Electrochemistry

to a study of solutions of electrolytes and the phenomena occurring at electrodes immersed in such solutions. Many analytical procedures of interest are based on electrochemical measurements. Also, automatic continuous stream monitors, which have wide application, use electrochemical methods to translate chemical characteristics into electrical impulses that can be recorded. Electrochemical principles are also useful in understanding oxidation-reduction reactions (Sec. 4.10). A brief review of the more fundamental concepts of electrochemistry will be presented. More detailed information can be obtained from standard texts on physical chemistry.

Current Flow in Solution

An electric current can flow through a solution of an electrolyte as well as through metallic conductors. However, there are some basic differences that are of importance and are summarized here:

Characteristics of current flow through a metal

1. Chemical properties of metal are not altered.

2. Current is carried by electrons

3. Increased temperature increases resistance.

Characteristics of current flow through a solution

1. Chemical change occurs in the solution.

2. Current is carried by ions.

3. Increased temperature decreases resistance

4. Resistance is normally greater than with metals.

A significant feature of current flow through a solution is that the current is carried by ions which move toward electrodes immersed in the solution. Also, a chemical change takes place in the solution at the electrodes, and this alters the chemical properties of the solution. These two phenomena, current flow or conductivity and chemical change at electrodes, will first be considered separately.

Conductivity

The conductivity of a solution is a measure of its ability to carry an electric current and varies both with the number and type of ions the solution contains. Conductivity can be measured in a conductivity cell connected to a Wheatstone bridge circuit as shown in Fig. 3.7. Such an arrangement allows measurement of the electrical resistance provided by the cell. The measurement consists of altering the variable resistance until no current flows through the detecting circuit containing the meter A. Modern instruments can do this automatically to give a direct readout. When this state of balance is achieved, the potential at D must be the same as that at E, and the resistance offered by the solution is determined by the relationship

Resistan«

Soiuti

Resistan«

Soiuti

-/vVWWvVv •®1 E ®2

Alternating current -1000 cycles/second

Figure 3.7

Conductivity-measuring apparatus.

Special care must be taken if this measured resistance is to be meaningful. If direct current is used, the apparent resistance changes with time, because of a polarization effect at the electrodes. This unwanted effect can be overcome by rapidly changing the direction of current flow. This is done by using an alternating current of several thousand cycles per second. In addition, a more reproducible state of balance is normally obtained when the platinum electrodes of the cell are coated with platinum black. For continuous monitoring and field studies, electrodes made of durable common metals such as stainless steel are often used.

When these precautions are taken, it can be shown that the conductivity cell filled with an electrolytic solution obeys Ohm's law:

where I is the length and A is the cross-sectional area of the conductor. The value p (ohm-cm) is called the specific resistance of the conductor. Our interest is normally in the specific conductance of a solution rather than in its specific resistance. These quantities are reciprocally related as follows:

where E - electromotive force, volts I = current, Amperes R = resistance of cell contents, ohm

The resistance depends upon the dimensions of the conductor:

where k is the specific conductance and has units of 1/ohm-cm, one unit of which is called a siemen (S). The specific conductance can be thought of as the conductance afforded by 1 cm3 of a solution of electrolyte.

In practice, a conductivity cell is calibrated by determining the resistance Rs of a standard solution, and from this the cell constant C is determined:

Normally, 0.0100 N KC1 is used as a standard solution for this calibration and has a specific conductance ks of 0.0014118 S at 25°C, or in more convenient units, 1411,8 ju.S. The specific conductance of an unknown sample can be determined by measuring its resistance R in the cell and then using the following relationship:

Specific conductance has a marked temperature dependence, and caution must be taken to measure the resistance of the standard and the unknown at the same temperature.

Specific conductance measurements are frequently used in water analysis to. obtain a rapid estimate of the dissolved solids content of a water sample. If a flow-through cell is used and water from a river or waste stream is pumped through the cell, a continuous recording of specific conductance can be obtained. The dissolved solids content can be approximated by multiplying the specific conductance in microsiemens by an empirical factor varying from about 0.55 to 0.9. The proper factor to use depends upon the ionic components in the solution, as will be indicated by the introduction of a new parameter, the equivalent conductance A, which is defined as follows:

where N is the normality of the salt solution. For an ideal ionic solution, k should vary directly with N, and thus A should remain constant with varying solution normality. However, because of deviation from ideal behavior, A decreases somewhat as the salt concentration increases.

Current is carried by both anions and cations of a salt, but to a different degree. The equivalent conductance of a salt is thus the sum of the equivalent ionic conductances of the cation Aq and the anion Ao:

The zero subscript is used to indicate equivalent conductance at infinite dilution, where the deviation from ideal behavior is at a minimum. Several values for equivalent ionic conductance are shown in Table 3.3. It should be noted that these values are strongly temperature-dependent. It is apparent that the equivalent ionic conductances are in general of the same order of magnitude, with the exception of the hydrogen ion and the hydroxyl ion. The latter two are more mobile than the others in aqueous solution and so can carry a larger portion of the current. This fact should be considered when estimating the dissolved solids concentration from conductivity

Table 3.3! Equivalent ionic conductance at infinite dilution at 25°C in S-cmVeq

Table 3.3! Equivalent ionic conductance at infinite dilution at 25°C in S-cmVeq

Source: J. A. Dean, "Lange's Handbook of Chemistry," 15th ed„ McGraw-Hill, Inc., New York, 1999.

measurements of solutions with either a high or a low pH. If the approximate chemical composition of a water solution is known, the equivalent ionic conductance values will allow a better choice of the appropriate factor for conversion from conductance to dissolved solids concentration.

Another important point is that only ions can carry a current. Thus, the unionized species of weak acids or bases will not carry a current, although they are a portion of the total dissolved solids in a water sample. Also, uncharged soluble organic materials, such as ethanol and glucose, cannot carry a current and so are not measured by conductance.

iySj'ln^ ^Siriili^

Current and Chemical Change

When electrodes are introduced into a water solution in such a way as to allow a direct current to flow through the solution, a chemical change will take place at the electrodes. The nature of the chemical change depends upon the composition of the solution, the nature of the electrodes, and the magnitude of the imposed electromotive force.

Consider first the chemical changes occurring when platinum electrodes are introduced into a solution of HC1 as indicated in Fig. 3.8. When a voltage of about 1.3

Figure 3.8

Electrolysis of a hydrochloric acid solution.

volts is applied, it is found that H2 is evolved at the cathode and Cl2 at the anode. The current movement is as follows: Electrons flow through the external metallic conductor in the direction shown, as a result of the driving force of the battery. Such a flow maintains the negative charge at the cathode and the positive charge at the anode. The flow of current through the solution is maintained by movement of the cations (H+) to the negatively charged cathode and anions (CT) to the positively charged anode.

When an B+ ion reaches the cathode, it picks up an electron and is reduced to H2 gas, according to the half reaction

When the CI™ ion reaches the anode, it gives up an electron and is oxidized to Cl2 gas by the following half reaction:

The electrons released by the Cl~ ions are "pumped" through the external circuit by the driving force of the battery to be picked up by the H* ions at the cathode. Thus, the battery acts as a driving force to keep the current flowing and the reaction going. As indicated above, reduction takes place at the cathode and oxidation at the anode. The overall chemical change which takes place in the solution is as follows:

The flow of electrons in the external circuit is necessary to bring about the chemical change. It is apparent that in order to bring about an equivalent of chemical change at an electrode, an Avogadro's number of electrons must flow through the external circuit. This quantity of electrons is called the faraday, (F). The rate of flow of electrons gives the current 1, which is normally measured in amperes. One faraday is equivalent to an ampere of current flowing for 96,485 seconds. An ampere is also defined as a coulomb per second, so that a faraday is equivalent to 96,485 coulombs.

EXAMPLE 3.10 | If a current is passed through a sodium chloride solution, hydrogen gas'is evolved at the

The amount of current flowing in this time period is The amount of current flowing m thrs tune penod is

™ \ __________• <------- -Ii™:«., ^^„.„l.™..,. .17 «WOK 4SS nr ft 170

™ \ __________• <------- -Ii™:«., ^^„.„l.™..,. .17 «WOK 4SS nr ft 170

Electrochemical Cell

As indicated previously, the nature of a chemical change occurring at an electrode is partially dependent upon the type of electrode used. A single electrode dipping into a solution is said to constitute a half-cell; the combination of two half-cells as indicated in Fig. 3.8 is a typical electrochemical cell. Some half-cell systems are used for analysis of various constituents and properties in water. These are discussed in detail in Chap. 12 of this book.

When two half-cells are connected so that ions can pass between them, an electrochemical or galvanic cell is obtained. The electrochemical cell shown in Fig. 3.8 is quite simple, as only one solution is involved. However, in most electrochemical analyses the solutions associated with each half-cell are different, and they must be kept from mixing. In such a case, some type of salt bridge is used which allows passage of ions while keeping interdiffusion of the solutions to a minimum (see Fig. 3.9).

If the two electrodes of an electrochemical cell are connected through a metallic conductor, electrons will flow through the external circuit, and a chemical change will begin to take place in the solutions. If a voltmeter is connected across the half-cells as indicated in Fig. 3.9, it will be found that electromotive force (emf)

Salt bridge (KC1 + gelatin)

Figure 3.9

An electrochemical cell.

is being generated by the cell. This emf is a measure of the driving force of the chemical reaction that is occurring in the half-cell solutions. Thus, it gives a measure of the chemical potential or free energy of the reaction. From this fact, a relationship between electrochemical potential and chemical free energy can be found. Electric energy is measured in terms of the joule, which is the energy generated by the flow of 1 A in 1 second against an emf of 1 volt. Electric energy is given by the product, Elt and has units of the volt coulomb or joule.

The electric energy expended in bringing about 1 mol of chemical change is zEF, where z is the number of electron-equivalents per mole, F is the faraday or coulombs per equivalent, and E is the emf of the cell in volts. By convention, if the reaction proceeds, E is positive, so the relation between free energy and electrical energy is

AG = -zFE Consider the following chemical reaction:

If we substitute the relationship for E from Eq. (3.41) into the free-energy equation (3.12), the following relationship between cell emf and concentration of reactants and products results:

Here the value of the gas constant R, in electrical units, is 8.314 J/K-mol. This important equation indicates the relationship between the standard electrode potential of a cell and the activities of the products and reactants. It is sometimes called the Nernst equation. For a temperature of 25°C, and converting In to log, Eq. (3.42) becomes:

When the activities of products and reactants are unity, the logarithmic term is unity, and E = E° (that is, the emf for the standard state).

The emf of a cell can be calculated from tabulated values just like free-energy and enthalpy values. Such tables list the standard potentials of various half-cells with respect to the standard hydrogen electrode, which is assigned by convention the value E° = 0. By taking the difference between the standard potentials of two half-cells, the potential of the whole cell can be determined. Standard potentials for various half-cells of interest are listed in Table 3,4. The E° values listed in Table 3.4 are for a reaction written for 1 mol of e~ change, for example:

If an electrochemical cell has reached a state of equilibrium, no current can flow, and the emf of the cell is zero. For this case a relationship between the standard-ceil potential and the equilibrium constant for the reaction can be obtained by using Eqs. (3.14) and (3.41):

zF zF

Table 3.4 i Standard electrode potentials in water at 25°C

Half-cell reaction. |

Ot(g)+ 4H+ + 4e~ -> 2H20

1.229

Ag+ + e" -* Ag(s) Fe3 * + e~ ~> Fei+

0.799

0.771

Ag2Cr04(i) + 2e~ -> 2 Ag(r) + CrOj"

0.446

Cu2+ + 2e~ -> Cu(s)

0.337

AgCl(i) + e~ -» Ag(j) + CI"

0.222

S(J) + 2H+ + 2<T -> HjS(i)

0.141

2H+ + 2e~ -> H2(g)

0.000

Pb2+ + 2e~ Pb(j)

-0.126

Sn2+ + 2<T -» Sn(i)

-0.136

Fe2+ + 2s" -> Fe(i)

-0.441

S(i) + 2e~ S2~

-0.48

Zn2* + 2e~ Zn(j)

-0.763

Zn(OH)2(s) + 2e~ -> Zn(j) + 20H"

-1.245

ZnS(j) + 2e- -> Zn(j) + S2"

-1.44

Al3+ + 3<T -> Al(s)

-1.66

Mg2+ + 2e~ -i> Mg(i)

-2.37

Mg(OH)2(i) + 2e~ -> MgC?) + 20H~

-2.69

Source: W. M. Latimer, "Oxidation Potentials," 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1952.

Source: W. M. Latimer, "Oxidation Potentials," 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1952.

Alternatively, from Eq. (3.43):

A '-cellconsistingof: the following -two half-cells from-Table 3.4 will produce the overall

VoliS ,

Ag(i) Ag+ H- e~

AgCl(j) + <T Ag(s) + CP

Net AgCl(i) Ag+ + CI"

Thus, for the net reaction as written is -0.577 volt, and can be determined by

EXAMPLE 3.11

< -u(Cl2(s) be used to oxidize NH4 to NOj . ' /^ :: ■ ;';:r | EXAMPLE 3.12

! -v: The half reactions listed m Table 2.4 can be used to'.constract-a'balanced oxidation-::.. reduction reaction and an E° can be calculated for the overall reaction. For this particular problem, half reaction 20 in Table 2.4 can be reversed (with a corresponding sigri change for £?) aiid added to half reaction 3 to produce; the ¿verall pxidation-^^ ireacUpn: •

iNHi,.+ |J

i2o = im;+iiV + e-

Viv '

—0.882 1,361

?NHi +

i2o = |Nor + cr + |

H*

0.479

Since is positive, yes, the reaction cot theoretically proceed as written.

Additional discussion of these concepts is given in Sec. 4.10 on oxidation-reduction reactions.

Galvanic Protection

If a zinc metal electrode is connected to an iron metal electrode by means of a conducting salt bridge and an external metallic conductor as indicated in Fig. 3.9, a cell will result. The cell reaction and standard potential of the cell will be

Since the potential is positive, the reaction can proceed as written when products and reactants are near unit activity. Zinc ions will tend to pass into solution, and iron ions will tend to plate out on the iron electrode. Thus, the iron is kept from passing into solution, while the zinc acts in a sacrificial manner. As electrochemical cells are sometimes called galvanic cells, this method of corrosion prevention is called galvanic protection. It is the basic principle involved in the protection of iron by galvanizing with zinc,

From this consideration, it is apparent that when two metals are in electrical contact, the metal with the greater single-electrode potential will sacrifice itself to protect the other. Since the protected electrode assumes a negative charge, it is the cathode, and this can be called cathodic protection. From these considerations, the engineer can explain why discontinuous coatings of tin aggravate the rusting of iron. These principles are also the basis of regulations prohibiting the joining of copper and iron pipe without the use of insulating connectors.

If a battery is placed in the external circuit connecting two half-cells, either electrode can be made to be the cathode and thus be protected. Hence, electric energy can be made to counterbalance the chemical energy of the cell, and so reverse the reaction. Such electrochemical principles are widely used for the cathodic protection of steel pipelines, tanks, and structures by means of sacrificial anodes or artificially impressed negative potentials.

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