Potentiometry: Galvanic Cells & Electrodes

• Potentiometry involves using electrodes to measure voltages that provide chemical information.
• Various electrodes have been designed for specific analytes.

Galvanic Cell Usage

• It Uses a galvanic cell.
• An unknown solution becomes a half-cell.
• An electrode that transfers/accepts electrons from unknown analytes is added.
• The unknown solution is connected by a salt bridge to a second half-cell at a fixed composition and potential.

Indicator Electrode

• Responds to the analyte and donates/accepts electrons.

Reference Electrode

• A second half-cell at a constant potential.
• Cell voltage is the difference between the indicator and reference electrode potentials.

Heparin Sensor Example

• Voltage response is proportional to heparin concentration in blood sensors that are selective for heparin.

Reference Electrode Details

• It is a known half-cell.
• Insensitive to the solution under examination.
• Reversible and obeys the Nernst equation.
• Maintains a constant potential and returns to its original potential.

Calomel Electrode

• Mercury is in contact with mercury(I) chloride.
• Silver/silver chloride (Ag/AgCl) is also used.

Nernst Equation

• It determines the equilibrium reduction potential of a half-cell in an electrochemical cell.
• Determines the total voltage (electromotive force) for a full electrochemical cell.
• Named after Walther Nernst, who first formulated it.

Reference Electrodes Overview

• Potential change is dependent on only one half-cell concentration.
• The reference electrode potential is fixed or saturated.
• It's potential doesn’t change.

Silver-Silver Chloride Reference Electrode

• Reaction: AgCl(s) + e- ⇌ Ag(s) + Cl- with E°= +0.222V.
• The activity of Cl- is not 1, so E (sat, KCl) = +0.197 V.
• Convenient, but a common problem is the porous plug becomes clogged.

Saturated Calomel Reference Electrode (S.C.E)

• Reaction: HgCl(s) + 2e- ⇌ 2Hg (I) + Cl- with E° = +0.268 V.
• The activity of Cl- is not 1, so E (sat (KCl) = 0.241 V.
• Saturated KCl maintains constant [Cl-] even with some evaporation.
• Standard Hydrogen electrodes are cumbersome, requiring H2 gas and a freshly prepared Pt surface.

Calomel Electrode (General)

• It explains the Potentials of reference electrodes in aqueous solution.

Junction Potential

• Occurs whenever dissimilar electrolyte solutions are in contact.
• Develops at the solution interface (salt bridge).
• It is a small potential (a few millivolts).
• It puts a fundamental limitation on the accuracy of direct potentiometric measurements.
• The contribution to measured voltage is unknown.
• An electric potential is generated by a separation of charge.

Indicator Electrodes

• They are metal electrodes.

Platinum Electrodes

• Platinum is the most common metal indicator electrode.
• Inert: does not participate in many chemical reactions.
• Simply used to transmit electrons.
• Other electrodes include Gold and Carbon.
• Metals (Ag, Cu, Zn, Cd, Hg) can be used to monitor their aqueous ions.
• Most metals are not usable as Equilibrium is not really established at the metal surface.

Metal Electrode Example

• Mn+ + e- ⇌ M(s) is a general reaction.
• Half-reaction at Ag indicator electrode: Ag+ + e- ⇌ Ag(s) E° = 0.799 V.
• Half-reaction at Calomel reference electrode: HgCl(s) + 2e- ⇌ 2Hg(I) + Cl- E (sat, KDI) = 0.241 V.
• Explains how to get the cell potential from the Nernst Equation.

Metallic Redox Indicator

• Inert Metals like Pt, Au, and Pd.
• They are an electron source or sink.
• They evaluate Redox of metal ions.
• May not be reversible.

Membrane Indicator Electrodes

• Non-crystalline membranes:
  • Glass - silicate glasses for H+, Na+.
  • Liquid - Liquid ion exchanger for Ca2+.
  • Immobilized Liquid - liquid/PVC matrix for Ca2+ and NO3-.
• Crystalline membranes:
  • Single crystal- LaF, for F-
  • Polycrystalline or mixed Crystal- AgS for S2- and Ag+.

Membrane Properties

• Low solubility in solids, semi-solids, and polymers.
• Some electrical conductivity, often by doping.
• Selectivity is when part of the membrane binds/reacts with the analyte.

Ion-Selective Electrode

• Responds selectively to one ion.
• Contains a thin membrane capable of only binding the desired ion.
• Does not involve a redox process.
• An electric potential is generated by a separation of charge.

pH Electrodes

• pH measurement with a glass electrode.
• The glass electrode is the most common ion-selective electrode.
• A combination electrode incorporates both glass and reference electrodes in one body.
• Electric potential is generated by [H+] difference across the glass membrane.

Glass Membrane Electrode

• It is a pH Electrode type.
• Irregular structure of silicate lattice.
• Two surfaces of glass “swell” as they absorb water, and surfaces are in contact with [H+].
• H+ diffuses into the glass membrane and replaces Na- in the hydrated gel region.
• Ion-exchange equilibrium is selective for H+ as it is the only ion that binds significantly to the hydrated gel layer.

Glass Membrane Structure

• H+ carries current near the surface.
• Na+ carries current in the interior.
• Ca2+ carries no current (immobile).

Calibration of pH Electrodes

• A pH electrode should be calibrated with two or more standard buffers before use.
• The pH of the unknown should lie within the range of the standard buffers.
• Measured voltage is correlated with a pH, which is then used to measure an unknown.

Errors in pH Measurements

• Standards: pH measurements cannot be more accurate than standards (±0.01).
• Junction potential: If ionic strengths differ between analyte and standard buffer, the junction potential will differ, resulting in an error of ±0.01.
• Junction Potential Drift: Caused by slow changes in [KCl] and [AgCl], so re-calibrate.
• Sodium Error: At very low [H+], the electrode responds to Na+, and the apparent pH is lower than the true pH.
• Acid Error: At high [H-], the measured pH is higher than the actual pH because the glass is saturated.
• Equilibration Time: Takes 30s to minutes for the electrode to equilibrate with the solution.
• Hydration of glass: A dry electrode will not respond to H+ correctly.
• Temperature: Calibration needs to be done at the same temperature as the measurement.
• Cleaning: Contaminates on the probe will cause reading to drift until properly cleaned or equilibrated with the analyte solution.
• pH measurements are accurate to ±0.02 pH units.

Solid-State Electrode

• Other Ion-Selective Electrodes
• Based on an inorganic crystal.
• Fluoride Electrode: LaF3 crystal doped with Eu2+.
• The potential is caused by charge imbalance from the migrating ion across the membrane.

Liquid-Based Ion-Selective Electrodes

• Similar to solid-state electrodes.
• Hydrophobic membrane impregnated with hydrophobic ion exchanger.
• Hydrophobic ion exchanger selective for analyte ion.
• Ion-selective electrodes create a potential from a charge imbalance caused by analyte ion migration across the membrane.

Compound Electrodes

• A conventional electrode surrounded by a membrane isolates or generates the analyte to which the electrode responds.
• A pH electrode is surrounded by a membrane permeable to CO2.
• As CO2 passes through the membrane and dissolves in the solution, the pH changes.
• The pH change is an indirect measure of CO2 concentration.

Standard Addition

• Corrects for analyte dissolved in a complex or unknown matrix, such as blood, urine, or biomass.
• Procedure:
  • Measure the potential for the unknown analyte solution.
  • Add a small (known) volume of a standard solution.
  • Measure the new potential.
  • Repeat and graph data.
• The x-intercept yields the unknown (Cx) concentration.

Boundary Potential

• The difference in potentials at a surface.
• Potential difference is determined by:
  • Eref 1 - SCE (constant)
  • Eref 2 - Ag/AgCl (constant)
  • Eb (Boundary Potential)
• Eb = E1 - E2 = 0.0592 log(a1/a2)
  • a1 = analyte
  • a2 = inside red electrode 2
• If a2 is constant, then Eb = L + 0.0592log a1 = L - 0.0592 pH, where L = -0.0592log a2.
• Since Eref1 and Eref2 are constant, Ecell = constant - 0.0592 pH.

Alkaline Error

• Electrodes respond to H+ and cation pH differential.
• Glass Electrodes for other Ions:
  • Maximize kH/Na for other ions by modifying the glass surface with Al2O3 or B2O3.
  • Possible to make glass membrane electrodes for Na+, K+, NH4+, Cs+, Rb+, Li+, Ag+.

Crystalline Membrane Electrode

• Usually an ionic compound.
• Single crystal.
• Crush powder, melt, and form.
• Sometimes doped (Li+) to increase conductivity.
• Operation similar to the glass membrane.
• Example: F- electrode.

Liquid Membrane Electrodes

• Based on the potential that develops across two immiscible liquids with different affinities for the analyte.
• A porous membrane separates liquids.
• They selectively bond certain ions.
• Activities of different cations.
• Calcium dialkyl phosphate is insoluble in water but binds Ca2+ strongly.

Molecular Selective Electrodes

• Response towards molecules.

Gas Sensing Probes

• A simple electrochemical cell with two reference electrodes and a gas-permeable PTFE membrane.
• Allows small gas molecules to pass and dissolve into the internal solution.
• Examples: O2, NH3/NH4+, and CO2/HCO3-/CO32-.

Biocatalytic Membrane Electrodes

• Immobilized enzyme bound to a gas-permeable membrane.
• Catalytic enzyme reaction produces a small gaseous molecule (H+, NH3, CO2).
• A gas-sensing probe measures the change in gas concentration in the internal solution.
  • Fast and very selective.
  • Used in vivo.
  • Expensive.
  • Only a few enzymes are immobilized.
  • Immobilization changes activity.
  • Limited operating conditions (pH, temperature, ionic strength).

Electrode Calibration

NH4+ Electrode

Potentiometric Titration

Coulometry

• Quantitative conversion of an ion to a new oxidation state.
• Types:
  • Constant potential coulometry
  • Constant current coulometry
  • Coulometric titration
• Measures the electricity needed to complete electrolysis.
• Electrogravimetry measures the mass of the deposit on the electrode.

Constant Voltage Coulometry

• Electrolysis is performed with a constant applied cell potential and a constant working electrode potential.
• Ecell = Ecathode - Eanode + (cathode polarization) + (anode polarization) - IR
• Constant potential leads to a decrease in current.
• This follows 1st order kinetics: It = Ioe-kt
• Constant current leads to a change in potential.
• Variation in electrochemical reaction (metal ion, then water).

Coulometry Analysis

• Measurement of electricity needed to convert an ion to a different oxidation state.
• Coulomb (C): Charge transported in 1 second by a current of 1 ampere.
• Q = It (I = ampere, t in seconds)
• Faraday (F): Charge in coulombs associated with a mole of electrons.
  • 1.602E-19 C for an electron.
  • F = 96485 C/mole e-
• Q = nFN
• Find the amount of Cu2+ deposited at the cathode when current = 0.8 A and t = 1000s; Q = 0.8(1000) = 800 C, n=2, N= 800/(2*96485)= 4.1mM

Coulometric Methods

• Potentiostatic Coulometry: Maintains the potential of the working electrode at a constant level so oxidation or reduction can be quantifiably measured without the involvement of other components in the solution; Current is initially high but decreases; Measure electricity needed for redox; Arsenic is determined by oxidation of arsenous acid (H3AsO3) to arsenic acid (H3AsO4) at a platinum electrode.
• Coulometric Titration: Titrant is generated electrochemically by constant current; The concentration of the titrant is equivalent to the generating current; The volume of the titrant is equivalent to the generating time; An indicator is used to determine the endpoint.