AP Chemistry: Electrochemistry

Electrochemistry connects chemical change to electrical energy. In AP Chemistry, it is the unit where redox reactions stop being abstract bookkeeping and become measurable with voltmeters, wires, and electrodes. The central questions are practical and testable: Which redox reactions are spontaneous? How does concentration affect voltage? How much product forms when you run current through a cell?

This article ties together galvanic and electrolytic cells, cell potential, the Nernst equation, and Faraday’s laws of electrolysis in a way that mirrors how these ideas actually work in the lab and on the AP exam.

Redox fundamentals: electrons, oxidation states, and half-reactions

Electrochemistry is built on oxidation-reduction (redox) reactions, where electrons transfer from one species to another.

• Oxidation is loss of electrons.
• Reduction is gain of electrons.
• The substance oxidized is the reducing agent (it causes reduction).
• The substance reduced is the oxidizing agent (it causes oxidation).

A useful AP habit is to write redox reactions as half-reactions:

• an oxidation half-reaction that produces electrons
• a reduction half-reaction that consumes electrons

Balancing in aqueous solution often requires adding $H_{2}O$, $H^{+}$ (acidic), or $O{H}^{-}$ (basic) to conserve mass and charge. Even when balancing is not explicitly required, the half-reaction approach clarifies what happens at each electrode in an electrochemical cell.

Galvanic (voltaic) cells: making electricity from a spontaneous reaction

A galvanic cell converts chemical energy into electrical energy. The key feature is spontaneity: the redox reaction proceeds on its own and produces a positive cell potential.

Anatomy of a galvanic cell

A typical galvanic cell has:

• Two half-cells (often metal electrodes in their ion solutions)
• A salt bridge (or porous barrier) to maintain charge balance
• An external wire allowing electrons to flow

There are two electrodes:

• Anode: oxidation occurs here.
• Cathode: reduction occurs here.

A reliable memory tool is:

• AnOx, RedCat: Anode Oxidation, Cathode Reduction.

In a galvanic cell:

• Electrons flow from anode to cathode through the wire.
• Ions flow through the salt bridge to prevent charge buildup:
• Anions migrate toward the anode compartment (to balance the increase in positive ions from oxidation).
• Cations migrate toward the cathode compartment (to replace cations being reduced/removed from solution).

Cell notation

AP Chemistry uses line notation to represent cell structure, for example:

Single lines separate phases; the double line indicates the salt bridge. The anode half-cell is written on the left, cathode on the right.

Standard cell potential and predicting spontaneity

The driving force of a galvanic cell is quantified by the cell potential, $E_{\text{cell}}$, measured in volts. Under standard conditions (1 M solutes, 1 atm gases, 25°C), you use standard reduction potentials from a table to compute $E_{\text{cell}}^{\circ }$.

Using reduction potentials correctly

Reduction potential tables list half-reactions as reductions. The more positive the $E^{\circ }$ value, the greater the tendency for that species to be reduced.

To find standard cell potential:

• Identify which half-reaction is reduction at the cathode (keep $E^{\circ }$ as written).
• Identify which half-reaction is oxidation at the anode (reverse the half-reaction and change the sign of $E^{\circ }$).
• Add:

$E_{\text{cell}}^{\circ }=E_{\text{cathode}}^{\circ }-E_{\text{anode}}^{\circ }$

A crucial point: do not multiply __MATH_INLINE_14__ values when balancing electrons. Potentials are intensive properties; scaling a reaction does not scale the voltage.

What the sign of $E_{\text{cell}}$ means

• If $E_{\text{cell}}^{\circ }>0$, the reaction is spontaneous as written.
• If $E_{\text{cell}}^{\circ }<0$, the reverse reaction is spontaneous.
• If $E_{\text{cell}}^{\circ }=0$, the system is at equilibrium.

Electrochemistry also links to thermodynamics. The relationship between cell potential and Gibbs free energy is:

$$\Delta G=-nF{E}_{\text{cell}}$$

where:

• $n$ is moles of electrons transferred
• $F$ is Faraday’s constant ($96485{\text{C mol}}^{-1}{e}^{-}$)

So a positive $E_{\text{cell}}$ corresponds to negative $\Delta G$, which matches the definition of spontaneity.

The Nernst equation: how concentration changes voltage

Standard conditions are rare in real cells. As concentrations shift, the cell potential changes. The Nernst equation quantifies this dependence:

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

At 25°C (298 K), it is commonly written as:

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

Here, $Q$ is the reaction quotient, built like an equilibrium expression using activities approximated by concentrations for dilute solutions. Pure solids and liquids do not appear in $Q$.

What the Nernst equation tells you conceptually

• If $Q$ increases (more products relative to reactants), $\log Q$ increases, and $E$ decreases.
• As a galvanic cell runs, reactants are consumed and products accumulate, so voltage gradually drops.
• At equilibrium, $E=0$ and $Q=K$. This gives a powerful connection:

$$0=E^{\circ }-\frac{0.0592}{n}\log K$$

so

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

Large positive $E^{\circ }$ implies a large equilibrium constant, meaning products are strongly favored at equilibrium.

Concentration cells as a practical application

A concentration cell uses identical electrodes and half-reactions, but different ion concentrations. The voltage is produced purely by the tendency to equalize concentrations. The Nernst equation is essential here, and it reinforces the idea that electrochemical potential depends on more than identity of substances; it depends on conditions.

Electrolytic cells: using electricity to drive nonspontaneous chemistry

An electrolytic cell uses electrical energy to force a nonspontaneous redox reaction to occur. Common examples include metal plating, refining metals, and splitting water.

The anode and cathode definitions do not change:

• Anode is still oxidation.
• Cathode is still reduction.

What changes is the sign of the cell potential:

• Electrolytic processes have $E_{\text{cell}}<0$ for the reaction as written, so an external power source must supply energy.

Electrolysis in aqueous solution: competition matters

In aqueous electrolysis, water can be oxidized or reduced, so there is competition between:

• reduction of dissolved cations vs reduction of water to $H_2$
• oxidation of anions vs oxidation of water to $O_2$

AP-level predictions often rely on comparing standard reduction potentials and recognizing that some ions (like alkali metal cations) are difficult to reduce in water, making water reduction more likely. Electrode material (inert vs active) can also affect what happens, especially at the anode.

Faraday’s laws: converting current into chemical amounts

Faraday’s laws connect electrical charge to the amount of chemical change. The core relationships are:

1. Total charge passed: $q=It$

where $I$ is current (A = C/s) and $t$ is time (s)

1. Moles of electrons transferred: $\text{mol }{e}^{-}=\frac{q}{F}$

1. Stoichiometry links electrons to product via the balanced half-reaction.

A typical AP workflow

If a current runs through an electrolytic cell and you want the mass of metal plated:

1. Compute charge: $q=It$
2. Convert to moles of electrons: $q/F$
3. Use the reduction half-reaction to convert moles of electrons to moles of metal
4. Convert to grams using molar mass

For example, if a metal ion requires 2 electrons to become metal (like $M^{2+}+2e^{-}\to M$), then moles of metal deposited equals half the moles of electrons delivered.

Faraday’s approach also applies to gas formation, such as $H_2$ generated at a cathode. Once moles of gas are known, ideal gas relationships can be used if pressure, volume, and temperature are relevant.

Putting it all together for AP Chemistry

Electrochemistry problems tend to mix concepts, so it helps to keep a compact roadmap:

• Use half-reactions to determine what is oxidized and reduced.
• Use standard reduction potentials to compute $E_{\text{cell}}^{\circ }$ and predict spontaneity.
• Use the Nernst equation when