Electrochemistry: Nernst, Conductance & Cells

Electrochemistry links chemical reactions to electrical energy through oxidation-reduction processes. JEE tests three main areas: electrochemical cells (galvanic and electrolytic), the Nernst equation, and conductance/electrolysis.

Electrochemical Cells: A galvanic (voltaic) cell converts chemical energy to electrical energy spontaneously ($\delta_{G}$ < 0, $E_{cell}$ > 0). An electrolytic cell uses external electrical energy to drive a non-spontaneous reaction ($\delta_{G}$ > 0). Cell notation: Anode (oxidation) || Cathode (reduction). Example: Zn(s)|Zn₂+(aq)||Cu₂+(aq)|Cu(s). The single vertical line represents a phase boundary; the double line represents the salt bridge.

Standard Electrode Potential ($E_{standard}$): Measured against the Standard Hydrogen Electrode (SHE, E = 0.00 V).
$E_{cell_standard}$ = $E_{cathode_standard}$ - $E_{anode_standard}$. A positive $E_{cell_standard}$ means the reaction is spontaneous. The more positive the reduction potential, the stronger the oxidising agent. The more negative, the stronger the reducing agent.

Electrochemical Series: Li (-3.04 V) < K (-2.93 V) < Na (-2.71 V) < Zn (-0.76 V) < Fe (-0.44 V) < H₂ (0.00 V) < Cu (+0.34 V) < Ag (+0.80 V) < Au (+1.50 V). Metals above hydrogen displace H₂ from acids. A metal higher in the series reduces the cation of a metal lower in the series.

Nernst Equation: $E_{cell}$ = $E_{cell_standard}$ - (RT/nF)ln(Q) = $E_{cell_standard}$ - (0.0592/n)log(Q) at 25 degrees C.

Where n = number of electrons transferred, F = 96485 C/mol (Faraday constant), Q = reaction quotient. At equilibrium, $E_{cell}$ = 0 and Q = K, so: $E_{cell_standard}$ = (0.0592/n)log(K). This connects cell potential to equilibrium constant.

Gibbs Free Energy: $\delta_{G}$ = -nFE_cell.
$\delta_{G_standard}$ = -nFE_cell_standard. Spontaneous reaction: $E_{cell}$ > 0, $\delta_{G}$ < 0.

Conductance and Conductivity: Conductance (G) = 1/Resistance = 1/R (unit: Siemens, S). Conductivity (kappa) = 1/resistivity = (1/R)(l/A) where l = distance between electrodes, A = area. Cell constant = l/A ($cm^{-1}$). kappa = G * cell constant.

Molar Conductivity: Lambda_m = kappa * 1000 / C (in S.$cm^{2}$/mol) where C is in mol/L. Lambda_m increases with dilution for both strong and weak electrolytes, but in different ways.

Kohlrausch's Law: Lambda_m_infinity (at infinite dilution) = sum of limiting ionic conductivities. Lambda_m_infinity(NaCl) = $\lambda_{infinity}$(Na+) + $\lambda_{infinity}$(Cl-). Application: finding Lambda_m_infinity for weak electrolytes (which cannot be measured directly by extrapolation).

Lambda_m_infinity(CH₃COOH) = Lambda_m_infinity(CH₃COONa) + Lambda_m_infinity(HCl) - Lambda_m_infinity(NaCl)

Acetic acid (CH₃COOH) — Kohlrausch's law is commonly applied to find its Lambda_m_infinity

Degree of Dissociation from Conductivity: $\alpha$ = Lambda_m / Lambda_m_infinity. For weak electrolytes, this combined with Ostwald's dilution law gives Ka = C*$\alpha$²/(1-$\alpha$).

Faraday's Laws of Electrolysis: First Law: m = ZIt = (M * I * t) / (n * F), where m = mass deposited, Z = electrochemical equivalent, I = current, t = time, M = molar mass, n = electrons transferred per ion. Second Law: When the same charge passes through different electrolytes, the masses deposited are proportional to their equivalent weights. m1/m2 = E₁/E₂.