Chapter 23- Potentiometry

A: Reference Electrodes

A reference is an electrode that has the half-cell potential known, constant, and completely insensitive to the composition of the solution under study. In conjunction with this reference is the indicator or working electrode, whose response depends upon the analyte concentration.

Ideal Reference Electrode:

  • Is reversible and obeys the Nernst equation
  • Exhibits a potential that is constant with time
  • Returns to its original potential after being subjected to small currents
  • Exhibits little hysteresis with temperature cycling

Calomel Electrodes

Consist of mercury in contact with a solution that is saturated with mercury (I) chloride (calomel) and that also contains a known concentration of potassium chloride. The saturated calomel electrode (SCE) is widely used by analytical chemists because of the ease with which it can be prepared. However, its temperature coefficient is greatly larger than those of other calomel electrodes. Also, when the temperature is changed, its potential comes to a new value only slowly because of the time required for solubility equilibrium for the potassium chloride and for the calomel to be reestablished. The body of the outer electrode consists of an outer glass or plastic tube that is 5 to 15cm in length and 0.5 to 1.0cm in diameter. A mercury/mercury (I) chloride paste in saturated potassium chloride is contained in an inner tube, which is connected to the saturated potassium chloride solution in the outer tube through a small opening. A sleeve-type electrode is particularly useful for measurements of nonaqueous solutions and samples in the form of slurries, sludges, viscous solutions, and colloidal suspensions.

Silver/Silver Chloride Electrodes

The most widely marketed reference electrode system consists of a silver electrode immersed in a solution of potassium chloride that has been saturated with silver chloride. The electrode potential is determined by the half-reaction

AgCl(s) + e- = Ag(s) + Cl-

Silver/silver chloride electrodes have the advantage that they can be used at temperatures greater than 60C, whereas calomel electrodes cannot. On the other hand, mercury (II) ions react with fewer sample components than do silver ions; such reactions can lead to plugging of the junction between the electrode and the analyte solution.

Precautions in the Use of Reference Electrodes

In using reference electrodes, make sure the level of the internal liquid should always be kept above that of the sample solution to prevent:

  • Contamination of the electrode solution.
  • Plugging of the junction due to reaction of the analyte solution with silver or mercury (I) ions from the internal solution.

The amount of contamination is so slight that it is of no concern. In determining ions such as chloride, potassium, silver, and mercury, however, precaution must be taken to avoid this source of error. A way to enforce this is to interpose a second salt bridge between the analyte and the reference electrode; this bridge should contain a noninterfering electrolyte, such as potassium nitrate or sodium sulfate.

B: Metallic Indicator Electrodes

An ideal indicator electrode responds rapidly and reproducibly to changes in activity of the analyte anion. There are two types of indicator electrodes: metallic and membrane. There are four types of metallic indicator electrodes:

  1. Electrodes of the first kind.
  2. Electrodes of the second kind.
  3. Electrodes of the third kind.
  4. Redox electrodes.

Electrodes of the First Kind

They are in direct equilibrium with the cation derived from the electrode metal. Here, a single reaction is involved. For example,

Cu 2+ + 2e- = Cu(s)

They are not widely used for potentiometric analyses for several reasons:

  • They are not very selective.
  • Respond not only to their own cations, but also to other more easily reduced cations.
  • Many metal electrodes can be only used in neutral or basic solutions because they dissolve in the presence of acids.
  • Some metals are so easily oxidized that their use is restricted to solutions that have been deaerated.
  • Certain harder metals do not provide reproducible potentials.
  • These electrodes have plots of pX versus activity yield slopes that differ significantly and irregularly fro the theoretical.

Electrodes of the Second Kind

A metal electrode can often be made responsive to the activity of an anion with which its ion forms a precipitate or a stable complex ion. The electrode reaction can then be written as

AgCl(s) + e- = Ag(s) + Cl-E0= 0.222V

An important electrode of the second kind for measuring the activity of EDTA anion Y4- is based upon the response of a mercury electrode in the presence of a small concentration of the stable EDTA complex of Hg(II). To employ this electrode system, it is necessary to introduce a small concentration of HgY2- into the analyte solution at the outset. The complex is so stable that its activity remains essentially constant over a wide range of Y4- activities. This electrode is useful for establishing the end points for EDTA titrations.

Electrodes of the Third Kind

A metal electrode can, under some circumstances, be made to respond to a different cation.

Metallic Redox Indicators

Electrodes fashioned from platinum, gold, palladium, or other inert metals often serve as indicator electrodes for oxidation/reduction systems. In these applications, the inert electrode acts as a source or sink for electrons transferred from a redox system in the solution. For example, the potential of a platinum solution containing Ce(III) or CE(IV). Thus, a platinum electrode serves as the indicator electrode in a titration in which Ce(IV) serves as the standard reagent. However, the electron-transfer processes at inert electrodes are frequently no reversible.

C: Membrane Indicator Electrodes

A wide variety of membrane electrodes are available from commercial sources that permit the rapid and selective determination of numerous cations and anions by direct potentiometric measurements. Often, membrane electrodes are called ion-selective electrodes because of the high selectivity of most of these devices.

Classification of Membranes

Properties of Ion-Selective Membranes

1. Minimal solubility. A necessary property of an ion-selective medium is that its solubility in analyte solutions approaches zero.

  1. Electrical conductivity. A membrane must exhibit some electrical conductivity, albeit small. Generally, this conduction takes the form of migration of singly charged ions within the membrane.
  2. Selective reactivity with the analyte. A membrane or some species contained within the membrane matrix must be capable of selectively binding the analyte ion. Three types of binding:
  3. Ion-exchange
  4. Crystallization
  5. Complexation

The Glass Electrode for pH Measurements

The Composition and Structure of Glass Membranes

Corning 015 glass, which has been widely used for membranes, consists of approximately 22% Na2O, 6% CaO, and 72% SiO2. The membrane is specific in its response toward hydrogen ions up to a pH of about 9. The glass consists of an infinite three-dimensional network of SiO44- groups in which each silicon is bonded to four oxygens and each oxygen is shared by two silicons. Singly charged cations, such as sodium and lithium, are mobile in the lattice and are responsible for electrical conduction within the membrane.

The Hygroscopicity of Glass Membranes

The surface of a glass membrane must be hydrated before it will function as a pH electrode. The amount of water involved is approximately 50mg per cubic centimeter of glass. The hydration of a pH sensitive glass membrane involves an ion-exchange reaction between singly charge cations in the glass lattice and protons from the solution. In general, the ion-exchange reaction can be written as

H+ + Na+Gl- = Na+ + H+Gl-

The equilibrium constant for this process is so large that the surface of a hydrated glass membrane ordinarily consists entirely of silica acid groups. An exception to this situation exists in highly alkaline media, where the hydrogen ion concentration is extremely small and the sodium ion concentration is large; here, a significant fraction of the sites are occupied by sodium ions.

Electrical Conduction Across Glass Membranes

To serve as an indicator for cations, a glass membrane must conduct electricity. Conduction within the hydrated gel layer involves the movement of hydrogen ions. Sodium ions are the charge carriers in the dry interior of the membrane. Conduction across the solution/gel interfaces occurs by the reactions. It is the potential difference that serves as the analytical parameter in potentiometric pH measurements with a membrane electrode.

Membrane Potentials

The Boundary Potential

The boundary potential is simply the difference between these potentials:

Eb = E1 – E2

Eb = E1 – E2 = 0.0592 log (a1/a2)

The boundary potential Eb depends only upon the hydrogen ion activities of the solutions on either side of the membrane. For a glass pH electrode, the hydrogen ion activity of the internal solution a2 is held constant so that it simplifies to

Eb = L’ + 0.0592 log a1 = L’ – 0.0592 pH

Where L’ = -0.0592 log a2.

The boundary potential is then a measure of the hydrogen ion activity of the external solution.

The Potential of the Glass Electrode

The potential of a glass indicator electrode has three components:

  1. The boundary potential.
  2. The potential of the internal Ag/AgCl reference electrode.
  3. A small asymmetry potential.

The Alkaline Error

Glass electrodes respond to the concentration of both hydrogen ion and alkali metal ions in basic solution. The magnitude of this alkaline error for four different glass membranes can be shown on a graph. The error is negative, which suggests that the electrode is responding to sodium ions as well as to protons. This observation is confirmed by data obtained for solutions containing different sodium ion concentrations. All singly charged cations induce an alkaline error whose magnitude depends upon both the cation in question and the composition of the glass membrane.

Selectivity Coefficients

The effect of an alkali metal ion on the potential across a membrane can be accounted for by inserting an additional term in the previous equation to give

Eb = L’ + 0.0592 log (a1 + kb1)

Where k is the selectivity coefficient for the electrode and b1 is the activity of the alkali metal ion. It applies not only to glass indicator electrodes for hydrogen ion but also to all other types of membrane electrodes. Selectivity coefficients range from zero to values greater than unity. A selectivity coefficient of unity means the electrode responds equally to the analyte ion and the interfering ion. If an electrode for ion A responds 20 times more strongly to ion B than to ion A, then k has the value of 20. If the response of the electrode to ion C is 0.001 of its response to A, k is 0.001.

The Acid Error

A typical glass electrode exhibits an error, opposite in sign to the alkaline error, in solutions of pH les than about 0.5; pH readings tend to be too high in this region. The magnitude of the error depends upon a variety of factors and is generally not very reproducible. The causes of acid error are not well understood.

Glass Electrodes for Other Cations

The alkaline error in early glass electrodes led to investigations concerning the effect of glass composition upon the magnitude of this error. One consequence has been the development of glasses for which the alkaline error is negligible below about pH 12. Other studies have discovered glass compositions that permit the determination of cations other than hydrogen. This application requires that the hydrogen ion activity a1 be negligible relative to kb1; under these circumstances, the potential is independent of pH and is a function of pB instead. Glass electrodes that permit the direct potentiometric measurement of such singly charged species as Na+, K+, NH4+, and total concentration of univalent cations are now available from commercial sources.

Crystalline Membrane Electrodes

The most important type of crystalline membranes is manufactured from an ionic compound or a homogeneous mixture of ionic compounds. In some instances the membrane is cut from a single crystal; in others, disks are formed from the finely ground crystalline solid by high pressures or by casting from a melt. The typical membrane has a diameter of about 10mm and a thickness of 1 or 2 mm. To form an electrode, the membrane is sealed to the end of a tube made from a chemically inert plastic such as Teflon or polyvinyl chloride.

Conductivity of Crystalline Membranes

Most ionic crystals are insulators and do not have sufficient electrical conductivity at room temperature to serve as membrane electrodes. Those that are conductive are characterized by having a small singly charged ion that is mobile in the solid phase. Examples are fluoride ion in certain rare earth fluorides, silver ion in silver halides and sulfides, and copper (I) ion in copper (I) sulfide.

The Fluoride Electrode

Lanthanum fluoride, LaF3, is a nearly ideal substance for the preparation of a crystalline membrane electrode for the determination of fluoride ion. Although this compound is a natural conductor, its conductivity can be enhanced by doping with europium fluoride, EuF2. Membranes are prepared by cutting disks from a single crystal of the doped compound. At the two interfaces, ionization creates a charge on the membrane surface as shown by the equation

LaF3 = LaF2+ + F-

The magnitude of the charge is dependent upon the fluoride ion concentration of the solution. Thus, the side of the membrane encountering the lower fluoride ion concentration becomes positive with respect tot eh other surface; it is this charge difference that provides a measure of the difference in fluoride concentration of the two solutions. The potential of a cell containing a lanthanum fluoride electrode is given by an equation analogous to previous equations. That is,

E = L – 0.0592 log aF = L + 0.0592 pF

In most respects, the fluoride ion electrode approaches the ideal for selective electrodes.

Electrodes Based on Silver Salts

Membranes prepared from single crystals or pressed disks of various silver halides act selectively toward silver and halide ions. Generally, their behavior is far from ideal, however, owing to low conductivity, low mechanical strength, and a tendency to develop high photoelectric potentials. It has been found, though, that these disadvantages are minimized if the silver salts are mixed with crystalline silver sulfide in an approximately 1:1 molar ratio. The resulting disk exhibits good electrical conductivity owing to the mobility of the silver ion in the sulfide matrix.

Liquid Membrane Electrodes

Liquid membranes are formed from immiscible liquids that selectively bond certain ions. Membranes of this type are particularly important because they permit the direct potentiometric determination of the activities of several polyvalent cations and of certain singly charged anions and cations as well. The active substances in liquid membranes are of three kinds:

  1. Cation exchangers
  2. Anion exchangers
  3. Neutral macrocyclic compounds, which selectively complex certain cations

D: Ion-Selective Field-Effect Transistors (ISFETs)

The metal oxide semiconductor field-effect transistor (MOS-FET), which is widely used in computers and other electronic circuits as a switch to control current flow in circuits. One of the problems in employing this type of device in electronic circuits has been its pronounced sensitivity to ionic surface impurities, and a great deal of money and effort has been expended by the electronic industry in minimizing or eliminating this sensitivity in order to produce stable transistors.

Mechanism of ISFET Ion-Selective Behavior

An ion-selective field-effect transistor is very similar in construction and function to an n-channel enhancement mode MOSFET. The ISFET differs only in that variation in the concentration of the ions of interest provides the variable gate voltage to control the conductivity of the channel. The conductivity of the channel can be monitored electronically to provide a signal that is proportional to the logarithm of the concentration of hydronium ion in the solution. Note that the entire ISFET except the gate insulator is coated with a polymeric encapsulant to insulate all electrical connections from the analyte solution.

Application of ISFETs

The ion-sensitive surface of the ISFET is naturally sensitive to pH changes, but the device may be rendered sensitive to other species by coating the silicon nitride gate insulator with a polymer containing molecules that tend to form complexes with species other than hydronium ion. Several ISFETs may be fabricated on the same substrate so that multiple measurements may be made simultaneously. All of the ISFETs may detect the same species to enhance accuracy and reliability, or each ISFET may be coated with a different polymer so that measurements of several different species may be made simultaneously. Their small size, rapid response time relative to glass electrodes, and ruggedness suggest that ISFETs may be the ion detectors of the future for many applications.

E: Molecular-Selective Electrode Systems

Two types of membrane electrode systems have been developed that act selectively toward certain types of molecules. One of these is used for the determination of dissolved gases, such as carbon dioxide and ammonia. The other permits the determination of a variety of organic compounds, such as glucose and urea.

Gas-Sensing Probes

These devices are not, in fact, electrodes but instead are electrochemical cells made up of a specific ion and a reference electrode immersed in an internal solution that is retained by a this gas-permeable membrane. Thus, gas-sensing probes is a more suitable name for these gas sensors. They are remarkably selective and sensitive devices for determining dissolved gases or ions that can be converted to dissolved gases by pH adjustment.

Membrane Probe Design

The heart of the probe is a thin, porous membrane, which is easily replaceable. This membrane separates the analyte solution from an internal solution containing sodium bicarbonate and sodium chloride. A pH-sensitive glass electrode having a flat membrane is fixed in position so that a very thin film of the internal solution is sandwiched between it and the gas-permeable membrane. A silver/silver chloride reference electrode is also located in the internal solution. It is the pH of the film of liquid adjacent to the glass electrode that provides a measure of the carbon dioxide content of the analyte solution on the other side of the membrane.