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\(E^0_{\text{cell}} = E^0_{\text{cathode}} - E^0_{\text{anode}}\), where \(E^0_{\text{cell}}\) is the standard cell potential, and \(E^0_{\text{cathode}}, E^0_{\text{anode}}\) are the standard reduction potentials of the cathode and anode respectively.

Anode: \(Pb + SO_4^{2-} \rightarrow PbSO_4 + 2e^-\), Cathode: \(PbO_2 + SO_4^{2-} + 4H^+ + 2e^- \rightarrow PbSO_4 + 2H_2O\), Overall: \(Pb + PbO_2 + 2SO_4^{2-} + 4H^+ \rightarrow 2PbSO_4 + 2H_2O\)

\(E = E^0 - \frac{RT}{nF} \ln Q\), where E is the cell potential, E^0 is the standard cell potential, R is the gas constant, T is temperature in kelvins, n is the number of electrons, F is Faraday's constant, and Q is the reaction quotient.

\(m = \frac{Q}{F} \times \frac{M}{z}\), where m is the mass of the substance altered at an electrode during electrolysis, Q is the total electric charge passed through the substance, F is Faraday's constant, M is the molar mass of the substance, and z is the valence number of ions of the substance.

\(\Delta G = -nFE_{\text{cell}}\), where \(\Delta G\) is the Gibbs free energy change, n is the number of moles of electrons transferred, F is Faraday's constant, and \(E_{\text{cell}}\) is the cell potential.

\(j = j_0\left [ \text{exp}\left( -\frac{\alpha nf(\eta)}{RT} \right) - \text{exp}\left( \frac{(1-\alpha)nf(\eta)}{RT} \right) \right ]\), where j is the current density, j_0 is the exchange current density, \(\alpha\) is the charge transfer coefficient, n is the number of electrons, f is a function of the overpotential \(\eta\), R is the gas constant, and T is the temperature.

\(\ln K = \frac{nFE^0}{RT}\), where K is the equilibrium constant, n is the number of moles of electrons, \(E^0\) is the standard cell potential, R is the gas constant, and T is the temperature in kelvins.

\(\frac{m_1}{m_2} = \frac{M_1 \times z_2}{M_2 \times z_1}\), where m1 and m2 are the masses of different substances produced at the electrodes, while M1 and M2 are their molar masses, and z1 and z2 their valences respectively.

Typically written as 'Anode | Anode electrolyte || Cathode electrolyte | Cathode', it represents the shorthand for the cell reaction where a single vertical line indicates a phase boundary, and a double vertical line represents the salt bridge.

Charge transfer resistance (Rct) is the resistance to the transfer of electrons from the electrode to the reactant in the electrochemical cell, affecting the rate of the reaction.

Electrode potential is the tendency of a chemical species to lose or gain electrons and oxidize or reduce. Measured in volts (V), it is determined by the relative ease with which the species can be oxidized or reduced.

\(E^0_{\text{SHE}} = 0\,\text{V}\), This is the assigned potential at all temperatures for the standard hydrogen electrode which is used as a reference electrode in measuring electrode potentials.

The voltage required for an electrolytic cell is higher than the difference in electrode potentials of the half-cells due to overpotential and resistance within the cell.

\(\lambda_{\infty} = \lambda_{\infty}^+ + \lambda_{\infty}^-\), where \(\lambda_{\infty}\) is the molar conductivity at infinite dilution, and \(\lambda_{\infty}^+\) and \(\lambda_{\infty}^-\) are the molar conductivities at infinite dilution for the cation and anion, respectively.