ElectroChemical Methods

4 main types of electrochemical methods:

1. POTENTIOMETRY
   Measure electrical potential developed by an electrode in an electrolyte solution at zero current flow. Use NERNST EQUATION relating potential to concentration of some ion in solution.
   
2. VOLTAMMETRY
   Determine concentration of ion in dilute solutions from current flow as a function of voltage when POLARIZATION of ion occurs around the electrode.
   POLARIZATION = depletion of concentration caused by electrolysis.
   If using a dropping mercury electrode, method is termed POLAROGRAPHY.
   
3. COULOMETRY
   Electrolysis of a solution and use of Faraday's law^* relating quantity of electrical charge to amount of chemical change. ^[* essentially states that it takes 9.65 x 10⁴ Coulombs of electrical charge to cause electrolysis of 1 mole of a univalent electrolyte species.]
   
4. CONDUCTIMETRY
   Measure conductance of a solution, using INERT ELECTRODES, ALTERNATING CURRENT, AND AN ELECTRICAL NULL CIRCUIT - thereby ensure no net current flow and no electrolysis. The concentration of ions in the solution is estimated from the conductance.

   ---

   NOTE:
   Methods 1 and 4,
     NO ELECTROLYSIS of solution. Sample recoverable, unaltered by analysis.
   Methods 2 and 3
     must cause ELECTROLYSIS OF THE SAMPLE.

   Potentiometry

   Electrodes and Electrochemical Cells

   ELECTRODE POTENTIAL - Electrode placed in a solution containing ions with which it can exchange acquires +ve or -ve potential relative to solution.
   egs

   Cu electrode		Electrode reaction Cu2+ + 2e- <--> Cu
   Ag/AgCl electrode		Electrode reaction AgCl + e- <--> Ag + Cl-

   Can't measure electrode potential of a HALF CELL (electrode system) without perturbing electrode equilibrium.
   Combine two half cells - measure combined voltage or EMF (electromotive force) of the complete cell, using potentiometer. This is a null circuit device, no current flow through cell so no perturbation of electrode potentials.
   eg
      

   Cell EMF (E) = E(Cu/Cu²⁺) - E(Ag/AgCl)

   Electronic voltmeter (not true null device but draws < 10^-11 Ampere current) now replaces potentiometer.

A Scale of Electrode Potentials: Standard Electrodes

To draw up a scale of electrode potentials, choose one half cell as a fixed standard and measure other half cells against it.
By convention, the primary standard is the STANDARD HYDROGEN ELECTRODE defined as having an electrode potential of ZERO.

Electrode reaction
      H₂ <--> 2H⁺ + 2 e^-

SECONDARY STANDARD electrodes are more convenient for laboratory use and have accurately known potentials relative to the hydrogen electrode.
The most widely used secondary standard electrode is the SATURATED CALOMEL ELECTRODE (SCE)

Electrode reaction
      Hg₂Cl₂ + 2e^- <--> 2Hg + 2Cl^-
Electrode potential = + 0.246 volts
Used, eg in pH meter and many ion-selective electrodes and biosensors as the reference electrode.

Nernst Equation

Reactions at electrodes are redox reactions

A_ox + ne <--> A_red

Nernst eqn: how electrode potential is related to thermodynamic activities of reduced and oxidised species.

E = electrode potential
E_o = electrode potential in the standard state (constant value for particular electrode at a particular temperature)
a_red & a_ox are thermodynamic activities of A_red and A_ox respectively.
R = gas constant (8.314 Joule.K^-1.mole^-1)
T = temperature (K)
n = no of electrons in the half cell reaction
F = Faraday constant (9.65 x 10⁴ Coulomb.mole^-1)
ln, as usual, denotes natural logarithm (base e)
Terms in the Nernst equation have units VOLTS.
(^RT/_nF reduces to Joules/Coulomb, which = volts)

Usual case is solid electrode in equilibrium with an ion in solution. As activity for the solid species = 1, the Nernst equation simplifies to..

The -sign becomes + if the ion in solution is the oxidised form. But sign of voltages in electrochemistry is a matter of convention.
If T = 298.2K (ie 25^oC) and use 2.303Log₁₀ instead of ln, then as ^2.303RT/_F evaluates to 0.059 volts, Nernst equation becomes...

Use Nernst equation to evaluate the activity of an analyte ion in solution if you can measure electrode potential by potentiometry.
activity = concentration reasonably valid approximation for ion concs < 10^-2 mole.L^-1.

Graphs Based on Nernst Equation

To evaluate unknowns by potentiometry: calibrate with standards, draw graph in accordance with Nernst equation and interpolate sample reading --> concentration.

or Plot E vs lnc	or semilog plot

Potentials Developing Away from Electrodes

Liquid Junction Potential

example

Potential at liquid junction due to different diffusion rates of H⁺ vs Na⁺.
Hence cell EMF not equal to E_Pt(H2) - E_Ag/AgCl
Avoid error in experimental measurement by "swamping out" liquid junction potential using a SALT BRIDGE. Interpose conc soln of KCl or NH₄NO₃.
Use of conc KCl in many practical electrodes to serve this purpose.

Membrane Potentials

2 compartments within electrochemical cell separated by membrane more permeable to the anion or cation on one side than the other.
Or
Greater extent of binding of ion to one side of the membrane than the other.

If potentials at electrodes kept constant (use reference electrodes), cell EMF becomes indicator of membrane potential at various ion concentrations.
Basis of ION-SELECTIVE ELECTRODES.

The pH Glass Electrode

The original and still most widely used ion-selective electrode.

Cross-section of glass membrane	Ag/AgCl external reference electrode -also dips in test soln.

pH Measurement with Glass Electrode

Cell EMF in accordance with Nernst eqn.

where:
E_Ref   = combined potential of the two reference electrodes
        = a constant at constant temperature

Ion-Selective Electrodes

An ion-selective electrode measures:

• FREE ION - no response to complexes (eg Ca²⁺ but not Cacitrate)
  
• Ion concn. in WATER PART OF THE SAMPLE, not in total fluid volume
  
• THERMODYNAMIC ACTIVITY rather than the concentration of an ion.
  Standardise "ionic strength" for constant ratio: activity a concentration.

Classification & Examples of ISE'S

  A   Solid state membrane
Membrane = single crystal or compacted disc of electro-active material. Must be insoluble and conductive as well as reversibly reactive to test ion.
Construction as in 12.2.8.

Example: Fluoride (F^-) electrode

NOTE: Many ISE'S can be used for titrations, similar to pH titration using glass electrode.
eg Titrate Mg²⁺ with standard NaF soln using F^- ISE. MgF₂ complex is formed; when all Mg²⁺ consumed, sharp change in pF occurs.

  B   Heterogeneous membrane
Electroactive material dispersed in inert binder (eg silicone rubber). Cheaper.

  C   Liquid ion-exchanger membrane
Inert porous membrane eg cellulose acetate or porous ceramic, permeated with organic solvent containing dissolved ionogenic molecule (hydrophobic organic species with an ion-complexing group for the analyte ion).
eg Ca²⁺ electrode:

  D   Glass membrane
Originally only for H^{+ (}pH glass electrode), but special glasses since developed for other ions, in particular: Na⁺ glass electrode

Voltammetry

Principle illustrated by example: analysis of solution containing analyte ions Pb²⁺ and Cd²⁺ in supporting electrolyte (KCl) solution.

Displace potentiometer from balance by voltage measured on V. Measure resulting current flow on microammeter.
Resulting Current vs Voltage curve provides data for qualitative and quantitative analysis.

Principles of Voltammetry

1. Voltage insufficient to cause electrolysis - no current flow
   
2. Discharge potential of Cd²⁺ reached, current flows (voltammetric wave)
   
3. Polarization of Cd²⁺ around micro-electrode, current levels off because limited by diffusion of Cd²⁺ into discharge layer
   
4. Discharge potential of Pb²⁺ reached, second polarographic wave
   
5. Polarization of both Cd²⁺ and Pb²⁺

Qualitative and Quantitative Voltammetry

QUALITATIVE ANALYSIS
Measure HALF-WAVE POTENTIAL - species undergo electrode discharge at characteristic potentials.

QUANTITATIVE ANALYSIS
Measure DIFFUSION CURRENT - diffusion rate (hence current) proportional to concentration of species in the test solution.
Calibrate with standards, prepare linear standard curve of diffusion current vs concentration, interpolate to get concn. of samples.
Or use standard addition technique

Voltammetric sensors used in some electrochemical detectors for HPLC.
Also the OXYGEN ELECTRODE - polarization of O₂ and diffusion through teflon sheath around electrode.

Polarography

Pt wire microelectrode unsuitable for some applications. Fouled by discharged samples.
Polarography uses mercury droplet electrode that is regularly renewed during analysis.

Applications
Metal ions (especially heavy metal pollutants) - high sensitivity.
Organic species able to be oxidised or reduced at electrodes - quinones, reducing sugars and derivatives, thiol and disulphide compounds, oxidation cofactors (coenzymes etc), vitamins, pharmaceuticals.
Alternative when spectroscopic methods fail.

APPENDIX

Some Thermodynamic Principles Relevant to Potentiometric Analysis

^* THERMODYNAMIC ACTIVITY may be thought of as "corrected concentration". The Free Energy per mole (G) of a species in solution is logarithmically related to its concentration [ G = G₀ + RTlnc ] only for IDEAL SOLUTIONS (in which the solute particles behave like the molecules in an ideal gas). For real solutions, and in particular where the solute species are ions, interactions cause the Free Energy to be less (usually) than given by the above logarithmic relationship. The thermodynamic activity is the quantity that has to be substituted for concentration to give the correct Free Energy. For very dilute solutions, concentration is usually a close approximation to activity, and the approximation that a = c is made in much biochemical work. However, in electrochemistry the distinction becomes important and must be kept in mind.
^# STANDARD STATE = a defined set of conditions under which thermodynamic quantities of different species may be compared. Activity =1 in the standard state. For solids, liquids, gases the standard state is the pure substance at 1 atmosphere pressure, but for a species in solution the standard state is a hypothetical state in which both concentration and activity =1. For practical purposes it is only important to recognise that the standard state value is constant at a particular temperature, in this case a characteristic voltage for any electrode.
^* It should be log of activity (rather than concentration) that is plotted, the use of log of concentration will give a linear plot if the activity is proportional to the concentration (because if a = c x constant, then loga = logc + logconstant, so any plot of E vs logc will run parallel to a plot of E vs loga). Then if the method is calibrated using standards of known concentration, the concentration of a test sample may validly be interpolated from its measured E. It is found that for most solutions, activity is proportional to concentration if the IONIC STRENGTH of the solution is constant. This is achieved experimentally using an unreactive salt solution to adjust all samples and standards to the same ionic strength.

Ionic strength (see above) is a measurement of the thermodynamic effect of ions in a solution in creating non-ideal solution behaviour. Multivalent ions have more impact than univalent ions and the ionic strength parameter takes account of this. It is defined as I = 0.5S(c_iz_i²), the summation being over all ions in the solution.