Electrochemistry

Redox Separated in Space

Any redox reaction transfers electrons. If the two half-reactions are physically separated and connected by a wire, those electrons must travel through the circuit and can do electrical work. That is a galvanic cell.

Oxidation is loss of electrons and always happens at the anode; reduction is gain and always happens at the cathode. In a galvanic cell the anode is negative and the cathode positive. A salt bridge completes the circuit and keeps both compartments electrically neutral, without which the cell stops almost immediately.

Each half-reaction has a standard electrode potential $E^\circ$, measured against the standard hydrogen electrode defined as exactly 0 V. The cell potential is

$$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$$

A positive $E^\circ_{cell}$ means a spontaneous reaction, tying electrochemistry to thermodynamics through

$$\Delta G^\circ = -nFE^\circ_{cell}$$

with $n$ the number of electrons transferred and $F = 96{,}485$ C/mol. Note that $E^\circ$ is an intensive property: it does not scale when you multiply a half-equation, even though $\Delta G^\circ$ does.

Away from standard conditions the Nernst equation applies:

$$E = E^\circ - \frac{0.0592}{n}\log Q$$

at 25 °C. As the reaction proceeds, $Q$ rises and $E$ falls, reaching zero exactly when $Q = K$, a flat battery is a cell that has reached equilibrium.

An electrolytic cell reverses the arrangement, using an external supply to drive a non-spontaneous reaction. The electrode names follow the chemistry, not the sign: oxidation is still at the anode, but in electrolysis the anode is positive.

Common pitfall: multiplying a standard potential when balancing electrons. If a half-equation is doubled to balance a cell, its $\Delta G^\circ$ doubles but its $E^\circ$ does not change at all, potential is energy per unit charge, and both the energy and the charge scale together.