Voltammetry and Polarography Lecture 1

Basic Concepts

Oxidation - Reduction Reactions (Redox rxns) involve the transfer of electrons from one species of the reactants to another. This results in an increase in oxidation number (O.N.) of a specific species and a complementary decrease in oxidation number of another species. Example: Ce4+ + Fe2+ D Ce3+ + Fe3+ The O.N. of cerium was decreased while that of iron was increased. Cerium is reduced while iron is oxidized. A process that involves an increase in O.N. is an oxidation process and vice versa

Usually, a redox reaction can be separated into two halves Usually, a redox reaction can be separated into two halves. Ce4+ + e D Ce3+ Reduction Fe2+ D Fe3+ + e Oxidation Electrons appear in each half reaction while they do not show up in the overall equations.

Electrochemical Cells There are two types of electrochemical cells in the concept whether the cell generates potential (called a galvanic cell) or consumes potential (called an electrolytic cell). A cell is simply constructed from two electrodes immersed in solution. The electrode at which reduction occurs is called the cathode while that at which oxidation occurs is called the anode. In galvanic cells, the cathode is positive (+) while the anode is negative (-). The signs of the anode and cathode are the opposite in electrolytic cells.

Galvanic Cell Electrolytic Cell

Electrons generated by one half reaction will be consumed by the other half reaction forcing the current to flow.

The Standard Hydrogen Electrode (SHE) The standard hydrogen electrode is an electrode with an arbitrarily assigned potential of zero. It is also known as the normal hydrogen electrode (NHE), and is used in combination with other half cells at standard state in order to determine the standard electrode potential of the other half cell.

Hydrogen electrode is based on the redox half cell: 2H+(aq) + 2e → H2(g) This redox reaction occurs at platinized platinum electrode. The electrode is dipped in an acidic solution and pure hydrogen gas is bubbled through it. The concentration of both the reduced form and oxidized form is maintained at unity. That implies that the pressure of hydrogen gas is 1 atm and the activity of hydrogen ions in the solution is unity.

Standard Hydrogen electrode 2H+ + 2e- = H2 Eo = 0.000 V. when PH2 = 1 atm, [H+] = 1 M, 298K Standard Hydrogen electrode

Determination of Standard Electrode Potential The standard electrode potential of a half cell reaction can be determined using a conventional two electrode cell but replacing one electrode with the standard hydrogen electrode (SHE) for which the potential is zero (as arbitrarily assigned). Therefore, the electrode potential is the reading of the voltmeter. For example, when a 1.00 M Cu2+ solution is placed in contact with a Cu wire and the cell is completed with a SHE at standard conditions of temperature and pressure, the potential will read 0.342 V. This is due to reaction: Cu2+ + 2e D Cu (s) Eo = 0.342 V

H2 D 2H+ + 2e Cu2+ + 2e D Cu(s)

On the other hand, when Zn2+ solution is placed in contact with a Zn electrode in an electrochemical cell with a SHE as the second electrode, the potential will read -0.762 V. The reaction is: Zn2+ + 2e D Zn (s) Eo = - 0.762 V From these results we can predict that Cu2+ is a better oxidizing agent since the standard electrode potential is more positive than that for Zn2+.

The more positive the Eo, the better oxidizing agent is the oxidized form. The more negative the Eo, the better reducing agent is the reduced form .

However, SHE is troublesome and more convenient reference electrodes are used. Saturated calomel electrode (SCE) and Ag/AgCl electrodes are most common.

Shorthand notation For electrochemical cells Although cell drawing provides a useful picture of an electrochemical cell, it is not a convenient representation. A more useful way to describe an electrochemical cell is a shorthand notation that uses symbols to identify different phases and that lists the composition of each phase. We use a vertical slash (|) to identify a boundary between two phases where a potential develops, and a comma (,) to separate species in the same phase or to identify a boundary between two phases where no potential develops. Shorthand cell notations begin with the anode and continue to the cathode.

For the cell above, by convention, we identify the electrode on the left as the anode and assign to it the oxidation reaction; thus: Zn(s) = Zn2+ (aq) + 2e The electrode on the right is the cathode, where the reduction reaction occurs: Ag+ (aq) + e = Ag(s)

Zn(s)| ZnCl2(aq, aZn2+ = 0.0167) || AgNO3 (aq, aAg+ = 0.100)|Ag(s) We describe the electrochemical cell in the figure below using the following shorthand notation. Zn(s)| ZnCl2(aq, aZn2+ = 0.0167) || AgNO3 (aq, aAg+ = 0.100)|Ag(s)

SCE and Ag/AgCl Reference Electrodes The cell half-reaction is: Hg2Cl2 + 2e- D 2Hg + 2Cl- E = 0.242 V for saturated KCl The cell half-reaction is: AgCl + e- D Ag + Cl- E = 0.197 V for saturated KCl

Saturated Calomel Electrode The saturated calomel electrode (SCE), which is constructed using an aqueous solution saturated with KCl, has a potential at 25 °C of +0.242 V. A typical SCE consists of an inner tube, packed with a paste of Hg, Hg2Cl2, and saturated KCl, situated within a second tube filled with a saturated solution of KCl. A small hole connects the two tubes, and an asbestos fiber serves as a salt bridge to the solution in which the SCE is immersed. The stopper in the outer tube may be removed when additional saturated KCl is needed. The shorthand notation for this cell is Hg(l) | Hg2Cl2 (sat’d), KCl (aq, sat’d) || The SCE has the advantage that the concentration of Cl–, and, therefore, the potential of the electrode, remains constant even if the KCl solution partially evaporates.

A significant disadvantage of the SCE is that the solubility of KCl is sensitive to a change in temperature. At higher temperatures the concentration of Cl– increases, and the electrode’s potential decreases. For example, the potential of the SCE at 35 °C is +0.2376 V. Electrodes containing unsaturated solutions of KCl have potentials that are less temperature-dependent, but experience a change in potential if the concentration of KCl increases due to evaporation. Another disadvantage to calomel electrodes is that they cannot be used at temperatures above 80 °C.

Ag/AgCl Reference Electrode Another common reference electrode is the silver/silver chloride electrode, which is based on the redox couple between AgCl and Ag. AgCl(s) + e D Ag(s) + Cl–(aq) As with the saturated calomel electrode, the potential of the Ag/AgCl electrode is determined by the concentration of Cl– used in its preparation. E = E°AgCl/Ag – 0.05916 log [Cl–]

Ag(s) | AgCl (sat’d), KCl (x M) || A typical Ag/AgCl electrode consists of a silver wire, the end of which is coated with a thin film of AgCl. The wire is immersed in a solution that contains the desired concentration of KCl and that is saturated with AgCl. A porous plug serves as the salt bridge. The shorthand notation for the cell is Ag(s) | AgCl (sat’d), KCl (x M) || where x is the concentration of KCl.

When prepared using a saturated solution of KCl, the Ag/AgCl electrode has a potential of +0.197 V at 25 °C. Another common Ag/AgCl electrode uses a solution of 3.5 M KCl and has a potential of +0.205 at 25 °C. The Ag/AgCl electrode prepared with saturated KCl, of course, is more temperature-sensitive than one prepared with an unsaturated solution of KCl. In comparison to the SCE, the Ag/AgCl electrode has the advantage of being useful at higher temperatures. On the other hand, the Ag/AgCl electrode is more prone to reacting with solutions to form insoluble silver complexes that may plug the salt bridge between the electrode and the solution.

Zn2+ + 2e D Zn (s) Eo = - 0.762 V Schematic representation of Zn2+/Zn(s) electrode potential relative to different reference electrodes (EoSHE = 0.000V)

The potential of the following half cell reaction at standard state was measured versus SCE giving a value of - 0.103V. Find Eo of the half cell reaction: Sn4+ + 2e D Sn2+

Effect of Concentration on Electrode Potential The IUPAC convention for writing half-cell reactions is to represent the process as a reduction. The more positive half-cell reaction is the oxidizing agent, and the less positive half-cell reaction is the reducing agent. The relationship between the concentration and the electrode potential for a half-cell reaction is represented by Nernst equation, where for the half-cell reaction, we have: aA + bB + ne D cC + dD Eo = x V

The Nernst equation can be written as: Where, R is the molar gas constant (R = 8.314 J mol-1 K-1), T is the absolute temperature in Kelvin ( T = oC + 273) and F is the Faraday constant ( F = 96485 Coulomb.eq-1) and n is the number of electrons per mole. One may write after substitution:

Example Calculate the electrode potential for the half-cell below if the solution contains 0.100 M Cu2+. The half-cell reaction is: Cu2+ + 2e D Cu (s) Eo = 0.342 V Solution E = Eo – (0.0592/n) log [Cu(s)]/[Cu2+] E = 0.342 – (0.0592/2) log 1/0.100 E = 0.312 V

Example Calculate the electrode potential of a half-cell containing 0 Example Calculate the electrode potential of a half-cell containing 0.100 M KMnO4 and 0.0500 M MnCl2 at pH 1.000. Solution MnO4- + 8 H+ + 5 e D Mn2+ + 4 H2O Eo = 1.51 V E = Eo – (0.0592/n) log [Mn2+]/[MnO4-][H+]8 E = 1.51 – (0.0592/5) log 0.0500/0.100*(0.100)8 E = 1.42 V

Junction Potentials A junction potential develops at the interface between two ionic solutions if there exists a difference in the concentration and mobility of the ions. Consider, for example, a porous membrane separating solutions of 0.1 M HCl and 0.01 M HCl. Because the concentration of HCl on the membrane’s left side is greater than that on the right side of the membrane, H+ and Cl– diffuse in the direction of the arrows. The mobility of H+, however, is greater than that for Cl–, as shown by the difference in the lengths of their respective arrows. Because of this difference in mobility, the solution on the right side of the membrane has an excess of H+ and a positive charge

Origin of the junction potential between a solution of 0 Origin of the junction potential between a solution of 0.1 M HCl and a solution of 0.01 M HCl

The magnitude of the junction potential depends upon the concentration of ions on the two sides of the interface, and may be as large as 30–40 mV. For example, a junction potential of 33.09 mV has been measured at the interface between solutions of 0.1 M HCl and 0.1 M NaCl. The magnitude of a salt bridge’s junction potential is minimized by using a salt, such as KCl, for which the mobilities of the cation and anion are approximately equal. We can also minimize the magnitude of the junction potential by incorporating a high concentration of the salt in the salt bridge. For this reason salt bridges are frequently constructed using solutions that are saturated with KCl. Nevertheless, a small junction potential, generally of unknown magnitude, is always present.

When we measure the potential of an electrochemical cell, the junction potential also contributes to Ecell; thus, we write the equation: Ecell = Ec – Ea + Ej If we do not know the junction potential’s actual value—which is the usual situation—then we cannot directly calculate the analyte’s concentration using the Nernst equation. Since reference electrodes use saturated KCl solution, and mobilities of both ions are almost the same, it can be fairly assumed that the resulting junction potential will primarily depend on the composition of the outer sample solution. A good selection of supporting electrolyte can result in negligible junction potentials at the reference electrode interface.

HOW DOES CURRENT AFFECT THE POTENTIAL OF ELECTROCHEMICAL CELLS? When a current develops in an electrochemical cell, the measured potential across the two electrodes is no longer simply the difference between the two electrode potentials (the thermodynamic cell potential). Two additional phenomena, IR drop and polarization, require application of potentials greater than the thermodynamic potential to operate an electrolytic cell and result in the development of potentials smaller than theoretical in a galvanic cell.

A typical cell for the determination of cadmium ion takes the following form: Here, the right-hand electrode is a metal electrode that has been coated with a layer of cadmium. Because this is the electrode at which the reduction of Cd2+ ions occurs, it is called the working electrode. The left-hand electrode is a silver/silver chloride electrode whose electrode potential remains more or less constant during the analysis. The left-hand electrode is thus the reference electrode.

this cell, as written, has a thermodynamic potential of - 0. 734 V this cell, as written, has a thermodynamic potential of - 0.734 V. Here, the negative sign for the cell potential indicates that the spontaneous reaction is not the reduction of Cd2+ on the right and the oxidation of Ag on the left. To reduce Cd2+ to Cd(s), we must construct an electrolytic cell and apply a voltage somewhat more negative than - 0.734 V in order to make the cadmium electrode electron-rich enough to reduce Cd2+ to Cd(s).

Ohmic Potential; IR Drop Electrochemical cells, like metallic conductors, resist the flow of charge. Ohm’s law describes the effect of this resistance on the magnitude of the current in the cell. The product of the resistance R of a cell in ohms and the current I in amperes (A) is called the ohmic potential or the IR drop of the cell. In following figure, we have used a resistor R to represent the cell resistance. To generate a current of I amperes in this cell, we must apply apotential that is IR volts more negative than the thermodynamic cell potential, Ecell = Eright - Eleft . That is, Eapplied = Ecell - IR Where Ecell is the thermodynamic cell potential

Minimization of IR drop Usually, we try to minimize the IR drop in the cell by having a very small cell resistance (high ionic strength) or by using a special three-electrode cell in which the current passes between the working electrode and an auxiliary (or counter) electrode. With this arrangement, only a very small current passes between the working electrode and the reference electrode, which minimizes the IR drop.