Faraday's Laws

The electrochemical cell with zinc and copper electrodes had an overall potential difference that was positive (+1.10 volts), so the spontaneous chemical reactions produced an electric current. Such a cell is called a voltaic cell. In contrast, electrolytic cells use an externally generated electrical current to produce a chemical reaction that would not otherwise take place.

An instance of such electrolysis is the decomposition of water to elemental hydrogen and oxygen. The pertinent half‐reactions are given in Table 1.

The overall reaction for the electrolysis of water is given by adding the two half‐reactions to obtain

with an overall potential of –1.23 volts. With a negative potential, it requires an externally imposed electrical current to decompose water by the reaction shown. Figure 1 shows two platinum electrodes in water containing a little salt or acid so that the solution can conduct electricity.

Figure 1. The electrolysis of water.


The reduction at the cathode yields H 2 gas, and the oxidation at the anode yields O 2 gas. Notice that the figure shows that the volume of hydrogen is twice the volume of oxygen—look at the bubbles. The molar coefficients in the decomposition reaction imply 2 volumes of H 2 gas for each 1 volume of O 2 gas.

Electrolysis is used to decompose many compounds into their constituent elements. You have seen this process with water. Another example is the electrolysis of molten sodium chloride to yield molten sodium metal and chlorine gas:

Chemists throughout the nineteenth century discovered new elements from the electrolytic decomposition of many compounds.

The quantitative laws of electrochemistry were discovered by Michael Faraday of England. His 1834 paper on electrolysis introduced many of the terms that you have seen throughout this book, including ion, cation, anion, electrode, cathode, anode, and electrolyte. He found that the mass of a substance produced by a redox reaction at an electrode is proportional to the quantity of electrical charge that has passed through the electrochemical cell. For elements with different oxidation numbers, the same quantity of electricity produces fewer moles of the element with the higher oxidation number.

The basic unit of electrical charge used by chemists is appropriately called a faraday, which is defined as the charge on one mole of electrons (6 × 10 23 electrons). Incidentally, note that chemists have extended the original definition of the mole as a unit of mass to a corresponding number (Avogadro's number) of particles. Use the electrolysis of molten sodium chloride to see the relationship between faradays of electricity and moles of decomposition products.

The reduction half‐reaction is 

so to produce 1 mole of sodium metal requires 1 mole of electrons, so 1 faraday of charge must pass through the cell.

The oxidation half‐reaction is


and to produce 1 mole of chlorine gas, 2 faradays of electric charge must pass through the apparatus. Notice how the number of electrons in redox reactions determines the quantity of electricity needed for the reaction.

These half‐reactions sum to the overall reaction in the electrolytic cell: 

The passage of 2 faradays of charge yields 2 moles of sodium metal and 1 mole of chlorine gas.

The first of Faraday's laws states that the mass of substance produced is proportional to the quantity of electricity. To apply this law to the NaCl example, where 1 mole of Cl 2 was produced by 2 faradays, means that to produce 10 moles of Cl 2 requires the passage of 20 faradays through the apparatus.

The second of Faraday's laws states that a given quantity of electricity produces fewer moles of substances with higher oxidation numbers. Compare the reduction of sodium and calcium ions: 

It requires twice as much electricity to produce 1 mole of calcium metal as 1 mole of sodium metal.

The electrolytic decomposition of sodium chloride and calcium oxide appear similar: 

but the NaCl decomposition requires the transfer of only half as many electrons as does the CaO decomposition. For the NaCl electrolysis, it was previously calculated that the passage of 20 faradays of electric charge produced 20 moles of sodium metal and 10 moles of chlorine gas. The same amount of electric charge passing through the CaO cell yields only 10 moles of calcium metal and 5 moles of oxygen gas.

The reduction half‐reaction with balanced coefficients:


The oxidation half‐reaction with balanced coefficients: 

  • Aluminum metal is produced by the electrolysis of molten cryolite, Na 3AlF 6. How many faradays of electric charge are needed to produce 1 kilogram of aluminum?