text{CH}_2\rightarrow(-\text{CH}_2\text{-CH}_2\text{-})_n

Chain growth; no byproduct; monomers with π bond

Condensation Polymerisation

Bifunctional monomers→−small molecule (H2O/HCl)polymer\text{Bifunctional monomers}\xrightarrow{-\text{small molecule (H}_2\text{O/HCl)}}\text{polymer}

Step growth; nylon, dacron, bakelite

Nylon 6,6

Hexanedioic acid+1,6-diaminohexane→nylon-6,6\text{Hexanedioic acid} + \text{1,6-diaminohexane}\rightarrow\text{nylon-6,6}

Polyamide: 6 carbons from each monomer unit

Glass Transition Temperature (Tg)

T<Tg: glassy; T>Tg: rubberyT < T_g:\text{ glassy; }T > T_g:\text{ rubbery}

Amorphous polymers soften above Tg

Drug-Receptor Interaction

Agonist: mimics natural molecule; Antagonist: blocks receptor\text{Agonist: mimics natural molecule; Antagonist: blocks receptor}

Shape and functional group complementarity determines activity

Antacid Action

Mg(OH)2+2HCl→MgCl2+2H2O\text{Mg(OH)}_2 + 2\text{HCl}\rightarrow\text{MgCl}_2 + 2\text{H}_2\text{O}

Neutralises excess stomach acid; raises pH

Soap Saponification

Fat (ester)+NaOH→ΔSoap (carboxylate)+Glycerol\text{Fat (ester)} + \text{NaOH}\xrightarrow{\Delta}\text{Soap (carboxylate)} + \text{Glycerol}

Base hydrolysis of triglyceride

CMC (Critical Micelle Concentration)

Above CMC: micelles form and trap grease\text{Above CMC: micelles form and trap grease}

Hydrophilic head faces water; hydrophobic tail faces grease

Artificial Sweetener Relative Sweetness

Saccharin≈550×,  Aspartame≈200×,  Sucralose≈600× (vs sucrose)\text{Saccharin}\approx550\times,\;\text{Aspartame}\approx200\times,\;\text{Sucralose}\approx600\times\text{ (vs sucrose)}

Sweetness relative to sucrose; used by diabetics

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