POTENTIOMETRY CHAPTER 5

CHAPTER 5. POTENTIOMETRY

I. Introduction

Potentiometric methods of analysis are based upon measurements of the potential of electrochemical cells under conditions of zero current, where the Nernst equation governs the operation of potentiometry.

O + ne RE = E + (RT/nF)In{(O)/(R)}

FIGURE 5-1. "Janata" Fig. 4-1 (p. 83).The domain of potentiometric methods of analysis lies at the zero-current axis.

The cell can be depicted asReference electrodesalt bridgeanalyte solutionindicator electrode

Eref Ej Eind

Ecell = Eind Eref + Ej

Eref is independent of the concentration of analyte or any other ions in the solution.Eind depends upon the activity of the analyte.

FIGURE 5-2. “Skoog” Fig. 18-1 (p. 387).The salt bridge prevents components of analyte solution from mixing with those of reference solution. The two potentials develop across the liquid junctions at each end of the salt bridge tend to cancel one another if mobilities of cations and anions in the bridge solution are about the same. Net Ej is therefore usually less than a few millivolts. This uncertainty in junction potential places a limit on accuracy of potentiometric analysis.

II. Reference Electrodes

Requirements:1. Stable2. Reversible3. Reproducible

i/. Standard Hydrogen Electrode (SHE)Pt

2H+ + 2e H2; E = 0 V

Disadvantages:1. Rather difficult to prepare properly and inconvenient to use;2. Its potential is sensitive to oxidants and reductants in solution (i.e., anything that will

oxidize H2 or reduce H+);3. Catalytic Pt surface is poisoned by a variety of substances including As, CN, H2S, and Hg.

ii/. Calomel Electrode FIGURE 5-3. “Harris” Fig. 15-5 (p. 317).Hg/Hg2Cl2(saturated), Cl (x M)Hg2Cl2(s) + 2e 2Hg(l) + 2Cl; E = + 0.2415 V

The potential is governed by the Cl- ion activity. The most common type is the saturated (with KCl) calomel electrode (SCE).

Advantage: Easily made and maintained.Disadvantage: Potential varies strongly with temperature.

iii/. Silver/Silver-Chloride ElectrodeFIGURE 5-4. “Harris” Fig. 15-3 (p. 316).

Ag/AgCl(saturated), Cl (x M)AgCl(s) + e Ag(s) + Cl; E = +0.2223 V

The potential is governed by the Cl ion activity.Advantage: Stable for use at temperature up to ca. 275C, a useful alternative to calomel electrodes at elevated temperature.

iv/. Mercury/Mercurous Sulfate ElectrodeHg/Hg2SO4 (saturated), SO4

2 (xM)A substitution of calomel or silver-chloride electrodes when leakage of chloride ion through the reference electrode into the test solution is not permissible (e.g., in titrations involving Ag+).

v/. Thallium-Amalgam/Thallous-Chloride ElectrodeTl(Hg)/TlCl (saturated), KCl (saturated)

Superior to either calomel or silver-chloride electrodes when measurements are made over a range of temperature, because it attains its equilibrium potential very rapidly after changes in temperature.Some commercial glass pH electrode use Thalamid (Tl(Hg)/Tl+) electrode as internal reference electrode.

III. Ion-Selective Electrode (ISE)

(A) Thermodynamics of Ion-Selective ElectrodesISEs do not involve redox processes and often have a thin membrane ideally capable of binding only the intended ion.FIGURE 5-5. “Harris” Fig. 15-8 (p. 383).

G = RTIn(a1/a1’) = nFE

where a1 = activity of analyte solutiona1’ = activity of internal solution

i.e., E = (0.05916/n)log(a1/a1’)In the steady state, free energy decrease due to diffusion is balanced by the free energy increase from repulsion of like charges.

(B) Types of Ion-Selective Electrodesi/. Glass Electrodes for pH MeasurementsFIGURE 5-6. “Harris” Fig. 15-9 (p. 324).When immersed in aqueous solution, cations from the glass surface are leached out and replaced by protons to form a hydrated silica-rich layer (ca. 500 A thick). The external part of this hydrated gel layer can act as a cation exchange membrane which has a particularly high degree of selectivity among the various cations.FIGURE 5-7. Glass electrode.

H+ + Na+Gl Na+ + H+Gl

soln. solid soln. solid

The equilibrium constant for this reaction is so large that the surface of a hydrated glass membrane will consist almost entirely of silicic acid (H+Gl), except in very basic media. Current conduction through the dry glass region is ionic and involves movement of the alkali ions from one site to another. Within the two hydrated gel layers the current is carried by both alkali and hydrogen ions. At each gel-solution interface, current passage involves the transfer of protons.FIGURE 5-8. “Harris” Fig. 15-13 (p. 325).

Theory:The potential across a glass membrane consists of a boundary potential and a diffusion potential. Under ideal conditions only the former is affected by pH.The boundary potential is given by,

Eb = V2 - V1

in which, V1 = j1 - (RT/nF)In(a1/a1')V2 = j2 - (RT/nF)In(a2/a2') (1)where j = constant (assymmetry potential)

a = H+ activity in solutiona' = H+ activity in gel

If the two gel surfaces have the same number of sites from which protons can leave, then j1 = j2 and a1' = a2'.Since a2 = constant,

Eb = constant + (RT/F)In(a1)

Diffusion potential also develops in each of the two gel layers due to the difference between the mobilities of hydrogen ions and alkali metal ions in the membrane. If the two solution-gel interfaces are the same, the two diffusion potentials are equal and opposite in sign, i.e., the net diffusion potential is zero.

Some glass membranes also respond to the concentration of alkali metal ions.M+ + H+Gl H+ + M+Gl, where M+ = singly charged cationsoln. solid soln. solidKex = (a1b1')/(a1'b1)where a1 and b1 are activities of H+ and M+ in solution, respectively

a1' and b1' are activities of H+ and M+ in gel surface, respectivelyKex is usually small in value except when [H+] is low and [M+] is high.Rewriting,

a1/a1' = (a1 + Kexb1)/(a1' + b1') (2)Substituting (2) into (1),

Eb = V2 - V1 = j1 - j2 + (RT/F)In{[(a1 + Kexb1)a2']/[(a1' + b1')a2]}If the number of sites on the two sides of the membrane is the same, a2' (a1' + b1') and j1 = j2.Thus,

Eb = (RT/F)In{(a1 + Kexb1)/a2}Since a2 = constant,

Eb = constant + (RT/F)In(a1 + Kexb1)

Alkaline error: Diffusion potentials on each side of the membrane also change when some of the surface sites are occupied by cations other than hydrogen and do not cancel out as they did in the previous case.

Eb = constant + (RT/F)In{a1 + Kex(UM/UH)b1}where UM and UH are mobilities of M+ and H+ in the gel

For many glasses the term Kex(UM/UH)b1 is small with respect to the hydrogen ion activity a1 so long as the pH of the solution is less than about 9.

Acid error: The typical glass electrode exhibits an error, opposite in sign to the alkaline error, in solutions of pH less than 1. The causes of the acid error are not well understood.

ii/. Glass Electrodes for Determination of Other CationsBy varying the chemical composition of the thin, ion-selective glass membrane, glass electrodes can be prepared that are differentially responsive to (primarily monovalent) cations, e.g., Na+, K+, NH4

+, Rb+, Cs+, Li+, and Ag+.Eb = constant + (RT/F)In{a1 + Kex(UM/UH)b1}

The application for the determination of cations other than hydrogen requires that the hydrogen activity a1 be negligible with respect to the second term containing the activity b1 of the other cation.TABLE 5-9. "Christian" Table 2.4 (p. 33).

iii/. Solid State Crystalline and Pressed-Pellet ElectrodesFIGURE 5-10. "Christian" Fig. 2.6 (p. 33).

a) Single Crystale.g., Fluoride electrode- Europium doped LaF3 single crystal.- Internal electrolyte: NaF/NaCl.FIGURE 5-11. “Harris” Fig. 15-17 (p. 331).- At low pH, F- forms HF (pKa 3) and interferes.- At pH > 8, OH intereferes.

b) Pressed Pellete.g., Ag2S pressed-pellet membrane- To detect Ag+ or S2.- The mechanism is due to very low solubility product of Ag2S (Ksp = 1051).

Ag2S 2Ag+ + S2

FIGURE 5-12. Ag2S electrode.

For Ag+, E = Econstant + (RT/F)In(aAg+)

For S2, E = Econstant (RT/2F)In(aS2)

c) Mixed Pellete.g., AgX-Ag2S (X= Cl, Br, I, or SCN)- Responsive to X.- The Ag+ activity at the surface of the electrode is controlled by the activity of X in solution via its solubility equilibrium.

AgX Ag+ + X

- This in turn controls the electrode potential by being coupled with the Ag2S solubility equilibrium.

E = Econst. + (RT/F)In(aAg+) = Econst. + (RT/F)In(Ksp/aX

) = Econst. (RT/F)In(aX)

- Also responsive to Ag+ and S2.- Anything with a lower solubility product than the ion being determined will interfere.TABLE 5-13. "Christian" Table 2.5 (p. 35).iv/. Liquid-Membrane Ion-Exchange ElectrodesFIGURE 5-14. "Christian" Fig. 2.7 (p. 36).An ion-exchange equilibrium is set up at both the inner and outer surfaces of the membrane, and the difference in activity of the ion of interest in the inner electrolyte and outer test solutions give rise to the potential response of the electrode.The sensitivity and selectivity of these electrodes is determined primarily by the selectivity of the particular organic ion-exchanger for the ion of interest and, secondarily, by the organic solvent used to dissolve the exchanger.The extent of interference is related to the solubility of the complex formed between the ion and the ion-exchanger in the membrane, and the mobility of the complexes within the membrane.

Examples:1. M2+ electrodesinternal reference electrode: Ag-AgClaqueous reference electrolyte solution: saturated AgCl + MCl2

RH2x + xM2+ RMx + 2xH+

organic phase aq. phase organic phase aq. phasephosphate diesters ((RO2PO2

, R = C8 - C16) dissolved in dioctylphenylphosphonate is selective for Ca2+.

2. Ion-exchangers of the form R-S-CH2COO for Cu2+ and Pb2+ (form 5-membered ring chelate with Cu2+ and Pb2+).

3. Orthophenanthrolines metal complexes, M(o-phen)32+, for nitrate, fluoroborate, or

perchlorate.4. Dimethyl-distearyl-ammonium ion, R4N+, for chloride.5. Valinomycin electrode (antibiotics) for K+.TABLE 5-15. “Harris” Table 15-6 (p. 334).

v/. Enzyme-Substrate ElectrodesConstructed by coating the surface of an appropriate ion-selective electrode with an enzyme

immobilized in some matrix.e.g., ISE enzyme gel test solution (urea)

ureaseurea + H2O HCO3

+ NH4+

vi/. Gas-Sensing ElectrodesFIGURE 5-16. "Skoog" Fig. 17-12 (p. 398).The dissolved gas passes through the membrane into a small volume of internal filling solution, where a chemical equilibrium is established.e.g., SO2 (aq.) SO2 (g) ; SO2(g) SO2 (aq.)

external solution membrane pores membrane pores internal solution

SO2(aq) + H2O HSO3 + H3O+

K = ([H3O+][HSO3])/[SO2(aq)]ext.

If [HSO3] is high in internal solution, i.e., [HSO3

] constantThen, [H3O+]/[SO2(aq)]ext. = K/[HSO3

] = Kg

i.e., [H3O+] = Kg[SO2(aq)]ext a1 (internal hydrogen ion activity) E = Econst. + (RT/F)In(a1)

= Econst. + (RT/F)In(Kg[SO2(aq)]ext)

= Econst. + 0.0591log(Kg) + 0.0591log([SO2(aq)]ext)

= Econst. + 0.0591log(Kg) 0.0591pSO2

The species that will interfere with the measurement are dissolved gases that can pass through the membrane and that will alter the pH of the internal solution.TABLE 5-17. "Skoog" Table 17-5 (p. 400).

IV. Field-Effect Transistors

Semiconductors such as Si (FIGURE 5-18), Ge, and GaAs are materials whose electrical resistivity lies between those of conductors and insulators.FIGURE 5-18. “Harris” Fig. 15-26 (p. 338).A semiconductor with excess conduction electrons is called n-type, and one with excess holes is called p-type. A diode is a pn junction.FIGURE 5-19. “Harris” Fig. 15-27 (p. 339).If an electric field is applied to the surface of the semiconductor from whatever source, the density of the mobile charge, say, electrons (holes), will be either enhanced or depleted depending on the polarity of the field. If the field enhances the concentration of electrons (holes), the surface is said to be accumulated and the semiconductor surface behaves much like a metal in that the excess charge appears at the surface and the electric field does not penetrate it further. If, on the other hand, the field forces the mobile electrons (holes) away from the surface, a thin depletion region devoid of charge carriers near the pn junction is formed. The thickness of the depletion region is a function of the strength of the field at the surface and the semiconductor doping profile, as is the difference between the surface and bulk potentials of the semiconductor. If the surface potential deviates sufficiently far from the bulk potential, the surface will invert, that is, it will contain an excess of mobile holes (electrons).The metal oxide field effect transistor (MOSFET), a tiny solid state semiconductor device, is used as a switch to control current flow in circuits.FIGURE 5-20. “Harris” Fig. 15-28 (p. 339).

The potential of the gate regulates the current flow between source and drain.The surface field can be produced in a number of ways. The semiconductor can be built into a capacitor and an external potential applied (MOSFET), or the field can arise from the electrochemical effects between different materials (chemically-sensitive field-effect transistors, CHEMFET). In both cases, variations in the surface electric field change the density of mobile charge carriers in the surface inversion layer.In CHEMFET, the metal gate is replaced by a chemically sensitive layer.FIGURE 5-21. “Harris” Fig. 15-29 (p. 340).

e.g., FIGURE 5-22. “Harris” Fig. 15-30 (p. 340).When a AgBr chemically sensitive layer is exposed to silver nitrate solution, Ag+ is adsorbed on AgBr, giving a positive charge and increasing current between source and drain. The voltage that must be applied by an external circuit to bring the current back to its initial value represents the response of the device to Ag+. Similarly, adsorption of Br makes the gate more negative. The response is close to 59 mV for a 10-fold concentration change.

Two types of chemically sensitive field-effect transistor (CHEMFET):1. Ion-sensitive field-effect transistors (ISFET)FIGURE 5-23. "Janata" Fig. 4-28 (p. 132).2. Enzymatic field-effect transistors (ENFET)FIGURE 5-24. "Janata" Fig. 4-41 (p. 146).

Advantages: smaller and more rugged than ISE.

FIGURE 5-1. Janata, Principles of Chemical Sensors, Plenum.

FIGURE 5-2. Skoog, et al, Principles of Instrumental Analysis, 4th Ed.

Figure 15-5. A saturated calomel electrode (SCE).

FIGURE 5-3. Harris, Quantitative Chemical Analysis, 6th Ed.

Figure 15-3. Silver-silver chloride reference electrode.



Figure 15-9. A glass combination electrode incorporating both glass and reference electrodes in one body.


FIGURE 5-7. Glass electrode.

Figure 15-13. Ion-exchange equilibria on surfaces of a glass membrane: H+ replaces metal ions bound to the negatively charged oxygen atoms. The pH of the internal solution is fixed. As the pH of the external solution (sample) changes, the electric potential difference across the glass membrane changes.


FIGURE 5-9. Christian et al, Instrumental Analysis, 2nd Ed.


Figure 15-17. Migration of F－ through LaF3 doped with EuF2. Because Eu2+ has less charge than La3+, an anion vacancy occurs for every Eu2+. A neighboring F－

can jump into the vacancy, thereby moving the vacancy to another site. Repetition of this process moves F－ through the lattice.


FIGURE 5-12. Ag2S electrode.



TABLE 5-15. Harris, Quantitative Chemical Analysis, 6th Ed.

FIGURE 5-16. Skoog et al, Principles of Instrumental Analysis, 4th Ed.

FIGURE 5-17. Skoog et al, Principles of Instrumental Analysis, 4th Ed.

Figure 15-26. (a) The electrons of pure Si are all involved in the bonding framework. (b) An impurity atom such as P adds one extra electron, which is relatively free to move through the crystal. (c) An Al impurity atom lacks one electron needed for the bonding framework. The hole introduced by the Al atom can be occupied by an electron from a neighboring bond, effectively moving the hole to the neighboring bond.


Figure 15-27. Behavior of a pn junction, showing that (a) current can flow under forward bias conditions, but (b) is prevented from flowing under reverse bias.


Figure 15-28. Operation of a field effect transistor. (a) Nearly random distribution of holes and electrons in the base in the absence of gate potential. (b) Positive gate potential attracts electrons that form a conductive channel beneath the gate. Current can flow through this channel between source and gain.


Figure 15-29.Operation of a chemical-sensing field effect transistor. The transistor is coated with an insulating SiO2 layer and a second layer of Si3N4, which is impervious to ions and improves electrical stability. The circuit at the lower left adjusts the potential difference the reference electrode and the source in response to changes in the analyte solution, such as a constant drain-source current is maintained.


Figure 15-30.Response of a silver bromide-coated field effect transistor.




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POTENTIOMETRY CHAPTER 5