Quantitative Applications of Electrolysis

The quantitative treatment of electrolysis was developed primarily by Faraday. He observed that the mass of product formed (or reactant consumed) at an electrode was proportional to both the amount of electricity transferred at the electrode and the molar mass of the substance being produced (or consumed). In the electrolysis of molten NaCl, for example, the cathode reaction tells us that one Na atom is produced when one Na ion accepts an electron from the electrode. To reduce 1 mole of Na ions, we must supply an Avogadro s number (6.02 X 10 ) of electrons to the cathode. On the other hand, stoichiometry tells us that it takes 2 moles of electrons to reduce 1 mole of ions and 3 moles of electrons to reduce 1 mole of AP ions  

In an electrolysis experiment, we generally measure the current (in amperes) that passes through an electrolytic cell in a given period of time. The relationship between charge (in coulombs) and the current is 

To illustrate this approach, consider an electrolytic cell in which molten CaCU is separated into its constituent elements. Ca and CH. Suppose a current of 0.452 A is passed through the cell for 1.50 h. How much product will be formed at each electrode The first step is to determine which species will be oxidized at the anode and which species will be reduced at the cathode. Here the choice is straightforward because we have only Ca and Cl ions. The cell reactions are 

The quantities of calcium metal and chlorine gas formed depend on the number of electrons that pass through the electrolytic cell, which in turn depends on chai-ge, or current X time  

Because 1 mol e = 96,500 C and 2 mol e are required to reduce 1 mole of Ca ions, the mass of Ca metal formed at the cathode is calculated as follows  

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Now that we have reviewed the important electrical concepts in quantitative applications of electrolysis, we can put these factors together with our customary approach to stoichiometry problems. In problems such as these, we generally encounter one of two questions. First, how much material is plated, given a specified current or electrical energy expenditure And, second, how long must a given current pass through the cell to yield a desired mass of plated material Example Problems 13.6 and 13.7 illustrate these two types of problems. 

This chapter explains the fundamental principles and applications of electrochemical cells, the thermodynamics OF electrochemical reactions, and the cause and prevention of corrosion BY ELECTROCHEMICAL MEANS. SOME SIMPLE ELECTROLYTIC processes and the QUANTITATIVE ASPECTS OF ELECTROLYSIS ARE ALSO discussed. 

Technetium metal can be electrodeposited from an acidic solution of pertechnetate using a platimun, nickel or copper cathode. Electrolysis of neutral, unbuffered solutions, alkaline solutions, and sulfuric acid solutions lower than 2 N yield a black deposit of hydrated TcOj The current efficiencies are generally poor but the deposition is reasonably quantitative. The deposition requires the application of relatively negative cathode potentials and is therefore non-selective. Polaro-graphy indicates that the overpotentials for the evolution of hydrogen on technetium are rather low hence, electrolysis from acidic media will always include concurrent discharge of hydrogen . ... 

The second important quantity, the half-wave potential can be a measure of the standard free energy change (AG°) or free energy of activation AG ) associated with the electrolytic process. The value of the half-wave potential depends on the nature of the electroactive species, but also on the composition of the solution in which the electrolysis is carried out. If the composition of the solution electrolysed, consisting of the electroactive substance and a proper supporting electrolyte, often buffered, is kept constant, it is possible to compare the half-wave potentials of various substances. When the mechanism of the electrode process is similar for all compounds compared, the halfwave potential can be considered to be a measure of the reactivity of the compound towards the electrode. Hence the half-wave potentials are physical constants that characterize quantitatively the electrolysed compound, or the composition of the electrolyzed solution. In the application of polarography to reaction kinetics the half-wave potentials are of importance both for slow and fast reactions. For slow reactions a large difference in half-wave potentials makes a simultaneous determination of several components of the reaction mixture possible. In... 

In DPP, after application of the pulse, the potential returns to a continually increasing value, which eventually is sufficient to cause electrolysis during the nonpulse part of the experiment. Therefore, DPP does not have the advantage of restricted electrolysis times seen for normal-pulse polarography (NPP). Besides its application to trace analytical work, DPP can be advantageous because of the better resolution inherent in a peak-shaped output. The reaction of iron-sulfur protein site analogues [Fe S (SR)4] , with electrophiles is studied by DPP, where closely spaced reduction waves of the reactant and product are adequately resolved". The reduction of cobaltocene in the presence of phenol studied using DPP, allows quantitative measurement of the amount of cyclopentadienylcobalt cyclopentadiene produced in the electrolysis at the dme by" ... 

The shape of the response function and the height of the peak can be treated quantitatively in a straightforward manner. Note that the events during each drop s lifetime actually comprise a double-step experiment. From the birth of the drop at r = 0 until the application of the pulse at = r, the base potential E is enforced. At later times, the potential is E + A ", where A " is the pulse height. Each drop is bom into a solution of the bulk composition, but generally electrolysis occurs during the period before r and the pulse operates on the concentration profiles that prior electrolysis creates. This situation is analogous to that considered in Section 5.7, and it can be treated by the techniques developed there. Even so, we will not take that approach, because the essential simplicity of the problem is obscured. 

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