9.11 Electrolysis and Faraday's Law

Electrolysis uses an external power source to drive a thermodynamically unfavored redox reaction in an electrolytic cell. Faraday's law lets you connect current, time, charge, moles of electrons, and the mass of material deposited or removed at an electrode using $I = \frac{q}{t}$ and the Faraday constant, $96{,}485\ \text{C/mol e}^-$. For AP Chemistry, set up the dimensional-analysis chain before solving for mass, time, current, or charge.

Electrolysis in AP Chem

In AP Chem, electrolysis uses electrical energy to force a thermodynamically unfavored redox reaction to occur in an electrolytic cell. A power supply pushes electrons through the circuit, so the reaction can plate metal, remove material from an electrode, or recharge a battery.

For Topic 9.11, Faraday's law connects the visible change at an electrode to the amount of charge that flowed. The core chain is current and time to charge, charge to moles of electrons, moles of electrons to moles of product, and moles of product to mass.

Why This Matters for the AP Chemistry Exam

This topic asks you to calculate charge flow from changes in the amounts of reactants and products in an electrochemical cell. The main skill here is choosing the right relationship and following a logical computational pathway with correct units and significant figures. Expect to set up dimensional analysis chains that move between current, time, charge, moles of electrons, and grams of metal, and to rearrange that chain to solve for whichever quantity is unknown. Because Unit 9 ties together kinetics, thermodynamics, equilibrium, and electrochemistry, this topic often appears alongside reasoning about why an electrolytic reaction needs outside energy to run.

Key Takeaways

• Electrolytic cells run thermodynamically unfavored reactions, so they need an external power source with enough voltage to overcome the cell's negative E.
• Oxidation always happens at the anode and reduction always happens at the cathode, in both galvanic and electrolytic cells.
• Faraday's law links the stoichiometry of a redox reaction to the number of electrons transferred, mass deposited or removed, current, time, and ionic charge.
• Use I = q/t to relate current (amperes), charge (coulombs), and time (seconds): 1 A = 1 C/s.
• The Faraday constant, 96485 C per mole of electrons, converts charge into moles of electrons.
• The number of electrons (n) in the balanced half-reaction sets the mole ratio between electrons and the substance produced or consumed.

Review of Electrolytic Cells

An electrolytic cell uses power from an external source (usually a battery or power supply) to drive a redox reaction that would not happen on its own. These cells need energy because the reaction is thermodynamically unfavored, meaning it has a negative standard cell potential. The applied voltage pushes electrons in the direction the reaction would not naturally go, so a species that would normally be oxidized is instead reduced, or the reverse.

Consider an electrolytic cell built from copper and zinc. Suppose electrons are pushed so that copper metal is oxidized to Cu2+ and Zn2+ is reduced to zinc metal, giving the overall reaction:

Cu + Zn2+ -> Cu2+ + Zn

Using a table of standard reduction potentials, you can find the cell potential. Write the half-reactions:

Cu -> Cu2+ + 2e- (E = -0.34 V)

Zn2+ + 2e- -> Zn (E = -0.76 V)

Adding these gives Ecell = -1.10 V. The negative voltage tells you this reaction will not run on its own, so external power is required.

The battery in the cell must supply more than 1.10 V. The applied voltage has to overcome the non-spontaneity of the reaction you want and the favorability of the reverse reaction (which has E = +1.10 V). Once the battery is connected, it pulls electrons in the direction of the unfavored reaction. As a result, the copper electrode loses mass and the zinc electrode gains mass.

Comparing Electrolytic and Galvanic Cells

Knowing the differences between galvanic and electrolytic cells is important for the AP Chemistry exam.

In a galvanic (voltaic) cell, the reaction is thermodynamically favored, so it runs on its own and produces a positive voltage. Electrons flow spontaneously from the anode to the cathode through the wire, a voltmeter can measure the voltage produced, and a salt bridge keeps each half-cell neutral. The anode loses mass and the cathode gains mass.

In an electrolytic cell, the reaction is thermodynamically unfavored. Instead of a voltmeter, a power supply forces electrons in the opposite direction, driving the reverse of the spontaneous reaction. The applied voltage must be large enough to overcome the negative cell potential. A salt bridge still connects the two half-cells.

The most important similarity: oxidation always occurs at the anode and reduction always occurs at the cathode, no matter which type of cell you have. Note that the AP exam will not ask you to label an electrode as positive or negative.

Faraday's Law and Electrolysis Problems

A common problem type with electrolytic cells is calculating the mass of metal that deposits at or dissolves from an electrode. You handle these with a chain of conversions built on two relationships:

• The definition of an ampere: 1 A = 1 C/s, written as I = q/t, where I is current in amperes, q is charge in coulombs, and t is time in seconds.
• The Faraday constant: 1 mol e- = 96485 C.

Faraday's law lets you use the stoichiometry of the redox reaction to connect charge flow to the amounts of reactants and products in the cell.

Problem Solving

Determine the mass of chromium that can be produced when a solution of Cr(NO3)2 is electrolyzed for 60 minutes with a current of 15 amperes.

Step 1. Convert current and time into charge:

60 min * 60 s/min * 15 C/s = 54000 C

Step 2. Convert charge into moles of electrons using the Faraday constant:

54000 C * (1 mol e- / 96485 C) = 0.559 mol e-

Step 3. Use the half-reaction stoichiometry to convert moles of electrons to moles of chromium, then use the molar mass of chromium (52.0 g/mol) to find grams. In Cr(NO3)2, chromium is Cr2+, so its reduction is Cr2+ + 2e- -> Cr, giving 2 mol e- per mol Cr:

0.559 mol e- * (1 mol Cr / 2 mol e-) * (52.0 g/mol Cr) = 14.5 g Cr

You can run this same dimensional analysis as one continuous chain instead of separate steps.

Rearranging the Chain

The exam can ask you to solve for any of these: the number of electrons transferred, the mass deposited or removed, the current, the time elapsed, or the charge of the ionic species. A question might give you a mass and ask for the time needed, or give a time and ask for the current required.

To solve these, run the same chain in a different direction. For example, if a problem gives a mass and asks for time, start with the mass, convert to moles of substance, then to moles of electrons, then to charge, and finally divide by the current to get time. The key is careful unit cancellation so every conversion factor lines up.

How to Use This on the AP Chemistry Exam

Problem Solving

• Write and balance the relevant half-reaction first so you know n, the number of electrons per mole of substance. This ratio is what most students forget.
• Convert time to seconds before using current. Amperes are coulombs per second, so minutes or hours will give wrong answers.
• Build a dimensional analysis chain and check that units cancel from start to finish: time and current to coulombs, coulombs to moles of electrons, moles of electrons to moles of substance, moles to grams.
• Attend to significant figures and keep the Faraday constant (96485 C/mol e-) handy.

Common Trap

• When asked to reason instead of calculate, be ready to explain that an electrolytic cell needs an external voltage greater than the magnitude of its cell potential because the reaction is thermodynamically unfavored.
• Watch the charge on the ion. The mole ratio of electrons to metal depends on the ion's charge (n), so Cr2+, Cu2+, and Al3+ all require different numbers of electrons.

Common Misconceptions

• Oxidation is not always at the negative electrode. Anode means oxidation and cathode means reduction in every cell. The exam will not ask you to call an electrode positive or negative, so focus on oxidation and reduction.
• The Faraday constant is per mole of electrons, not per mole of metal. You still need the half-reaction's electron count to get from moles of electrons to moles of substance.
• Current is not charge. Amperes measure charge per second. You must multiply current by time to get total charge in coulombs.
• A negative cell potential does not mean nothing happens. It means the reaction will not run on its own, but an external power source can force it. That is exactly what electrolysis does.
• Electrolytic cells still use a salt bridge or equivalent connection when there are two separate half-cells, just like galvanic cells, to keep charge balanced.

Related AP Chemistry Guides

• 9.1 Introduction to Entropy
• 9.3 Gibbs Free Energy and Thermodynamic Favorability
• 9.2 Absolute Entropy and Entropy Change
• 9.8 Galvanic (Voltaic) and Electrolytic Cells
• 9.4 Thermodynamic and Kinetic Control
• Unit 9 Review: Thermodynamics and Electrochemistry