Potentiometry

reference || indicatorEcell = Eind − Eref + Ej

A potentiometer is used to determine the difference between the potential of two electrodes. Thepotential of one electrode—the working or indicator electrode—responds to the analyte’s activity, andthe other electrode—the counter or reference electrode—has a known, fixed potential.

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Potentiometry (zero current measurement!)

Zn(s) | ZnCl2(aq,aZn2+ = 0.0167) || AgNO3(aq,aAg

+ = 0.100) | Ag

Ecell = Ec − Ea

Ecell= (EoAg

+/Ag – (0.05916 / 1)log(1 / aAg

+)) – (EoZn

2+/Zn – (0.05916 / 2)log(1 / aZn

2+))= (0.7996 V – 0.05916 log(1 / 0.100)) – (–0.7618 – (0.05916 / 2)log(1 / 0.0167)) = +1.555 V

Potentiometry

A junction potential develops at the interface between two ionic solution if there difference in theconcentration and mobility of the ions. Consider, for example, a porous membrane separating solutions of0.1 M HCl and 0.01 M HCl. Because the concentration of HCl on the membrane’s left side is greater than thaton the right side of the membrane, H+ and Cl– diffuse in the direction of the arrows. The mobility of H+,however, is greater than that for Cl–, as shown by the difference in the lengths of their respective arrows.

Ecell = Ec − Ea + Ej

Potentiometry – Reference Electrodes

Hg2Cl2(s) + 2e−⇋ 2Hg(l) + 2Cl−(aq)

Hg(l) | Hg2Cl2(s), KCl(aq, sat'd) ||

AgCl(s) + e−⇋ Ag(s) + Cl−(aq)

Ag(s) | AgCl(s), KCl(aq,aCl− = x) ||

Potentiometry

Relationship between the potential of an Fe3+/Fe2+ half-cell relative to the reference electrodes in theexample. The potential relative to a standard hydrogen electrode is shown in blue, the potential relative to asaturated silver/silver chloride electrode is shown in red, and the potential relative to a saturated calomelelectrode is shown in green.

Potentiometry

The existence of this membrane potential led to the development of a whole new class of indicatorelectrodes called ion-selective electrodes (ISEs). In addition to the glass pH electrode, ion-selectiveelectrodes are available for a wide range of ions. It also is possible to construct a membrane electrode for aneutral analyte by using a chemical reaction to generate an ion that can be monitored with an ion-selectiveelectrode. The development of new membrane electrodes continues to be an active area of research.

reference(sample) || [A]samp(aq,aA = x) | [A]int(aq,aA = y) || reference(internal)

Ecell = Eref(int) − Eref(samp) + Emem + Ej

where Emem is the potential across the membrane. Because thejunction potential and the potential of the two referenceelectrodes are constant, any change in Ecell is a result of achange in the membrane’s potential.

Emem= Easym − (RT / zF)ln((aA)int / (aA)samp)

Potentiometry

Schematic diagram showing a combination glass electrode for measuring pH. The indicator electrode consists ofa pH-sensitive glass membrane and an internal Ag/AgCl reference electrode in a solution of 0.1 M HCl. Thesample’s reference electrode is a Ag/AgCl electrode in a solution of KCl (which may be saturated with KCl orcontain a fixed concentration of KCl). A porous wick serves as a salt bridge between the sample and its referenceelectrode.

H+ + −SiO−Na+ ⇋ −SiO−H+ + Na+ Ecell= K + 0.05916logaH+

The first commercial glass electrodes were manufactured usingCorning 015, a glass with a composition that is approximately22% Na2O, 6% CaO and 72% SiO2. When immersed in anaqueous solution for several hours, the outer approximately 10nm of the membrane’s surface becomes hydrated, resulting inthe formation of negatively charged sites, —SiO–. Sodium ions,Na+, serve as counter ions. Because H+ binds more strongly to—SiO– than does Na+, they displace the sodium ions

Potentiometry- Solid State Membrane

Ag2S(s) ⇋ 2Ag+(aq) + S2−(aq)

A solid-state ion-selective electrode uses a membrane consisting of either a polycrystalline inorganic salt or a singlecrystal of an inorganic salt. For example, one can fashion a polycrystalline solid-state ion-selective electrode by sealing a1–2 mm thick pellet of Ag2S—or a mixture of Ag2S and a second silver salt or another metal sulfide—into the end of anonconducting plastic cylinder, filling the cylinder with an internal solution containing the analyte, and placing a referenceelectrode into the internal solution.

Ecell = K + 0.05916logaAg+

Ecell = K − (0.05916 / 2)logaS2−

(Cd+2, Cu+2, Pb+2, Br-, Cl-, I-, SCN-, S2-

Potentiometry -Complexing Agents

Another class of ion-selective electrodes uses a hydrophobic membrane containing a liquid organic complexing agent that reacts selectively with the analyte. Three types of organic complexing agents have been used: cation exchangers, anion exchangers, and neutral ionophores. A membrane potential exists if the analyte’s activity is different on the two sides of the membrane. Current is carried through the membrane by the analyte.

An ionophore is a ligand whose exterior ishydrophobic and whose interior ishydrophilic. The crown ether shown hereis one example of an neutral ionophore.

Ca2+(aq) + 2(C10H21O)2PO2−(mem) ⇋ Ca[(C10H21O)2PO2]2(mem)

Ecell = K + (0.05916 / 2)logaCa2+

(Ca+2, K+, Li+, NH4+, ClO4

-, NO3-)

Potentiometry – Gas Sensing Electrodes

The basic design of a gas-sensing electrode is shown. It consisting of a thin membrane that separates the sample froman inner solution containing an ion-selective electrode. The membrane is permeable to the gaseous analyte, butimpermeable to nonvolatile components in the sample’s matrix. The gaseous analyte passes through the membranewhere it reacts with the inner solution, producing a species whose concentration is monitored by the ion-selectiveelectrode.

CO2(aq) + 2H2O(l) ⇋ HCO3−(aq) + H3O+(aq)

aH3O+ = Ka× (aCO2 / aHCO3

−)

Ecell = K′ + (0.05916)logaCO2

(CO2, HF, H2S, NH3, NO2)

Potentiometry - Quantitation

i

i

meas aFz

RTKE log

303.2

Sensitivity is 0.059 /zi V/dec

Selectivity has to be checked.

What limits the LOD?