Quantitative Aspects of Electrochemistry for AP Chemistry

Practice problems for these concepts can be found at:

• Electrochemistry Review Questions for AP Chemistry
• Electrochemistry Free-Response Questions for AP Chemistry

One of the most widely used applications of electrolytic cells is in electrolysis, the decomposition of a compound. Water may be decomposed into hydrogen and oxygen. Aluminum oxide may be electrolyzed to produce aluminum metal. In these situations, several questions may be asked: How long will it take; how much can be produced; what current must be used? Given any two of these quantities, the third may be calculated. To answer these questions, the balanced half-reaction must be known. Then the following relationships can be applied:

1 Faraday = 96,500 coulombs per mole of electrons

(F = 96,500 C/mol e^– or 96,500 J/V)

1 ampere = 1 coulomb/second (A = C/s)

For example, if liquid titanium(IV) chloride (acidified with HCl) is electrolyzed by a current of 1.000 amp for 2.000 h, how many grams of titanium will be produced? Answer:

Calculation of E °_cell also allows for the calculation of two other useful quantities—the Gibbs free energy (ΔG°) and the equilibrium constant (K ).

The Gibbs free energy is the best single thermodynamic indicator of whether a reaction will be spontaneous (review the Thermodynamics chapter). The Gibbs free energy for a reaction can be calculated from the E ° of the reaction using the following equation:

ΔG = – nFE°_cell

where F is Faraday's constant of 96,500 C/mol e^– = 96,500 J/V.

If the redox reaction is at equilibrium, E° = 0, the equilibrium constant may be calculated by:

Let's apply these relationships. Determine ΔG° and K for the following reaction:

Answer:

For this reaction, two electrons are transferred from the Ni to the Ag. Thus, n is 2 for this reaction. The value of F (96,500 J/V) is given on the exam, so you will not need to memorize it.

This gives a K of about 10³⁵ (actually K = 3 × 10³⁵). In many cases, the approximate value will be all you need for the AP exam.

Practice problems for these concepts can be found at:

• Electrochemistry Review Questions for AP Chemistry
• Electrochemistry Free-Response Questions for AP Chemistry