Electrochemistry — Galvanic Cells, Electrolysis & Nernst Equation

Electrochemistry explains how redox reactions and electricity affect each other. In a galvanic cell, a spontaneous redox reaction produces electrical energy. In an electrolytic cell, an outside power source drives a nonspontaneous reaction. The Nernst equation then tells you how the cell potential changes when concentrations, pressures, or other conditions are not at their standard values.

If you remember one idea, remember this: chemistry decides where electrons tend to go, and electrochemistry tracks the voltage that results.

What Electrochemistry Means

A redox reaction always involves electron transfer. Electrochemistry becomes useful when the oxidation and reduction half-reactions are separated into different locations, so electrons travel through an external circuit instead of transferring directly in one beaker.

That separation gives you measurable quantities such as current and cell potential. It also makes the chemistry easier to analyze, because you can label one electrode as the oxidation site and the other as the reduction site.

Galvanic Vs. Electrolytic Cells

Galvanic Cells Produce Electrical Energy

A galvanic cell, also called a voltaic cell, uses a spontaneous redox reaction to generate electrical energy.

The core rules stay the same:

• oxidation happens at the anode
• reduction happens at the cathode
• electrons move through the external wire from anode to cathode

In a galvanic cell, the reaction itself provides the driving force.

Electrolytic Cells Consume Electrical Energy

An electrolytic cell uses an external power source to force a reaction that is nonspontaneous under the stated conditions.

Electroplating and the electrolysis of molten salts are standard examples. The reaction labels do not change here either: oxidation is still at the anode, and reduction is still at the cathode. What changes is the energy direction. Electrical energy is supplied to make the chemistry happen.

How To Identify The Anode, Cathode, And Salt Bridge

Students often memorize electrode signs and get stuck. The safer rule is to define each electrode by the reaction happening there.

• anode = oxidation
• cathode = reduction

In many galvanic cells, the anode is negative and the cathode is positive. In many electrolytic cells, the signs are reversed because an external source is pushing electrons where they would not go on their own.

The salt bridge or porous barrier has a different job from the wire. Electrons move through the external circuit. Ions move through the solution or salt bridge to keep charge from building up too much in either half-cell.

Worked Example: Zinc-Copper Galvanic Cell

Consider the galvanic cell

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

The half-reactions are

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

So zinc is oxidized at the anode, and copper(II) ions are reduced at the cathode. Under standard conditions, the standard cell potential is

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

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

Now suppose the concentrations are no longer standard: $[\mathrm{Zn}^{2+}] = 1.0\ \mathrm{M}$ and $[\mathrm{Cu}^{2+}] = 0.010\ \mathrm{M}$ at $25^\circ\mathrm{C}$.

For the overall reaction

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

the reaction quotient is

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

Because solids do not appear in $Q$, only the aqueous ions matter here.

At general conditions, the Nernst equation is

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

At $25^\circ\mathrm{C}$, using base-10 logarithms, it is often written as

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

This shorter form is only valid at $25^\circ\mathrm{C}$.

For this cell, $n = 2$, so

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

The voltage is lower than the standard value because the stated conditions make the forward reaction less favorable than it is in the standard-state setup. That is the main job of the Nernst equation: it corrects $E^\circ$ to the actual conditions.

How To Read The Nernst Equation

The Nernst equation does not replace the standard cell potential. It adjusts it to the conditions you actually have.

If $Q = 1$, then $\ln Q = 0$, so $E = E^\circ$. If $Q$ gets larger for the reaction as written, the correction term becomes larger and $E$ decreases. If $Q$ gets smaller than $1$, $E$ increases.

At equilibrium, the forward and reverse tendencies balance, and $E = 0$ for the cell reaction under those conditions. That is why electrochemistry is closely tied to equilibrium chemistry.

Common Mistakes

Treating The Anode As Always Negative

Negative and positive signs depend on the kind of cell. 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, not electrons.

Using The $0.05916$ Form At Any Temperature

The form

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

is specific to $25^\circ\mathrm{C}$. If the temperature changes, use the full form with $RT/(nF)$.

Forgetting What Belongs In $Q$

Pure solids and pure liquids are omitted from the reaction quotient. In many introductory cell problems, only dissolved ions or gases appear in $Q$.

When Electrochemistry Is Used

Electrochemistry matters anywhere electron transfer meets energy conversion or chemical control. That includes batteries, fuel cells, corrosion, electroplating, metal refining, and analytical sensors.

It also gives a practical bridge between thermodynamics and real systems. Cell potential tells you not just that a reaction can happen, but how the driving force shifts when the conditions change.

Try A Similar Problem

Change the zinc-copper example to a case where $[\mathrm{Cu}^{2+}]$ is larger instead of smaller, then recompute $Q$ and $E$. That one change is enough to make the Nernst equation feel less like a formula to memorize and more like a way to describe what the cell is actually experiencing.