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Chapter 1: Solutions

Concepts Covered: Types of solution, Mass by volume%, Molarity, Mole Fraction, Normality, ppm, Volume by volume%, Henry's Law

Solution: A homogeneous mixture of two or more pure substances is known as a solution.

• Solute: A substance that is dissolved in another substance in lesser amount, forming a solution. Examples: sugar, salt in water.
• Solvent: A substance in which another substance is dissolved in larger amount, forming a solution. Examples: water, milk.

Note: Solvent determines the physical state of the solution.

Types of Solutions

• Aqueous solution: A solution containing water as solvent is known as aqueous solution.
• Non-aqueous solution: A solution containing solvent other than water.
• Saturated solution: A solution in which no more solute can be dissolved at the same temperature.
• Unsaturated solution: A solution in which more amount of solute can be dissolved at the same temperature.

Method of Expressing Concentration of Solution

1. Mass percentage $(w/W)$: $$\text{Mass\% of a solute} = \frac{\text{Mass of solute in the solution}}{\text{Total mass of the solution}} \times 100$$
2. Volume percentage $(v/V)$: $$\text{Volume\% of a solute} = \frac{\text{Volume of solute}}{\text{Total volume of the solution}} \times 100$$
3. Mass by volume percentage $(w/v)$: $$\text{Mass by volume\% of solute} = \frac{\text{Mass of solute}}{\text{Volume of solution}} \times 100$$
4. Parts per million (ppm): $$\text{ppm (A)} = \frac{\text{Number of parts of component (A)}}{\text{Total number of parts of all components}} \times 10^6$$
5. Mole Fraction $(\chi)$: $$\chi_A = \frac{n_A}{n_A + n_B}, \quad \chi_B = \frac{n_B}{n_A + n_B}, \quad \chi_A + \chi_B = 1$$
6. Molarity (M): $$M = \frac{\text{Number of moles of solute}}{\text{Volume of solution (in L)}} = \frac{W_B \times 1000}{M_B \times V \text{ (in mL)}}$$
7. Molality (m): $$m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (in kg)}} = \frac{W_B \times 1000}{M_B \times W_A \text{ (in g)}}$$
8. Normality (N): $$N = \frac{\text{Number of gram equivalents of solute}}{\text{Volume of solution in litre}} = \frac{W_B \times 1000}{E_B \times V \text{ (in mL)}}$$

Relationship between Molarity (M) and Molality (m):

$$\frac{1}{m} = \frac{d}{M} - \frac{M_B}{1000}$$

Relationship between Mole fraction of solute $(\chi_B)$ and Molality (m):

$$m = \frac{\chi_B \times 1000}{(1 - \chi_B) \times M_A}$$

Henry's Law

The partial pressure of the gas $(p)$ in vapour phase is proportional to the mole fraction of the gas $(x)$ in the solution:

$$p = K_H \cdot x$$

Example 1: If $N_2$ gas is bubbled through water at 293 K, how many millimoles of $N_2$ gas would dissolve in 1 litre of water? Assume $N_2$ exerts a partial pressure of 0.987 bar and $K_H = 76.48 \text{ kbar}$.

Answer:
$$x = \frac{p(N_2)}{K_H} = \frac{0.987 \text{ bar}}{76480 \text{ bar}} = 1.29 \times 10^{-5}$$ $$\text{Moles of } N_2 = 1.29 \times 10^{-5} \times 1000 = 0.0129 \text{ mmol/L}$$

Chapter 2: Electrochemistry

Concepts Covered: Electrolytic Conductivity, Kohlrausch's Law, Galvanic Cell, Nernst Equation, Gibbs Energy, Faraday's Laws

Electrolytic Conductivity

Resistance ($R$) and Resistivity ($\rho$):

$$R = \rho \frac{l}{A}$$

Conductance ($C$) and Conductivity ($\kappa$):

$$C = \frac{1}{R}, \quad \kappa = C \times \frac{l}{A}$$

Molar Conductivity ($\Lambda_m$):

$$\Lambda_m = \frac{\kappa}{C} \times 1000$$

Debye-Hückel-Onsager Equation:

$$\Lambda_m = \Lambda_m^\circ - A\sqrt{C}$$

Kohlrausch's Law of Independent Migration of Ions:

$$\Lambda_m^\infty = v^+ \lambda_+^\infty + v^- \lambda_-^\infty$$

Nernst Equation

For a general electrode reaction $M^{n+}(aq) + ne^- \rightarrow M(s)$:

$$E_{(M^{n+}/M)} = E^\circ_{(M^{n+}/M)} - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}$$

At 298 K for cell reaction $aA + bB \rightarrow mM + nN$:

$$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.059}{n} \log \frac{[M]^m [N]^n}{[A]^a [B]^b}$$

Gibbs Energy and EMF

$$\Delta_r G^\circ = -n F E^\circ_{\text{cell}}$$ $$\Delta_r G^\circ = -2.303 R T \log K_c$$

Faraday's Laws of Electrolysis

• First Law: $m = Z \times I \times t$
• Second Law: $\frac{w_1}{E_1} = \frac{w_2}{E_2}$

Chapter 3: Chemical Kinetics

Concepts Covered: Rate of chemical reaction, Order and Molecularity, Integrated Rate Equations, Half-Life, Arrhenius Equation

Rate of Reaction

For $A + B \rightarrow C$:

$$\text{Rate} = -\frac{d[A]}{dt} = -\frac{d[B]}{dt} = +\frac{d[C]}{dt}$$

Integrated Rate Laws and Half-Life

Arrhenius Equation

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

Chapter 4: d- and f-Block Elements

Concepts Covered: Transition Elements, Lanthanoids, Actinoids, Magnetic Properties, Potassium Dichromate, Potassium Permanganate

General Electronic Configurations

• d-Block Elements: $(n-1)d^{1-10} ns^{1-2}$
• f-Block Elements: $(n-2)f^{1-14} (n-1)d^{0-1} ns^2$

Magnetic Moment Formula:

$$\mu = \sqrt{n(n+2)} \text{ B.M.}$$

where $n$ is the number of unpaired electrons.

Important Reactions

Potassium Dichromate ($K_2Cr_2O_7$) in Acidic Medium:

$$Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O$$

Potassium Permanganate ($KMnO_4$) in Acidic Medium:

$$MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O$$

Chapter 5: Coordination Compounds

Concepts Covered: Coordination Number, Ligands, Denticity, Nomenclature, Isomerism

• Unidentate Ligands: $NH_3, H_2O, Cl^-$
• Bidentate Ligands: Ethylenediamine ($\text{en}$), Oxalate ($\text{C}_2\text{O}_4^{2-}$)
• Polydentate Ligands: EDTA

Types of Isomerism

1. Ionisation Isomerism: $[Co(NH_3)_5Cl]SO_4$ vs $[Co(NH_3)_5(SO_4)]Cl$
2. Coordination Isomerism: $[Co(NH_3)_6][Cr(C_2O_4)_3]$ vs $[Cr(NH_3)_6][Co(C_2O_4)_3]$
3. Solvate Isomerism: $[Cr(H_2O)_6]Cl_3$ vs $[Cr(H_2O)_5Cl]Cl_2 \cdot H_2O$
4. Linkage Isomerism: $[Co(NH_3)_5(NO_2)]^{2+}$ vs $[Co(NH_3)_5(ONO)]^{2+}$