CBSE Class 12 Chemistry Important Formulas All Chapters

Chapter 1: The Solid State

Number of Atoms per Unit Cell

• Simple Cubic (SC): 1 atom per unit cell, edge length \( a = 2r \)
• Body Centred Cubic (BCC): 2 atoms per unit cell, \( a = \dfrac{4r}{\sqrt{3}} \)
• Face Centred Cubic (FCC): 4 atoms per unit cell, \( a = 2\sqrt{2}\, r \)

Density of Unit Cell

\[ d = \frac{Z \times M}{a^3 \times N_A} \] where \( Z \) = number of atoms per unit cell, \( M \) = molar mass, \( a \) = edge length, \( N_A \) = Avogadro's number.

Packing Efficiency

\[ \text{Packing Efficiency} = \frac{Z \times \dfrac{4}{3}\pi r^3}{a^3} \times 100\% \]

• SC: 52.4%  |  BCC: 68%  |  FCC/HCP: 74%

Chapter 2: Solutions

Concentration Terms

\[ \text{Mole Fraction of A: } x_A = \frac{n_A}{n_A + n_B} \] \[ \text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution (L)}} \] \[ \text{Molality (m)} = \frac{\text{Moles of solute}}{\text{Mass of solvent (kg)}} \] \[ \text{ppm} = \frac{\text{Mass of component}}{\text{Total mass of solution}} \times 10^6 \]

Raoult's Law

\[ p_A = p_A^{\circ}\, x_A \qquad p_B = p_B^{\circ}\, x_B \] \[ p_{\text{total}} = p_A^{\circ}\, x_A + p_B^{\circ}\, x_B \]

Colligative Properties

\[ \frac{p^{\circ} - p_s}{p^{\circ}} = x_{\text{solute}} \quad \text{(Relative lowering of vapour pressure)} \] \[ \Delta T_b = i \cdot K_b \cdot m \quad \text{(Elevation of boiling point)} \] \[ \Delta T_f = i \cdot K_f \cdot m \quad \text{(Depression of freezing point)} \] \[ \pi = i\,C\,R\,T \quad \text{(Osmotic pressure)} \]

Van't Hoff Factor

\[ i = \frac{\text{Observed colligative property}}{\text{Theoretical colligative property}} = \frac{\text{Normal molar mass}}{\text{Abnormal molar mass}} \]

• \( i > 1 \): dissociation  |  \( i < 1 \): association  |  \( i = 1 \): ideal

Chapter 3: Electrochemistry

Conductivity

\[ \kappa = \frac{1}{\rho} = G \times G^* \qquad \text{where } G^* = \frac{l}{A} \text{ (cell constant)} \] \[ \Lambda_m = \frac{\kappa \times 1000}{C} \]

Kohlrausch's Law

\[ \Lambda_m^{\circ} = \lambda^{\circ}_{+} + \lambda^{\circ}_{-} \] \[ \Lambda_m = \Lambda_m^{\circ} - K\sqrt{C} \quad \text{(for strong electrolytes)} \]

Degree of Dissociation

\[ \alpha = \frac{\Lambda_m}{\Lambda_m^{\circ}} \]

Faraday's Laws

\[ m = Z \cdot I \cdot t \qquad Z = \frac{M}{n \times F} \] where \( F = 96500 \) C/mol, \( n \) = number of electrons.

Nernst Equation

\[ E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{RT}{nF} \ln Q = E^{\circ}_{\text{cell}} - \frac{0.0591}{n} \log Q \quad \text{(at 298 K)} \]

Gibbs Energy and EMF

\[ \Delta G^{\circ} = -nFE^{\circ}_{\text{cell}} \] \[ \Delta G^{\circ} = -RT \ln K \qquad \Rightarrow \quad E^{\circ}_{\text{cell}} = \frac{0.0591}{n} \log K \quad \text{(at 298 K)} \]

Chapter 4: Chemical Kinetics

Rate of Reaction

\[ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} \] \[ \text{Rate} = k[A]^m[B]^n \]

Integrated Rate Laws

Zero order: [ [A]_t = [A]0 - kt \qquad t{1/2} = \frac{[A]_0}{2k} ] First order: [ \ln[A]_t = \ln[A]_0 - kt \qquad k = \frac{2.303}{t}\log\frac{[A]_0}{[A]t} \qquad t{1/2} = \frac{0.693}{k} ]

Arrhenius Equation

\[ k = A\,e^{-E_a/RT} \] \[ \log\frac{k_2}{k_1} = \frac{E_a}{2.303\,R}\left(\frac{T_2 - T_1}{T_1 T_2}\right) \]

Chapter 5: d and f Block Elements

No major numerical formulas - key expressions to remember:

\[ \mu = \sqrt{n(n+2)} \text{ B.M.} \quad \text{(magnetic moment, where } n = \text{unpaired electrons)} \]

Chapter 6: Coordination Compounds

Stability Constant

\[ K_f = \frac{[\text{Complex}]}{[\text{Metal ion}][\text{Ligand}]^n} \]

Higher \( K_f \) = more stable complex. Crystal Field Splitting: \( \Delta_o \) (octahedral) and \( \Delta_t \) (tetrahedral), with \( \Delta_t = \dfrac{4}{9}\Delta_o \).

Chapter 7: Haloalkanes and Haloarenes

No major numerical formulas. Key reaction types for board exams:

• SN1 reaction: rate = \( k[\text{RX}] \) (first order, carbocation intermediate)
• SN2 reaction: rate = \( k[\text{RX}][\text{Nu}^-] \) (second order, backside attack)
• Optical rotation: \( [\alpha] = \dfrac{\alpha}{l \times c} \) where \( l \) = path length (dm), \( c \) = concentration (g/mL)

Chapter 8: Alcohols, Phenols and Ethers

No direct numerical formulas. Key relation for acidic strength:

• Acidic strength order: Phenol > Water > Alcohol
• \( \text{pKa} \): Phenol ≈ 10  |  Alcohol ≈ 16–18
• Lucas test distinguishes 1°, 2°, 3° alcohols - reaction rates follow: 3° > 2° > 1°

Chapter 9: Aldehydes, Ketones and Carboxylic Acids

• Acidic strength of carboxylic acids increases with electron-withdrawing groups on the \( \alpha \)-carbon
• \( \text{pKa} \) of acetic acid = 4.74
• Cannizzaro reaction (for aldehydes with no \( \alpha \)-H): disproportionation
• Aldol condensation: requires \( \alpha \)-hydrogen - product is \( \beta \)-hydroxy aldehyde/ketone

Chapter 10: Amines

Basicity

\[ K_b = \frac{[BH^+][OH^-]}{[B]} \qquad \text{pKb} = -\log K_b \]

• Basic strength order (in water): aliphatic amines > NH3 > aromatic amines
• Aniline is a much weaker base than aliphatic amines due to lone pair delocalisation into benzene ring

Diazonium Salt

\[ \text{ArNH}_2 \xrightarrow{\text{NaNO}_2/\text{HCl, 0--5°C}} \text{ArN}_2^+\text{Cl}^- \]

Chapter 11: Biomolecules

No numerical formulas - key structural facts:

• Glucose molecular formula: \( \text{C}_6\text{H}_{12}\text{O}_6 \)
• Sucrose: Glucose + Fructose (non-reducing sugar)
• Peptide bond: \( -\text{CO}-\text{NH}- \) (formed between –COOH and –NH2 groups)
• DNA: deoxyribose sugar + phosphate + nitrogenous bases (A, T, G, C)
• RNA: ribose sugar + phosphate + bases (A, U, G, C)

Solution

1. Mole fraction (x)

if the number of moles of A and B are nA and nB respectrively, the mole fraction of A and B will be

X_A= X/n_A+n_B , AND  X_B = n_B / n_A+n_B

2. Molarity (M) = Moles of solute/ Volume of solution in litres

3. Moality (m) = Moles of solute / Mass of solvent in kilograms

4. Parts per million (ppm) = Number of parts of the component 106 /Total number of parts of all components of the solution

5. Raoult’s law for a solution of volatile solute in volatile solvent :

p_A = p_A° x_A

p_B = p_B° x_B

Where p_A and p_B are partial vapour pressures of component ‘A’ and component ‘B’ in solution. p_A° and p_B° are vapour pressures of pure components ‘A’ and ‘B’ respectively.

6. Raoults law for a solution of non-volatile solute and volatile solvent :

p °_A – p °_A/ p °_A  = i  n_B /n_A =  i   W_B* M_A / M_B* W_A  (for dilute solution)

Where xB is mole fraction of solute, i is van’t Hoff factor and A A

p °_A – p °_A / p_A °  IS Nrelative lowering of vapour pressure.

Chemical Kinetics

1. Integrated rate law equation for zero order reaction
(a) k = [R]_º[R]/t
Where k is rate constant and [R]₀ is initial molar concentration.

(b) t_1/2 = [R]_º/2k

t_1/2 is half life period of zero order reaction.

2. Integrated rate law equation for first order reaction

(a) k = 2.303/k log [R]_º/[R]

Where k is rate constant, [R]_° is initial molar concentration and [R] is final concentration at time ‘t’.

(b) Half life period (t_1/2) for first order reaction :

t_1/2 = 0.693/k

3. Anhenius epuation

(a) k = A_e –Ea/RT 
Where ‘A’ is frequency factor, Ea is the energy of activation, R is universal gas contant and T is absolute temperature.

^–Ea/_RT gives the fraction of collisions having energy equal to or greater than Ea.

(b) log k₁/k₂ = Ea/ 2.303 R (T₂ - T₁/T₁ - T₂)
Where k₁ is rate constant at temperature T₁ and k₂ is rate constant at temperature T₂.

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