Key Points

An electrochemical cell is a device that converts chemical energy into electrical energy or vice versa. They are classified into two types: galvanic (voltaic) cells and electrolytic cells.

A galvanic cell converts the chemical energy of a spontaneous redox reaction into electrical energy. In this cell, the anode is negatively charged (oxidation) and the cathode is positively charged (reduction).

An electrolytic cell uses electrical energy from an external source to drive a non-spontaneous chemical reaction. In this cell, the anode is positively charged and the cathode is negatively charged.

The standard electrode potential ($E^{\circ}$) is the potential difference of a half-cell when all species are at unit concentration (1 M), 1 bar pressure for gases, at a specified temperature (usually 298 K), measured against the Standard Hydrogen Electrode (SHE), which is assigned $E^{\circ} = 0.00 \text{ V}$.

The potential difference between the two electrodes of a galvanic cell is the cell potential or electromotive force (EMF). The standard cell potential is calculated as $E^{\circ}_{\text{cell}} = E^{\circ}_{\text{cathode}} - E^{\circ}_{\text{anode}}$, where potentials are standard reduction potentials.

The Nernst equation relates the cell potential ($E_{\text{cell}}$) to its standard potential ($E^{\circ}_{\text{cell}}$) and the concentrations of reactants and products. For a general reaction, $E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{2.303RT}{nF} \log Q$, which simplifies to $E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{0.059}{n} \log Q$ at 298 K.

The standard Gibbs energy change for a cell reaction is related to the standard cell potential by the equation $\Delta_r G^{\circ} = -nFE^{\circ}_{\text{cell}}$. A positive $E^{\circ}_{\text{cell}}$ corresponds to a negative $\Delta_r G^{\circ}$, indicating a spontaneous reaction.

At equilibrium, $E_{\text{cell}} = 0$, and the reaction quotient $Q$ equals the equilibrium constant $K_c$. The relationship is given by $E^{\circ}_{\text{cell}} = \frac{2.303RT}{nF} \log K_c$.

Conductivity ($\kappa$) is the inverse of resistivity ($\rho$). Molar conductivity ($\Lambda_m$) is the conductivity of a solution per unit molar concentration, defined as $\Lambda_m = \frac{\kappa}{c}$. Its common unit is $\text{S cm}^2 \text{mol}^{-1}$.

Conductivity ($\kappa$) always decreases with a decrease in concentration (dilution) because the number of ions per unit volume decreases. Molar conductivity ($\Lambda_m$) increases with a decrease in concentration for both strong and weak electrolytes.

This law states that the limiting molar conductivity of an electrolyte ($\Lambda^{\circ}_m$) is the sum of the individual contributions of its cations and anions. Mathematically, $\Lambda^{\circ}_m = \nu_+ \lambda^{\circ}_+ + \nu_- \lambda^{\circ}_-$, where $\lambda^{\circ}$ are ionic conductivities and $\nu$ are the number of ions.

The amount of substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity ($Q$) passed through the electrolyte. The charge is calculated as $Q = I \times t$, where $I$ is current in amperes and $t$ is time in seconds.

When the same quantity of electricity is passed through different electrolytes, the amounts of substances liberated are proportional to their chemical equivalent weights. One mole of electrons carries a charge of one Faraday ($F \approx 96500 \text{ C mol}^{-1}$).

Primary batteries are non-rechargeable cells where the cell reaction occurs only once. Examples include the dry cell (Leclanché cell) and the mercury cell.

Secondary batteries are rechargeable cells that can be used multiple times by reversing the cell reaction with an external current. The most common example is the lead-acid storage battery used in automobiles.

During discharge, the overall reaction is $\text{Pb}(s) + \text{PbO}_2(s) + 2\text{H}_2\text{SO}_4(aq) \rightarrow 2\text{PbSO}_4(s) + 2\text{H}_2\text{O}(l)$. This reaction is reversed during charging.

Fuel cells are galvanic cells that convert the energy from the combustion of fuels like hydrogen, methane, or methanol directly into electrical energy. The hydrogen-oxygen fuel cell produces water as its only product, making it pollution-free.

Corrosion, such as the rusting of iron, is an electrochemical phenomenon. Iron acts as the anode (oxidation: $\text{Fe} \rightarrow \text{Fe}^{2+} + 2e^-$) and atmospheric oxygen in the presence of water acts as the cathode (reduction: $\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$).