Molar conductivity $\Lambda_m = \kappa \times 1000/c$ (where $\kappa$ = specific conductivity in S/cm, $c$ = concentration in mol/L). Units: S cm² mol⁻¹. For strong electrolytes: $\Lambda_m = \Lambda_m^\infty - A\sqrt{c}$ (Debye-Hückel-Onsager equation). As $c \to 0$, $\Lambda_m \to \Lambda_m^\infty$ (molar conductivity at infinite dilution). The decrease in $\Lambda_m$ with increasing concentration for strong electrolytes is due to interionic attractions that slow down ion movement. For weak electrolytes, $\Lambda_m$ increases sharply with dilution because degree of dissociation increases — at very low concentrations, nearly complete dissociation occurs. This is why weak electrolytes cannot be treated like strong electrolytes in conductivity measurements.

Kohlrausch's Law states that at infinite dilution, each ion migrates independently of other ions. The molar conductivity at infinite dilution is the sum of contributions from individual ions: $\Lambda_m^\infty = \nu_+\lambda_+^\infty + \nu_-\lambda_-^\infty$ where $\nu_+$ and $\nu_-$ are the stoichiometric coefficients and $\lambda_+^\infty$, $\lambda_-^\infty$ are limiting molar conductivities of cation and anion. This law is extremely important because it allows calculation of $\Lambda_m^\infty$ for weak electrolytes (like acetic acid, NH₄OH) which cannot be determined by extrapolation. For example: $\Lambda_m^\infty(CH_3COOH) = \Lambda_m^\infty(CH_3COONa) + \Lambda_m^\infty(HCl) - \Lambda_m^\infty(NaCl)$. This uses strong electrolytes whose $\Lambda_m^\infty$ can be measured to find the weak electrolyte value indirectly.

For a weak electrolyte at concentration $c$: only a fraction $\alpha$ is dissociated. The molar conductivity $\Lambda_m$ at concentration $c$ is proportional to the fraction dissociated: $\alpha = \Lambda_m/\Lambda_m^\infty$. This is because ions are the charge carriers — more dissociation → more ions → higher conductivity. At infinite dilution, complete dissociation is assumed ($\alpha = 1$, $\Lambda_m = \Lambda_m^\infty$). The dissociation constant $K_a = c\alpha^2/(1-\alpha)$ (Ostwald dilution law). For small $\alpha$: $K_a \approx c\alpha^2$, so $\alpha \approx \sqrt{K_a/c}$ — degree of dissociation increases with dilution (as $c$ decreases, $\alpha$ increases). This is consistent with Le Chatelier's principle: dilution favours dissociation.

Specific conductance (conductivity) $\kappa = 1/\rho$ (where $\rho$ = resistivity). Unit: S/m or S/cm. Conductance $G = \kappa A/l$ (where $A$ = electrode area, $l$ = distance between electrodes). Cell constant $G^* = l/A$ (unit: cm⁻¹). Measured conductance $G = \kappa/G^*$. So $\kappa = G \times G^*$. Cell constant is determined using a solution of known conductivity (usually KCl solutions with precisely known $\kappa$). Once $G^*$ is known, measuring $G$ directly gives $\kappa$ for any solution. A conductivity cell is essentially a container with two platinum electrodes — AC is used (not DC) to prevent electrolysis and polarisation of electrodes.

Equivalent conductance $\Lambda_{eq} = \kappa \times 1000/N$ (where $N$ = normality). Molar conductance $\Lambda_m = \kappa \times 1000/M$ (where $M$ = molarity). Relation: $\Lambda_m = n \times \Lambda_{eq}$ where $n$ = n-factor (valence factor). For HCl: $n=1$, so $\Lambda_m = \Lambda_{eq}$. For H₂SO₄: $n=2$, so $\Lambda_m = 2\Lambda_{eq}$. For Al₂(SO₄)₃: $n=6$, so $\Lambda_m = 6\Lambda_{eq}$. Modern IUPAC recommends molar conductance. Equivalent conductance is older terminology but still appears in NEET questions. Both increase with dilution for weak electrolytes; for strong electrolytes, the variation is smaller and follows the Debye-Hückel-Onsager equation.

Galvanic (voltaic) cell: converts chemical energy to electrical energy. Spontaneous redox reaction. Examples: Daniel cell (Zn/ZnSO₄ || CuSO₄/Cu), standard hydrogen electrode, dry cell, lead-acid battery. EMF of cell $E_{cell} = E_{cathode} - E_{anode}$ (reduction potentials). For spontaneous reaction: $E_{cell} > 0$ and $\Delta G < 0$. Nernst equation: $E_{cell} = E°_{cell} - (RT/nF)\ln Q = E°_{cell} - (0.0592/n)\log Q$ at 298 K. Electrolytic cell: uses electrical energy to drive non-spontaneous redox reaction. $E_{cell} < 0$, external EMF must be applied. Examples: electrolysis of water, electroplating, Hall-Héroult process (Al extraction), Downs cell (Na from molten NaCl).

First Law: mass of substance deposited/liberated is proportional to quantity of electricity passed. $m = ZQ = ZIt$ where $Z$ = electrochemical equivalent, $Q$ = charge, $I$ = current, $t$ = time. Second Law: masses deposited by same quantity of electricity are proportional to their chemical equivalents (molar mass/n-factor). $m = MIt/(nF)$ where $F = 96485$ C/mol (Faraday constant) $\approx 96500$ C/mol. For depositing 1 mole of $M^{n+}$ ions: requires $nF$ coulombs. Example: depositing 1 mol Cu²⁺ needs $2F = 193000$ C. At 1 A current: time $= 193000$ s $\approx 53.6$ hours. Applications: electroplating (thin metal coating), electrorefining (purifying metals), electrochemical synthesis (NaOH by chlor-alkali process).

Standard hydrogen electrode (SHE): $E° = 0$ V (reference). Other electrode potentials measured relative to SHE. Standard reduction potentials: $F_2/F^-$: $+2.87$ V (strongest oxidising agent). $Li^+/Li$: $-3.04$ V (strongest reducing agent). $Cu^{2+}/Cu$: $+0.34$ V. $Zn^{2+}/Zn$: $-0.76$ V. Daniel cell: $E° = E°_{Cu} - E°_{Zn} = 0.34 - (-0.76) = 1.10$ V. Electrochemical series: predict: which metal displaces which from solution (more negative $E°$ displaces more positive), direction of cell reaction, relative reactivity of metals (used in activity series). Relation to thermodynamics: $\Delta G° = -nFE°$. $\Delta G° = -RT\ln K$. So $\ln K = nFE°/(RT) = nE°/0.0257$ at 298 K.