Potentiometric Methods

1

• Potentiometric Methods
• Theory of membrane electrodes
• It can be shown that if a single ion carries
  charge across a selectively permeable membrane

• And if ai is constant in, say, the b phase
• This response function is the same as the Nernst
  equation and expect a Nernstian response of
  Emembrane va. Ln ai

• The source of the potential is very much like
  that of a liquid junction potential
• Electrode selectivity depends on the extent to
  which charge transport can be dominated by a
  single ionic species
• In real devices things are more complicated
• Perfect selectivity is rarely achieved which may
  not be necessary

2

• Potentiometric Methods
• Theory of membrane electrodes
• Glass electrodes

• Glass membrane sealed to the end of another
  material
• 100 - 500 mm thick
• Inside the bulb is a Ag/AgCl electrode
• Cell AgAgCl(sat.), HCl(0.1M)
  KCl(sat.), Hg2Cl2Hg
• internal ref
  external ref
• glass electrode
  (const. E)

Glass Memb.
Test Soln

• Cross section of membrane system

• Charge transport in dry glass is Na or other
  alkali metal ion
• The hydrated layers consist of a silicate
  polymer that has an affinity for a particular
  ion or ions
• Serve as an ion exchanger
• Produce a charge separation as is in a liquid
  junction

3

• Potentiometric Methods
• Theory of membrane electrodes
• Glass electrodes
• At the a - m or b - m interface there exists an
  adsorption equilibrium

• At the m - m, m - m, similar kinds of
  equilibria involving Na
• The total potential across the membrane is
• EmembEbm Emm Emm Ema

• Ebm and Ema result from a selective charge
  exchange across the respective interfaces
• For H, the Donnan equilibrium occurs HGl
  H Gl
• Resulting in the Donnan boundary potential
• Eisenman has shown

4

• Potentiometric Methods
• Theory of membrane electrodes
• Glass electrodes

5

• Potentiometric Methods
• Theory of membrane electrodes
• Glass electrodes
• Emembrane is responsive to both H and Na
• If is small, the response is
  only to H
• Other types of electrodes
• Cations

• If the electrode is connected to the negative
  terminal of the voltmeter, one observes an
  increase in Ecell with pM

6

• Potentiometric Methods
• Theory of membrane electrodes
• Other types of electrodes
• Anions
• Inherent error in potentiometric measurements of
  activity
• Assume K is constant from the analytical
  solutions to the analytical solutions
• But this is not true as the electrolyte
  concentration not the same
• Junction potentials contained in K change because
  of changes in electrolyte concentrations
• Ecell Ethermo ELJ EIR
• The uncertainty in Ecell is at least ? 0.001 V

7

• Potentiometric Methods
• Theory of membrane electrodes
• Inherent error in potentiometric measurements of
  activity

• Example for a solution whose pH is 4.00,
  H1.00 x 10-4
• 4Zi 0.04 so H could be 1.04 x 10-4 or pH
  3.98 or
• H could be 0.96 x 10-4
  or pH 1.02
• Thus the pH is in the range of 4.00 ? 0.02 this
  uncertainty cannot be
  eliminated

8

• Potentiometric Methods
• Theory of membrane electrodes
• Other errors associated with glass electrodes
• Alkaline error at pH gt 9 or 10, glasses become
  sensitive to Na
• Must take into account
• This is given as a nomograph in the box with the
  electrode
• The result is a negative error in pH the pH is
  less than measured
• Acid error at very low pH (around 0 or 1, or
  less) a positive error is observe
• The origin of this error is not understood
• ISEs measure activity, not concentration
• Since activity coefficients change with ionic
  strength, this must be taken into account
• Standard Additions method (for cations)

• Solve these two equations for K and M

• Titration curves see Skoog, West and Holler for
  an example including how to calculate the
  discrete 1st and 2nd derivative curves