Electrochemistry — Galvanic Cells, Electrolysis & Nernst Equation

The one-line takeaway: chemistry decides where electrons want to go, and electrochemistry tracks the voltage that results — a galvanic cell turns a spontaneous redox reaction into electrical energy, an electrolytic cell spends electrical energy to force a nonspontaneous one, and the Nernst equation corrects the cell potential for nonstandard conditions.

Galvanic vs Electrolytic Cells

	Galvanic (voltaic) cell	Electrolytic cell
Reaction	spontaneous redox	nonspontaneous, forced
Energy direction	produces electrical energy	consumes electrical energy
Driving force	the reaction itself	external power source
Oxidation site	anode	anode
Reduction site	cathode	cathode
Typical electrode signs	anode $-$, cathode $+$	often reversed
Examples	batteries, fuel cells	electroplating, electrolysis of molten salts

The key is that the electrode labels never change — oxidation is always at the anode, reduction always at the cathode. What flips between the two cell types is the energy direction and, often, the electrode signs.

How to Identify Anode, Cathode, and Salt Bridge

Defining electrodes by sign causes endless confusion; define them by reaction instead:

• anode = oxidation
• cathode = reduction

In many galvanic cells the anode is negative and the cathode positive; in many electrolytic cells the signs reverse because an external source pushes electrons where they would not go on their own. The salt bridge plays a different role from the wire: electrons travel through the external circuit, while ions move through the solution or salt bridge to keep charge from building up in either half-cell.

Worked Example: Zinc-Copper Cell and the Nernst Correction

Consider the galvanic cell

$$\mathrm{Zn}(s)\,|\,\mathrm{Zn}^{2+}(aq)\,||\,\mathrm{Cu}^{2+}(aq)\,|\,\mathrm{Cu}(s)$$

with half-reactions

$$\mathrm{Zn}(s) \rightarrow \mathrm{Zn}^{2+}(aq) + 2e^-$$ $$\mathrm{Cu}^{2+}(aq) + 2e^- \rightarrow \mathrm{Cu}(s)$$

Zinc is oxidized at the anode, copper(II) reduced at the cathode. Under standard conditions,

$$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} = 0.34\ \mathrm{V} - (-0.76\ \mathrm{V}) = 1.10\ \mathrm{V}$$

A positive $E^\circ_{cell}$ means the reaction is spontaneous as written.

Now make the conditions nonstandard: $[\mathrm{Zn}^{2+}] = 1.0\ \mathrm{M}$ and $[\mathrm{Cu}^{2+}] = 0.010\ \mathrm{M}$ at $25^\circ\mathrm{C}$. For

$$\mathrm{Zn}(s) + \mathrm{Cu}^{2+}(aq) \rightarrow \mathrm{Zn}^{2+}(aq) + \mathrm{Cu}(s)$$

the reaction quotient (solids omitted) is

$$Q = \frac{[\mathrm{Zn}^{2+}]}{[\mathrm{Cu}^{2+}]} = \frac{1.0}{0.010} = 100$$

The general Nernst equation is

$$E = E^\circ - \frac{RT}{nF}\ln Q$$

and at $25^\circ\mathrm{C}$, using base-10 logarithms, the common form is

$$E = E^\circ - \frac{0.05916\ \mathrm{V}}{n}\log Q$$

valid only at $25^\circ\mathrm{C}$. With $n = 2$,

$$E = 1.10 - \frac{0.05916}{2}\log(100) = 1.10 - \frac{0.05916}{2}(2) = 1.10 - 0.05916 \approx 1.04\ \mathrm{V}$$

The voltage drops below the standard value because the stated conditions make the forward reaction less favorable. Correcting $E^\circ$ to actual conditions is precisely the Nernst equation's job.

Reading the Nernst Equation

The Nernst equation does not replace $E^\circ$; it adjusts it. If $Q = 1$, then $\ln Q = 0$ and $E = E^\circ$. If $Q$ grows for the reaction as written, the correction term grows and $E$ falls; if $Q$ drops below $1$, $E$ rises. At equilibrium the forward and reverse tendencies balance, $E = 0$, which is why electrochemistry is tightly tied to equilibrium chemistry.

When to Use Which Tool

• Use the galvanic/electrolytic distinction to decide whether a cell delivers or demands energy and which way electrons flow.
• Use the anode/cathode-by-reaction rule whenever electrode signs are ambiguous.
• Use the Nernst equation whenever concentrations, pressures, or temperature are not at standard values.

Common Mistakes

Treating the Anode as Always Negative

Signs depend on the cell type. The reliable definition is reaction type: oxidation at the anode, reduction at the cathode.

Putting Electrons in the Salt Bridge

Electrons travel in the external circuit. The salt bridge carries ions.

Using the $0.05916$ Form at Any Temperature

That form is specific to $25^\circ\mathrm{C}$. At other temperatures, use the full $RT/(nF)$ version.

Forgetting What Belongs in $Q$

Pure solids and pure liquids are omitted. In many introductory cells, only dissolved ions or gases appear in $Q$.

Where Electrochemistry Is Used

It matters wherever electron transfer meets energy conversion or chemical control: batteries, fuel cells, corrosion, electroplating, metal refining, and analytical sensors. It also bridges thermodynamics and real systems — cell potential tells you not just that a reaction can happen, but how the driving force shifts when conditions change.

To make the Nernst equation feel less like a formula and more like a description, redo the zinc-copper example with $[\mathrm{Cu}^{2+}]$ larger instead of smaller, then recompute $Q$ and $E$.