Cell Notation: $Anode | Anode \text{ ion} || Cathode \text{ ion} | Cathode$.

Electrolytic Cell: Electrical energy $\to$ Chemical energy. Non-spontaneous.

Standard Electrode Potential ($E^\circ$): Reduction potential measured against Standard Hydrogen Electrode (SHE, $E^\circ=0$).

Standard Cell Potential ($E^\circ_{cell}$): $$ E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} $$ (Both are standard reduction potentials).

Nernst Equation: Relates cell potential to concentrations. $$ E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q $$ At $25^\circ C$ (298 K): $$ E_{cell} = E^\circ_{cell} - \frac{0.0591}{n} \log Q $$

Relationship between $\Delta G^\circ$, $E^\circ_{cell}$, and $K_{eq}$: $$ \Delta G^\circ = -nFE^\circ_{cell} $$ $$ \Delta G^\circ = -RT \ln K_{eq} $$ $$ E^\circ_{cell} = \frac{RT}{nF} \ln K_{eq} = \frac{0.0591}{n} \log K_{eq} \quad (\text{at } 25^\circ C) $$ (where F = 96485 C/mol, Faraday's constant).

Faraday's Laws of Electrolysis:

First Law: Mass deposited/liberated is proportional to charge passed. $$ W = ZIt \quad (\text{where } Z = \text{Electrochemical equivalent} = \text{Equivalent weight}/F) $$
Second Law: If same charge is passed through different electrolytes, masses deposited are proportional to their equivalent weights. $$ \frac{W_1}{W_2} = \frac{E_1}{E_2} $$

9. Chemical Kinetics

Rate of Reaction: Change in concentration of reactant/product per unit time. For $aA + bB \to cC + dD$: $$ \text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt} $$
Rate Law: Rate $= k[A]^x[B]^y$.
- Order of Reaction: Sum of powers of concentration terms ($x+y$). Can be fractional or zero.
- Molecularity: Number of reacting species in an elementary step. Always a whole number.
Integrated Rate Laws and Half-Life ($t_{1/2}$):
- Zero Order: Rate $= k$. $$ [A]_t = [A]_0 - kt $$ $$ t_{1/2} = \frac{[A]_0}{2k} $$
- First Order: Rate $= k[A]$. $$ \ln[A]_t = \ln[A]_0 - kt \quad \text{or} \quad [A]_t = [A]_0 e^{-kt} $$ $$ t_{1/2} = \frac{0.693}{k} $$
- Second Order: Rate $= k[A]^2$. $$ \frac{1}{[A]_t} = \frac{1}{[A]_0} + kt $$ $$ t_{1/2} = \frac{1}{k[A]_0} $$
Arrhenius Equation: Effect of temperature on rate constant. $$ k = Ae^{-E_a/(RT)} $$ $$ \ln \left(\frac{k_2}{k_1}\right) = \frac{E_a}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right) $$ $E_a$ = Activation energy, $A$ = Pre-exponential factor.
Collision Theory: Reaction occurs when molecules collide with sufficient energy ($>E_a$) and correct orientation.

10. Solutions and Colligative Properties

Ideal Solutions: Obeys Raoult's Law. $\Delta H_{mix}=0, \Delta V_{mix}=0$.
Raoult's Law: For volatile components, partial vapor pressure of a component is proportional to its mole fraction. $$ P_A = X_A P_A^\circ $$ For non-volatile solute: $P_{solution} = X_{solvent} P_{solvent}^\circ$.
Colligative Properties: Depend only on number of solute particles, not their nature.
- Relative Lowering of Vapor Pressure (RLVP): $$ \frac{P^\circ - P_s}{P^\circ} =