Basic Concepts & Stoichiometry Class 11
Law of Conservation of Mass
Matter can neither be created nor destroyed during a chemical reaction. Therefore, the total mass of the reactants must equal the total mass of the products.
$$\text{Total Mass of Reactants} = \text{Total Mass of Products}$$
Law of Definite / Constant Proportions
A given chemical compound always contains its component elements in a fixed ratio by mass, regardless of its source or method of preparation. For example, pure water always contains hydrogen and oxygen in an 1:8 mass ratio.
Law of Multiple Proportions
When two elements combine to form more than one compound, the different masses of one element combining with a fixed mass of the other are in simple whole-number ratios. This explains the formation of distinct compounds like CO and CO₂.
Avogadro's Law
Equal volumes of all gases under identical conditions of temperature and pressure contain an equal number of molecules. This means the volume of a gas is directly proportional to its amount in moles.
$$V \propto n \quad (\text{at constant } T, P)$$
States of Matter & Gas Laws Class 11
Boyle's Law
At a constant temperature, the volume of a given mass of gas is inversely proportional to its pressure. Compressing a gas halves its volume when the pressure is doubled.
$$P_1 V_1 = P_2 V_2 \quad (\text{at constant } T, n)$$
Charles's Law
At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature in Kelvin. Heating a gas causes it to expand proportionally.
$$\frac{V_1}{T_1} = \frac{V_2}{T_2} \quad (\text{at constant } P, n)$$
Ideal Gas Equation
Combines Boyle's, Charles's, and Avogadro's laws into a single equation governing ideal gas behavior. It relates pressure, volume, temperature, and amount of gas using the universal gas constant R.
$$PV = nRT = \frac{m}{M}RT$$
Dalton's Law of Partial Pressures
The total pressure exerted by a mixture of non-reacting gases equals the sum of the partial pressures of each individual gas. Each gas's partial pressure is its mole fraction multiplied by total pressure.
$$P_{\text{total}} = p_1 + p_2 + p_3 + \dots$$
$$p_i = \chi_i \times P_{\text{total}}$$
Graham's Law of Diffusion / Effusion
The rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass or density. Lighter gases travel and escape through tiny openings significantly faster than heavier ones.
$$\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{d_2}{d_1}}$$
Thermodynamics & Thermochemistry Class 11
First Law of Thermodynamics
Energy can neither be created nor destroyed; it can only transform from one form to another. The change in internal energy equals the heat added to the system plus the work done on it.
$$\Delta U = q + w$$
$$\text{Reversible Expansion Work: } w = -2.303 \, nRT \log_{10}\left(\frac{V_2}{V_1}\right)$$
Hess's Law of Constant Heat Summation
The total enthalpy change in a reaction is the same whether the chemical transformation takes place in a single step or in multiple steps. Enthalpy is a state function independent of the reaction pathway.
$$\Delta_r H^\circ = \sum \Delta_f H^\circ(\text{products}) - \sum \Delta_f H^\circ(\text{reactants})$$
Gibbs Energy & Spontaneity
A chemical reaction occurs spontaneously at constant temperature and pressure if the change in Gibbs free energy ($\Delta G$) is negative. At equilibrium, $\Delta G$ becomes zero.
$$\Delta G = \Delta H - T\Delta S$$
$$\Delta G^\circ = -2.303 \, RT \log_{10} K_c$$
Solutions & Colligative Properties Class 12
Henry's Law
The solubility of a gas in a liquid at a given temperature is directly proportional to the partial pressure of that gas above the liquid surface. Higher gas pressure forces more gas molecules to dissolve.
$$p = K_H \cdot x$$
Raoult's Law
The partial vapour pressure of any volatile component in a solution is directly proportional to its mole fraction in that solution. For non-volatile solutes, adding solute lowers the liquid's vapour pressure.
$$p_A = p_A^\circ \cdot x_A, \quad p_B = p_B^\circ \cdot x_B$$
$$P_{\text{total}} = p_A^\circ x_A + p_B^\circ x_B$$
Colligative Properties (with van 't Hoff factor 'i')
Properties that depend strictly on the number of solute particles present, rather than their chemical identity. The van 't Hoff factor ($i$) accounts for solute dissociation or association in solution.
$$\text{Relative Lowering of Vapour Pressure: } \frac{p_A^\circ - p_A}{p_A^\circ} = i \cdot x_B$$
$$\text{Elevation of Boiling Point: } \Delta T_b = i \cdot K_b \cdot m$$
$$\text{Depression of Freezing Point: } \Delta T_f = i \cdot K_f \cdot m$$
$$\text{Osmotic Pressure: } \pi = i \cdot C R T$$
Electrochemistry Class 12
Nernst Equation
Calculates the cell potential of an electrochemical cell under non-standard concentrations and temperatures. It directly links cell EMF to ion concentrations and temperature.
$$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log_{10} Q \quad (\text{at } 298\text{ K})$$
$$\Delta G^\circ = -n F E^\circ_{\text{cell}}$$
Kohlrausch's Law of Independent Migration
The molar conductivity of an electrolyte at infinite dilution equals the sum of the individual ionic conductivities of its cations and anions. Each ion contributes independently regardless of the co-ion present.
$$\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$$
Faraday's Laws of Electrolysis
First law: Mass deposited at an electrode is proportional to electric charge passed. Second law: Masses of different substances deposited by the same electric charge are proportional to their equivalent weights.
$$\text{First Law: } m = Z \cdot I \cdot t \quad \left(Z = \frac{\text{Molar Mass}}{n \times 96500}\right)$$
$$\text{Second Law: } \frac{m_1}{m_2} = \frac{E_1}{E_2}$$
Chemical Kinetics Class 12
Integrated Rate Equations
Mathematical expressions that give reactant concentration as a function of time. Zero-order reactions proceed at a constant rate, while first-order reaction rates depend linearly on remaining concentration.
$$\text{Zero Order: } k = \frac{[A]_0 - [A]}{t}, \quad t_{1/2} = \frac{[A]_0}{2k}$$
$$\text{First Order: } k = \frac{2.303}{t} \log_{10}\left(\frac{[A]_0}{[A]}\right), \quad t_{1/2} = \frac{0.693}{k}$$
Arrhenius Equation
Describes how reaction rate constants increase exponentially with temperature. It quantifies the energy barrier (Activation Energy $E_a$) that reactants must overcome to form products.
$$k = A \cdot e^{-E_a / RT}$$
$$\log_{10}\left(\frac{k_2}{k_1}\right) = \frac{E_a}{2.303 R} \left( \frac{T_2 - T_1}{T_1 T_2} \right)$$
Atomic Structure Class 11
Bohr's Atomic Model Postulates
Electrons revolve around the nucleus only in specific stationary circular orbits with quantized angular momentum. Electrons emit or absorb energy as photons only when transitioning between these fixed energy levels.
$$\text{Angular Momentum: } mvr = \frac{nh}{2\pi}$$
$$\text{Radius: } r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}$$
$$\text{Energy: } E_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV/atom}$$
de Broglie Hypothesis & Heisenberg Uncertainty
de Broglie proposed that all moving matter exhibits dual wave-particle properties. Heisenberg proved it is impossible to simultaneously measure both the precise position and momentum of a subatomic particle.
$$\text{de Broglie: } \lambda = \frac{h}{p} = \frac{h}{mv}$$
$$\text{Uncertainty Principle: } \Delta x \cdot \Delta p \ge \frac{h}{4\pi}$$
Chemical Reactions & Acids, Bases, Salts Class 10
Neutralization Reaction
A chemical reaction in which an acid reacts with a base to form salt and water. Hydrogen ions ($H^+$) from the acid combine with hydroxide ions ($OH^-$) from the base to produce neutral water.
$$\text{Acid} + \text{Base} \longrightarrow \text{Salt} + \text{Water}$$
pH Scale Definition
A logarithmic scale used to specify the acidity or basicity of an aqueous solution based on hydrogen ion concentration. Solutions with pH below 7 are acidic, while those above 7 are basic.
$$\text{pH} = -\log_{10}[H^+], \quad \text{pH} + \text{pOH} = 14$$