Electrochemical Cells: Notation, Sign Conventions and the Nernst Equation

Cell notation

A single vertical line marks a phase boundary; a double line marks a salt bridge. The anode, where oxidation occurs, is written on the left; the cathode, where reduction occurs, on the right.

Cell potential

Both values are taken as reduction potentials from tables, and the subtraction handles the fact that oxidation occurs at the anode. Reversing the sign of the anode potential and adding is the same operation, but subtracting tabulated reduction potentials is less error-prone.

A positive cell potential means the reaction as written is spontaneous. A negative one means it runs the other way, and the cell has been written backwards — which is informative rather than an error.

Note also that electrode potentials are intensive: multiplying a half-reaction by two does not change its potential, though it does change n. Multiplying the potential is a common and serious mistake.

The Nernst equation

At 298 K and converting to base-10 logarithms this becomes the familiar form with the factor 0.0591/n. Two cautions apply:

• The 0.0591 value is specific to 298 K. At any other temperature the general form must be used.
• n is the number of electrons in the balanced overall cell reaction, not in one half-reaction as written in the tables.

Q is the reaction quotient for the cell reaction as written, with pure solids and liquids omitted and gases entered as partial pressures.

The links to thermodynamics

These connect electrochemistry to the rest of thermodynamics and give a practical route to equilibrium constants. Measuring a cell potential yields ΔG° and hence K, and this works for reactions whose equilibrium constants are far too large or small to measure directly by analysis.

At equilibrium the cell potential is zero, because ΔG is zero. A dead battery is at equilibrium — which is a useful way to remember that E = 0 does not mean E° = 0.

Concentration cells

A cell with identical electrodes but different concentrations has E° = 0, yet produces a potential because Q is not one. The entire driving force is the concentration difference, and the cell runs until the two concentrations equalise.

These appear regularly because they test whether the Nernst equation is understood rather than merely applied — with E° zero, the potential comes entirely from the logarithmic term.

A worked procedure

1. Write both half-reactions as reductions and find their tabulated potentials.
2. Decide which is the cathode — the one with the higher reduction potential, for a spontaneous cell.
3. Reverse the other and write the balanced overall reaction, cancelling electrons.
4. Note n from the cancelled electrons.
5. Compute E° as cathode minus anode.
6. Write Q for the balanced reaction and apply the Nernst equation.

Frequently asked questions

Why does multiplying a half-reaction not change its potential?

Because potential is energy per unit charge, an intensive property. Both the free energy and the charge scale together, so their ratio is unchanged.

What is the salt bridge for?

To complete the circuit and maintain electrical neutrality in each compartment as ions are produced and consumed. Without it charge builds up and the cell stops almost immediately.

Why is the cell potential zero at equilibrium?

Because ΔG is zero at equilibrium, and E is proportional to ΔG. The cell can do no more work.

How do I get n right?

From the balanced overall cell reaction after the electrons cancel — not from either half-reaction alone. This is why writing the overall reaction first matters.