Chapter: Potentiometry

Potentiometry is an electroanalytical technique that measures the potential (voltage) of an electrochemical cell under conditions of zero or negligible current. This measured potential is then related to the concentration (more accurately, activity) of a specific ion in the solution. It is a widely used method for determining the concentration of various ions, especially hydrogen ions (pH measurement), and for endpoint detection in titrations.

Fundamental Principles of Potentiometry

The core of potentiometry lies in the Nernst equation, which describes the relationship between the electrode potential and the concentration of electroactive species.

1. Electrochemical Cell: A potentiometric measurement involves an electrochemical cell typically composed of two half-cells:
   • Reference Electrode: An electrode whose potential is constant and known, independent of the composition of the analyte solution.
   • Indicator Electrode (Working Electrode): An electrode whose potential varies in a predictable and reproducible way with the concentration (activity) of the analyte ion.
   • Salt Bridge: Connects the two half-cells, allowing ion flow to maintain electrical neutrality while preventing mixing of the solutions.
   • Potentiometer/Voltmeter: Measures the potential difference (EMF) between the indicator and reference electrodes without drawing significant current.
2. Measured Potential (Ecell​): The measured cell potential is the difference between the potential of the indicator electrode and the potential of the reference electrode, plus any junction potentials: Ecell​=Eindicator​−Ereference​+Ejunction​
3. The Nernst Equation: For a half-reaction involving the transfer of ‘n’ electrons: Ox+ne−⇌Red The potential of the electrode is given by: E=E0−nFRT​lnaOx​aRed​​ At 25°C (298.15 K), converting to base 10 logarithm: E=E0−n0.0592​logaOx​aRed​​ Where:
   • E = measured electrode potential
   • E0 = standard electrode potential
   • R = ideal gas constant (8.314 J mol⁻¹ K⁻¹)
   • T = temperature in Kelvin
   • n = number of electrons transferred in the half-reaction
   • F = Faraday constant (96485 C mol⁻¹)
   • aRed​ and aOx​ = activities of the reduced and oxidized species, respectively. (For dilute solutions, activity is often approximated by concentration).

Components of a Potentiometric Setup

1. Reference Electrodes

These electrodes provide a stable and known potential, serving as a benchmark for potential measurements. They must be non-polarizable, meaning their potential does not change significantly even with small currents.

• Standard Hydrogen Electrode (SHE): The ultimate reference electrode, assigned a potential of exactly 0.000 V at all temperatures when hydrogen gas at 1 atm bubbles over a platinum electrode immersed in 1 M H⁺.
  • Disadvantages: Difficult to set up and maintain, not practical for routine use.
• Saturated Calomel Electrode (SCE): (Hg|Hg₂Cl₂ (s)|KCl (sat’d))
  • Mechanism: Consists of mercury in contact with mercurous chloride (calomel) and a saturated potassium chloride solution. The potential depends on the chloride concentration.
  • Advantages: Stable, easy to prepare and use, relatively inexpensive.
  • Disadvantages: Contains mercury, potential is temperature-dependent, not suitable for temperatures above 50°C (HgCl₂ solubility increases significantly), and chloride contamination is possible.
• Silver/Silver Chloride Electrode (Ag/AgCl): (Ag|AgCl (s)|KCl (x M))
  • Mechanism: Consists of a silver wire coated with silver chloride immersed in a potassium chloride solution of known concentration (often saturated).
  • Advantages: Stable, robust, more rugged and smaller than SCE, can be used at higher temperatures, no mercury. Most common in modern pH electrodes.
  • Disadvantages: AgCl can be light-sensitive, Ag⁺ can react with proteins, potential is dependent on KCl concentration.

2. Indicator Electrodes

These electrodes respond selectively to the activity of the analyte ion.

A. Metallic Indicator Electrodes

These electrodes consist of a metal in contact with its ion in solution.

• Electrodes of the First Kind: A pure metal electrode immersed in a solution containing its cation. (e.g., Ag in Ag⁺ solution, Cu in Cu²⁺ solution).
  • Reaction: Mn++ne−⇌M(s)
  • Nernst: E=E0−n0.0592​logaMn+​1​
  • Disadvantages: Not very selective (can be affected by other redox couples), easily oxidized by oxygen, some metals react with acids.
• Electrodes of the Second Kind: A metal electrode coated with one of its sparingly soluble salts, immersed in a solution containing the anion of the salt. (e.g., Ag electrode coated with AgCl in Cl⁻ solution).
  • Reaction: AgCl(s)+e−⇌Ag(s)+Cl−
  • Nernst: E=EAgCl/Ag0​−0.0592logaCl−​
  • Used for halide ions (Cl⁻, Br⁻, I⁻) or other anions that form sparingly soluble precipitates with the metal. Ag/AgCl is also a common reference electrode.
• Electrodes of the Third Kind: Respond to a third ion. (e.g., Ag electrode coated with AgI and immersed in solution containing iodide and lead(II) ions for Pb²⁺). Less common.
• Redox Electrodes (Inert Electrodes): An inert metal (e.g., Pt, Au) immersed in a solution containing a redox couple. The potential depends on the ratio of the activities of the oxidized and reduced forms.
  • Reaction: Fe3++e−⇌Fe2+ (Pt electrode)
  • Nernst: E=EFe3+/Fe2+0​−0.0592logaFe3+​aFe2+​​
  • Used for titrations involving redox reactions.

B. Membrane Indicator Electrodes (Ion-Selective Electrodes – ISEs)

ISEs are highly selective and respond to the activity of a specific ion. They develop a potential difference across a selective membrane.

• Glass Electrodes:
  • Mechanism: A thin glass membrane (special composition) separates two solutions with different H⁺ activities. A potential develops across the membrane due to ion exchange between the H⁺ ions in solution and alkali metal ions within the hydrated layer of the glass.
  • pH Electrode: Most common type of ISE. Contains an internal Ag/AgCl reference electrode and an internal buffer solution (e.g., 0.1 M HCl saturated with AgCl). The overall potential measured is proportional to the pH of the external solution.
    • Errors in pH Measurement:
      • Alkaline Error (Sodium Error): At very high pH (>10-12), the glass membrane responds not only to H⁺ but also to alkali metal ions (especially Na⁺), leading to a lower measured pH than actual.
      • Acid Error: At very low pH (<0.5), the measured pH is higher than actual. Not fully understood, but attributed to saturation of binding sites.
      • Dehydration: Drying out of the membrane can cause sluggish response and drift.
      • Temperature: Affects both the Nernstian slope and the dissociation constants of weak acids/bases.
      • Junction Potential: Potential developed at the interface of two dissimilar electrolyte solutions, contributing to measurement error.
  • Sodium Ion Electrode: By changing the glass composition (e.g., high Na₂O content), the membrane can be made selective for Na⁺ ions over H⁺.
• Liquid-Membrane Electrodes:
  • Mechanism: A porous hydrophobic membrane separates the analyte solution from an internal reference solution. The pores are filled with an organic solvent containing an ion exchanger (ligand) that selectively binds the analyte ion.
  • Examples: Calcium ion electrode (uses an organic phosphate), Potassium ion electrode (uses valinomycin, a cyclic polyether for K⁺ selectivity), Nitrate, Chloride, Perchlorate electrodes.
  • Advantages: High selectivity for many different ions.
  • Disadvantages: Limited lifetime due to loss of liquid membrane component, subject to interferences from lipophilic ions.
• Solid-State Electrodes:
  • Mechanism: The membrane is a thin slice of a crystalline inorganic salt or a mixture of salts, often doped to increase conductivity. The potential develops across the membrane due to selective ion exchange or defect sites in the crystal lattice.
  • Examples: Fluoride ion electrode (uses a LaF₃ crystal doped with EuF₂), Sulfide ion electrode (uses Ag₂S).
  • Advantages: Robust, long lifetime, excellent selectivity.
• Gas-Sensing Probes:
  • Mechanism: A conventional pH electrode (or other ISE) is encased in a gas-permeable membrane. A thin layer of internal solution (e.g., water) is trapped between the gas membrane and the electrode. The gas analyte (e.g., CO₂, NH₃) diffuses through the membrane, changes the pH of the internal solution, which is then detected by the pH electrode.
  • Examples: CO₂ probe, NH₃ probe, NOx probe.
  • Advantages: Selective, free from many solution interferences.
  • Disadvantages: Response time can be slow.
• Enzyme/Biocatalyst Electrodes (Biosensors):
  • Mechanism: An enzyme or other biological recognition element is immobilized on the surface of a conventional ISE (e.g., pH electrode, oxygen electrode). The enzyme catalyzes a reaction that produces or consumes a species that the underlying ISE can detect.
  • Examples: Urea electrode (uses urease to produce NH₃, detected by an NH₃ gas-sensing probe), Glucose electrode (uses glucose oxidase to produce H₂O₂, detected by an oxygen electrode).
  • Advantages: High specificity due to enzyme catalysis.
  • Disadvantages: Limited lifetime of enzyme, requires careful handling.

3. Potentiometer (pH Meter)

• A high-input impedance voltmeter specifically designed to measure the small potentials generated by electrochemical cells (typically in mV range) without drawing significant current. Drawing current would polarize the electrodes and alter the analyte concentration.
• Modern pH meters often have internal temperature compensation and calibration routines.

Potentiometric Titrations

Potentiometry is widely used to monitor the progress of a titration and determine the equivalence point. The potential of the indicator electrode is measured as a function of the volume of titrant added.

• Principle: The equivalence point is characterized by the largest and most rapid change in potential per unit volume of titrant added (ΔE/ΔV).
• Types:
  • Acid-Base Titrations: Using a glass pH electrode to monitor pH changes.
  • Redox Titrations: Using an inert electrode (e.g., Pt) to monitor potential changes in redox reactions.
  • Precipitation Titrations: Using an electrode sensitive to one of the ions involved in the precipitation reaction (e.g., Ag electrode for halide titrations with Ag⁺).
  • Complexometric Titrations: Using an ISE sensitive to the metal ion or the complexing agent.
• Advantages:
  • Applicable to colored or turbid solutions where visual indicators are difficult to use.
  • More accurate and precise endpoint determination, especially for weak acids/bases or when multiple equivalence points exist.
  • Can be automated.
  • No need for visual judgment of color change.

Sources of Potential Error/Limitations

1. Junction Potential (Ejunction​): A potential difference that develops at the interface between two dissimilar electrolyte solutions in the salt bridge. This potential is usually small (a few millivolts) but can be variable and difficult to quantify, contributing to measurement uncertainty. Minimized by using a salt bridge with a high concentration of ions with similar mobilities (e.g., KCl).
2. Activity vs. Concentration: The Nernst equation describes potential in terms of activity, not concentration. In dilute solutions, activity approaches concentration, but in concentrated solutions or complex matrices, activity coefficients can significantly deviate from unity. Ionic strength affects activity.
3. Calibration: ISEs must be calibrated regularly using standards of known activity (or concentration) that bracket the expected range of the samples.
4. Temperature Effects: Temperature affects the Nernstian slope (nFRT​), electrode potentials, and analyte activity coefficients. Temperature control or compensation is essential.
5. Interferences: Other ions present in the solution might also contribute to the potential of the indicator electrode, leading to inaccurate measurements (e.g., Na⁺ in high pH for glass electrodes).
6. Response Time: Some ISEs, especially liquid membrane or gas-sensing probes, can have slow response times.

Applications of Potentiometry

• pH Measurement: The most common application, used in virtually every field of chemistry, biology, environmental science, and industry.
• Environmental Monitoring: Determination of nitrate, ammonium, fluoride, chloride, sulfide, and heavy metal ions in water and soil samples.
• Clinical Analysis: Measurement of electrolytes (Na⁺, K⁺, Ca²⁺, Cl⁻) in blood serum, urine, and other biological fluids (often in blood gas analyzers).
• Industrial Quality Control: Monitoring process streams, controlling industrial reactions, quality assurance in food and beverage, pharmaceutical, and chemical industries.
• Food and Beverage Industry: pH control in dairy, brewing, soft drinks.
• Agriculture: Soil pH analysis.

Multiple Choice Questions (MCQs)

Here are 30 multiple-choice questions with answers and explanations, covering the concepts discussed in Potentiometry.

1. What is the primary measurement made in potentiometry? A) Current as a function of time. B) Resistance of a solution. C) Potential difference (voltage) at negligible current. D) Amount of light absorbed.Answer: C Explanation: Potentiometry measures the potential (voltage) of an electrochemical cell under conditions where very little to no current flows, reflecting the equilibrium state.
2. Which equation describes the relationship between electrode potential and the activity of electroactive species? A) Beer-Lambert Law B) Nernst Equation C) Faraday’s Law D) Ohm’s LawAnswer: B Explanation: The Nernst equation quantifies the relationship between the electrode potential and the activities (or concentrations, as an approximation) of the oxidized and reduced species involved in a half-reaction.
3. Which component of a potentiometric cell provides a stable and known potential? A) Indicator electrode B) Analyte solution C) Reference electrode D) Salt bridgeAnswer: C Explanation: The reference electrode is designed to maintain a constant and known potential, serving as a stable point of comparison for the indicator electrode.
4. What is a major disadvantage of the Standard Hydrogen Electrode (SHE) for routine laboratory use? A) It is too expensive. B) It is difficult to set up and maintain. C) Its potential is not stable. D) It requires high current.Answer: B Explanation: The SHE, while theoretically fundamental, is practically difficult to set up and maintain due to the need for pure hydrogen gas, precise pressure control, and a platinum surface.
5. An electrode consisting of a pure metal immersed in a solution containing its cation (e.g., Ag in Ag⁺ solution) is classified as an electrode of the: A) First Kind B) Second Kind C) Third Kind D) Redox ElectrodeAnswer: A Explanation: Electrodes of the first kind are directly responsive to the activity of their own metal ion in solution.
6. Which type of interference occurs in glass pH electrodes at very high pH values (>10-12), causing the measured pH to be lower than the actual pH? A) Acid error B) Junction potential error C) Alkaline (sodium) error D) Temperature errorAnswer: C Explanation: At high pH, the glass membrane starts responding to alkali metal ions (especially Na⁺) in addition to H⁺, leading to an underestimation of the actual pH.
7. What is the primary function of a salt bridge in a potentiometric cell? A) To measure the potential difference. B) To provide electrical contact and maintain charge neutrality. C) To heat the solution. D) To stir the solution.Answer: B Explanation: The salt bridge allows ions to flow between the two half-cells, completing the electrical circuit and preventing charge buildup while minimizing mixing of the analyte and reference solutions.
8. The potential of a Silver/Silver Chloride (Ag/AgCl) reference electrode depends on the concentration of: A) Silver ions B) Hydrogen ions C) Potassium chloride D) Mercurous chlorideAnswer: C Explanation: The potential of the Ag/AgCl electrode is determined by the concentration of chloride ions in the KCl solution it is immersed in, due to the equilibrium involving AgCl.
9. Which component of a potentiometric setup must have a high input impedance to avoid drawing significant current? A) Reference electrode B) Indicator electrode C) Potentiometer (pH meter) D) Salt bridgeAnswer: C Explanation: A high-input impedance voltmeter (potentiometer/pH meter) is crucial to ensure that only a negligible current is drawn, preventing polarization of the electrodes and alteration of the analyte concentration.
10. A Fluoride Ion-Selective Electrode (ISE) typically uses a membrane composed of: A) Glass B) A porous hydrophobic material filled with organic liquid. C) A LaF₃ crystal doped with EuF₂. D) An enzyme layer.Answer: C Explanation: Solid-state ISEs for fluoride are commonly based on a lanthanum fluoride (LaF₃) crystal.
11. Potentiometric titrations are advantageous because they can be used for endpoint detection in solutions that are: A) Only clear and colorless. B) Colored or turbid. C) Highly concentrated only. D) Highly volatile only.Answer: B Explanation: Unlike visual indicators that rely on color changes, potentiometric titrations monitor potential changes, making them suitable for samples where visual observation is difficult.
12. What is a “junction potential” in potentiometry? A) The potential of the indicator electrode. B) The potential of the reference electrode. C) A potential difference at the interface of two dissimilar electrolyte solutions. D) The potential measured by the voltmeter.Answer: C Explanation: A junction potential arises at the liquid-liquid interfaces within the salt bridge or where the salt bridge connects to the sample, due to differing mobilities of ions.
13. Which type of ISE is commonly used to measure blood glucose levels by incorporating an enzyme? A) Glass electrode B) Liquid-membrane electrode C) Solid-state electrode D) Enzyme electrode (biosensor)Answer: D Explanation: Enzyme electrodes (biosensors) utilize the specificity of enzymes to convert an analyte into a species detectable by an underlying ISE, such as glucose oxidase for glucose.
14. For a redox electrode (e.g., Pt), the potential depends on the ratio of the activities of the: A) Hydrogen ions. B) Oxidized and reduced forms of a redox couple. C) Metal ions. D) Chloride ions.Answer: B Explanation: Inert electrodes like platinum respond to the electron activity (or redox potential) of a redox couple present in the solution.
15. What is an “ionization error” in pH measurement? A) It refers to the alkaline error. B) It describes the deviation in measured pH at very low pH values. C) It’s a common error in potentiometric titrations. D) It relates to the Nernstian slope.Answer: B Explanation: The “acid error” (or ionization error in this context) refers to the deviation where the measured pH is higher than the actual pH at very low acid concentrations (<0.5 pH).
16. Why is temperature control or compensation essential in potentiometry? A) Temperature affects only the reference electrode potential. B) Temperature only affects the indicator electrode potential. C) Temperature affects the Nernstian slope and analyte activities. D) Temperature affects only the salt bridge.Answer: C Explanation: Temperature directly influences the RT/nF term in the Nernst equation (the slope of the response) and also affects the activity coefficients of ions in solution.
17. Which type of electrode is used to measure the concentration of gases like CO₂ or NH₃ by detecting a change in the pH of an internal solution? A) Metallic electrode of the first kind. B) Glass pH electrode. C) Liquid-membrane electrode. D) Gas-sensing probe.Answer: D Explanation: Gas-sensing probes incorporate a gas-permeable membrane and an internal pH electrode to detect gases that diffuse through the membrane and alter the pH of the internal solution.
18. The potential of an electrode of the second kind (e.g., Ag/AgCl) immersed in a solution containing chloride ions is dependent on the activity of: A) Silver ions. B) Hydrogen ions. C) Chloride ions. D) Oxygen.Answer: C Explanation: For an Ag/AgCl electrode (an electrode of the second kind), the potential is directly related to the activity of the chloride ions in the solution it contacts.
19. What is the approximate potential of a Saturated Calomel Electrode (SCE) relative to the SHE at 25°C? A) 0.000 V B) +0.244 V C) -0.244 V D) +0.763 VAnswer: B Explanation: The standard potential of a saturated calomel electrode is approximately +0.244 V versus the Standard Hydrogen Electrode at 25°C.
20. When approximating activity by concentration in the Nernst equation, this approximation is generally most valid for: A) Highly concentrated solutions. B) Solutions with very high ionic strength. C) Very dilute solutions. D) Non-aqueous solutions.Answer: C Explanation: In very dilute solutions, the activity coefficient approaches unity, meaning activity is approximately equal to concentration. As concentration or ionic strength increases, this approximation becomes less accurate.
21. Which of the following is NOT an advantage of potentiometric titrations over titrations using visual indicators? A) Applicable to colored solutions. B) More accurate endpoint determination. C) Faster analysis time. D) No need for visual judgment.Answer: C Explanation: While offering accuracy benefits, potentiometric titrations are often slower than titrations with visual indicators because they require a series of precise measurements.
22. What can cause a glass pH electrode to become sluggish or drift in its response? A) Over-calibration. B) Dehydration of the membrane. C) Excessive stirring. D) Low ionic strength solution.Answer: B Explanation: The glass membrane of a pH electrode needs to be hydrated for proper function. Drying out can damage the membrane and lead to poor response.
23. Clinical analysis often uses potentiometry for the determination of: A) Proteins. B) Electrolytes like Na⁺, K⁺, Ca²⁺. C) Glucose. D) Enzyme activity.Answer: B Explanation: Ion-selective electrodes are widely used in clinical diagnostics to measure crucial electrolyte concentrations in biological fluids.
24. In a potentiometric titration curve, the equivalence point is characterized by: A) A constant potential. B) The initial potential reading. C) The largest and most rapid change in potential per unit volume of titrant. D) A plateau in the potential curve.Answer: C Explanation: The equivalence point is identified by the steep inflection point on the titration curve, where the rate of change of potential with respect to titrant volume is maximized.
25. An electrode of the second kind can be used to measure the concentration of which type of species? A) Metal cations B) Hydrogen ions C) Anions that form sparingly soluble precipitates with the electrode metal. D) Redox active species.Answer: C Explanation: Electrodes of the second kind (e.g., Ag/AgCl for Cl⁻) are designed to respond to the concentration of an anion that forms a sparingly soluble salt with the electrode’s metal.
26. Why is it generally recommended to calibrate ISEs frequently? A) To account for changes in the analyte’s color. B) To compensate for electrode drift and changes in sensing membrane properties. C) To increase the ionic strength of the solution. D) To remove dissolved gases.Answer: B Explanation: ISEs can exhibit drift over time due to various factors (e.g., changes in the membrane, junction potential), so frequent calibration with known standards is necessary to ensure accuracy.
27. A liquid-membrane ion-selective electrode uses a porous hydrophobic membrane filled with an organic solvent containing a(n): A) Inert metal. B) Ion exchanger (ligand). C) Glass. D) Enzyme.Answer: B Explanation: The selectivity of liquid-membrane electrodes comes from an ion exchanger (or ligand) dissolved in the organic solvent within the membrane, which selectively binds the analyte ion.
28. Which of the following is a common application of potentiometry in environmental monitoring? A) Measurement of air pollution particles. B) Determination of heavy metals in water. C) Analysis of organic pollutants by chromatography. D) Measurement of light intensity.Answer: B Explanation: ISEs can be specifically designed or adapted to detect and quantify various heavy metal ions (e.g., lead, cadmium) in environmental water samples.
29. What is a major disadvantage of the Saturated Calomel Electrode (SCE)? A) It’s too expensive. B) It contains mercury, which is toxic. C) It is too large. D) Its potential is independent of temperature.Answer: B Explanation: The presence of mercury and mercurous chloride in the SCE raises environmental and health concerns, leading to its replacement by Ag/AgCl electrodes in many applications.
30. When performing potentiometric measurements, the potential difference is measured between the indicator electrode and the: A) Working electrode. B) Counter electrode. C) Reference electrode. D) Auxiliary electrode.Answer: C Explanation: The fundamental potentiometric measurement is the potential difference between the analyte-sensitive indicator electrode and the stable reference electrode.