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EA-ACLecture 21-15-03
The most convenient method for determining pH involves measuring the potential that develops across a thin glass membrane that separates two solutions with different hydrogen ion activities.
The phenomenon upon which the measurement is based was first reported in 1906 and by now has been extensively studied by many investigators. As a result, the sensitivity and selectivity of glass membranes toward hydrogen ions are reasonably well understood.
Furthermore, this understanding has led to the development of other types of membranes that respond selectively to more than two dozen other ions.
Membrane electrodes are sometimes called pIon electrodesbecause the data obtained from them are usually presented as pfunctions, such as pH, pCa, or pNO3.
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This transparency shows an old two-electrode cell for measuring pH. The cell consists of a glass indicator electrode and a saturated calomel reference electrode immersed in the solution whose pH is to be measured.
The indicator electrode consists of a thin, pH-sensitive glass membrane sealed onto one end of a heavywalled glass or plastic tube.
A small volume of dilute hydrochloric acid saturated with silver chloride is contained in the tube.
A silver wire in this solution forms a silver/silver chloride reference electrode, which is connected to one of the terminals of a potentialmeasuring device. The calomel electrode is connected to the other terminal.
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This representation of the cell shows that a glasselectrode system contains two reference electrodes: (1) the external calomel electrode and (2) the internal silver/silver chloride electrode.
While the internal reference electrode is a part of the glass electrode, it is not the pH-sensing element. Instead, it is the thin glass membrane at the tip of the electrode that responds to pH.
Special glass membranes have been studied extensively. The membranes are glass-like and gel-like at the same time. They are made with sodium or lithium oxide, calcium and barium oxide as well as silicon oxide.
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The membranes show excellent specificity toward hydrogen ions up to a pH of about 9 or so. Above this pH, some of the glasses become somewhat responsive to sodium as well as to other singly charged cations like lithium.
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This figure shows a silicate glass used for pH-sensing membranes as an infinite three-dimensional network of SiO44- groups in which each silicon is bonded to four oxygens and each oxygen is shared by two silicons.
Within the pores of this structure are sufficient cations to balance the negative charge of the membrane.
Protons are mobile in this gel layer. Conduction across the solution/gel interfaces occurs by the reaction
H+ + Gl- < == > H+Gl-
solnglass glass
on one side and the reverse reaction on the other.
Both membrane surfaces must be hydrated before a glass electrode will function as a pH electrode.
The positions of these two equilibria are determined by the hydrogen ion concentrations in the solutions on the two sides of the membrane. Where these positions differ from each other, the surface at which the greater dissociation has occurred is negative with respect to the other surface.
A boundary potential Eb thus develops across the membrane. The boundary potential is made up of two potentials, E1 and E2, which develop at the two surfaces of the glass electrode.
The magnitude of the boundary potential depends upon the ratio of the hydrogen ion concentrations of the two solutions. It is this potential difference that serves as the analytical parameter in a potentiometric pH measurement.
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Eb = E1 - E2 = 0.0592 log a1/a2 = 0.0592 log a1 - 0.0592 log a2
where a1is the activity of the analyte solution and a2 is constant activity of the internal solution.
For a glass pH electrode, the hydrogen ion activity of the internal solution is held constant so that the boundary potential is then a measure of the hydrogen ion activity of the external solution.
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This transparency shows how E2 is constant and how the boundary potential Eb varies with E1.
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In the pH meter the potential of the glass indicator electrode is
Eind = Eb + EAg/AgCl + Easy = L’ - 0.0592 log a2 - 0.0592 pH
= L - 0.0592 pH
You can see that the saturated calomel electrode just served as an external reference and that any electrode with constant potential could be used. Replacing the calomel electrode with a standard Ag/AgCl electrode allows the entire assembly to be placed in one glass cylinder.
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This gives what we call the combination electrode as seen this transparency. The internal reference electrode is Ag/AgCl and the sample reference electrode is also Ag/AgCl.
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The sample electrode is often twisted and looks like this.
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The chemistry of the pH electrode is now
Ag(s) AgCl(s) Cl- (aq) H+ (out) H+ (in), Cl-(aq) AgCl(s) Ag(s)
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In addition to the pH electrode, over twenty different types of specific-ion electrodes have been developed. They particularly involve the incorporation of A12O3 or B2O3 into the glass to achieve the desired selectivity.
Glass electrodes that permit the direct potentiometric measurement of such singly charged species as Na+, K+, NH4+, Rb+, Li+, and Ag+are commercially available.
Because these specific-ion electrodes depend on pore size and membrane selective and because these properties change with conditions of concentration and temperature, it is important that you read about the limitations of any selective ion electrode that you use.
As you have seen with the pH electrode, even though a pH meters has a scale from 0 to 14, the typical electrode is only good from about 1 to maybe 10 or 12 depending on the manufacturer. You need to know the limitations of your equipment.
Now lets turn to redox titrations.
There are three kinds of redox titrations. The first are potentiometry titrations where we follow changes in electrode potential during the titration. The second type involve redox reactions without using electrodes and uses a redox indicator.
In the third case, one of the reagents itself is colored, so that there is a color change at the endpoint without having a specific indicator present.
The y-axis in an oxidation/reduction titration curve is generally an electrode potential instead of the logarithmic p-functions that were used for precipitation and acid-base titration curves.
We have seen that the Nernst equation describes a logarithmic relationship between electrode potential and concentration of analyte; as a result, redox titration curves are similar in appearance to those for other types of titrations.
Consider the redox titration of iron(II) with a standard solution of cerium(IV). This reaction is widely used to determine ferrous iron in various kinds of samples.
The titration is described by the equation
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Fe2+ + Ce4+ < == > Fe3+ + Ce3+
This reaction is rapid and reversible, so the system is at equilibrium at all times throughout the titration. Consequently, the electrode potentials for the two half-reactions are always identical; that is,
ECe = EFe = Esys
The electrode potential of a system is readily derived from standard potential data. Thus, for the reaction under consideration, the titration mixture is treated as if it were part of the hypothetical cell
SHE Ce4+, Ce3+, Fe3+, Fe2+ Pt
where SHE symbolizes the standard hydrogen electrode. The potential of the platinum electrode with respect to the standard hydrogen electrode is determined by the Nernst equation from the current ratios of the ionic species.
At equilibrium, the concentration ratios of the oxidized and reduced forms of the two species are such that their attraction for electrons (and thus their electrode potentials) are identical.
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The upper curve in this transparency is a titration curve for this iron(II)/Cerium(IV) titration. What is the equivalence point? Where the amount of added cerium is exactly equal to the initial amount of iron(II).
What happens to the ratio of Fe2+ to Fe3+ during the titration?
What happens to the ratio of Ce4+ to Ce3+ during the titration?
These varying concentration ratios mean that the system potential must vary continuously throughout the titration as well. End points are determined from the characteristic variation in Esystemthat occurs during the titration.
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We can use the same type of data processing to obtain endpoints in redox titrations as we did for acid/base titrations. Here we can see the first and second derivative treatments of a titrations curve.
Calculations of titrations curves are given in the chapter and just like our use of acid/base constant to calculate concentrations, we use the assumptions of complete reactions and the Nernst equation to calculate points along the titration curve.
Ladder diagrams can also be used to evaluate equilibrium reactions in redox systems.
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This figure shows a typical ladder diagram for two half-reactions. The scale is Eh, the electrochemical potential referenced to the SHE. Areas of predominance are defined by the Nernst equation.
Remember that a reduction half reaction with a more positive Eo drives the oxidation of a half reaction with a less positive Eo. Thus iron(III) will be reduced when tin(II) is oxidized.
This is consistent with what we learned about ladder diagrams before. Tin(II) and iron(III) can not exist together, but iron(II) and tin(IV) can.
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i.e.E = Eo - 0.05916 log [Fe2+]/[Fe3+] = 0.771 - 0.05916 log [Fe2+]/[Fe3+]
For potentials more positive than the standard-state potential, the predominate species is iron(III), whereas iron(II) predominates for potentials more negative than Eo.
When coupled with the step for the Sn4+/Sn2+ half-reaction, we see that Sn2+ can be used to reduce Fe3+. If an excess of Sn2+ is added, the potential of the resulting solution will be near +0.154 V.
Using standard-state potentials to construct a ladder diagram can present problems if solutes are not at their standard-state concentrations, but deviations from standard-state concentrations can usually be ignored if the steps being compared are separated by at least 0.3 V.
A trickier problem occurs when a half-reaction’s potential is affected by the concentration of another species. For example, the potential of this reaction is pH dependent.
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UO22+(aq) + 4 H+ + 2 e- < == > U4+(aq) + 2 H2O
For this reaction we have
E = 0.327 - 0.05916/2 log [U4+]
[UO22+][H+]4
which can be reduced to
E = 0.327 - 0.05916/2 log [U4+] + 0.05916/2 log [H+]4
[UO22+]
From this equation we can see that areas of predominance for the ions are defined by a step whose potential is
E = 0.327 - 0.1183 pH
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This ladder diagram shows how a change in pH affects the step for the UO22+/U4+ half-reaction.
Just as in acid/base titrations, the completeness of the reaction determines how large the equilibrium constant is for the reactions which is the same as the size of the change in Esystem in the equivalence-point region.
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This is shown in this transparency. The greater the difference between the standard-state potentials of the analyte and the titrant, the larger the equilibrium constant and the larger the equivalence-point region.
As you are aware from lab, the titration of mixtures is possible if the standard potentials of the two analytes are far enough apart.
If this difference is greater than about 0.2 V, the end points are usually distinct enough to permit determination of each component. This situation is quite comparable to the titration of two acids with different dissociation constants.
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Here is the titration curve for a solution that is 0.0500 M in titanium(III) and 0.200 M in iron(II) being titrated with 0.0500 M KMnO4.
The reactions are
MnO4- + 8 H+ + 5 e- < == > Mn2+ + 4 H2OEo = +1.692 V
TiO2+ + 2 H+ + e- < == > Ti3+ + H2OEo = +0.099 V
Fe3+ + e- < == > Fe2+ Eo = +0.771 V
In addition, the behavior of a few redox systems is analogous to that of polyprotic acids. For example, consider the two half-reactions
VO2+ + 2H+ + e- < == > V3+ + H2O Eo = +0.359 V
V(OH)4+ + 2H+ + e- < == > VO2+ + 3 H2OEo = +1.00 V
The curve for the titration of V3+ with a strong oxidizing agent, such as permanganate, has two inflection points, the first corresponding to the oxidation of V3+ to VO2+ and the second to the oxidation of VO2+ to V(OH)4+.
Many redox titrations do not use indicator electrodes to determine the end point but instead involve all the different kinds of end point indicators that we studied last quarter.
One of the types we mentioned earlier involves colored reagents that change color at the endpoint. Permanganate is an example of a colored titrant. The substance is purple and reacts to form a colorless Mn2+.
As it oxidizes the analyte,the drops of purple permanganate turn colorless in the analyte solution. When the analyte has reacted completely, an excess of permanganate will turn the solution pink.
The third type of redox titration involves chemical indicators. These are used to detect end points for oxidation/reduction titrations: general redox indicatorsand specific redox indicators.
General oxidation/reduction indicators are substances that change color upon being oxidized or reduced.
In contrast to specific indicators, the color changes of general redox indicators are largely independent of the chemical nature of the analyte and titrant and depend instead upon the changes in the electrode potential of the system that occur as the titration progresses.
The half-reaction responsible for color change in a typical general oxidation reduction indicator can be written as
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Inox + ne- < == > Inred
If the indicator reaction is reversible, we can write
E = EoIn - 0.05916/n log [Inred]/[Inox]
Typically, as with acid/base indicators, a change from the color of the oxidized form of the indicator to the color of the reduced form requires a change of about 100 in the ratio of reactant concentrations; that is, a color change is seen when the ratio goes from 1/10 to 10/1.
This translates into a potential change required to produce the full color change of a typical general indicator. This potential can be found by substituting these two values into the above equation, which gives
E = EoIn ± 0.05916/n
This equation shows that a typical general indicator exhibits a detectable color change when a titrant causes the system potential to shift from EoIn + 0.0592/n to EoIn - 0.0592/n, or about (0.118/n) V. For many indicators, n = 2 and a change of 0.059 V is thus sufficient.
This transparency lists transition potentials for several redox indicators. Note that indicators functioning in any desired potential range up to about + 1.25 V are available.
You can see that these are just like acid/base indicator that change color at a particular pH. Instead we think about these as changing color at a particular Eh.
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Another type of indicator is one that complexes with the analyte or its redox product. The book describes orthophenanthroline commonly known as ferroin which form stable complexes with iron(II) and certain other ions.
The parent compound has a pair of nitrogen atoms located in such positions that each can form a covalent bond with the iron ions. Three orthophenanthroline molecules combine with each iron ion to yield a complex with the given structure.
The iron(III) complex is a very pale blue, so pale it is essentially colorless. The iron(II) complex is a deep red.
Of all the oxidation/reduction indicators, ferroin approaches most closely the ideal substance. It reacts rapidly and reversibly, its color change is pronounced, and its solutions are stable and readily prepared.
In contrast to many indicators, the oxidized form of ferroin is remarkably inert toward strong oxidizing agents. At temperatures above 600C, ferroin decomposes.
Several substituted phenanthrolines have been investigated for their indicator properties, and some have proved to be as useful as the parent compound. Some bind other cations besides iron.
Among these, the 5-nitro and 5-methyl derivatives are noteworthy; their transition potentials are + 1.25 V and + 1.02 V, respectively.
Another widely used complex-forming indicator is starch, which forms a blue complex with the triiodide ion, I3-. It is a widely used as an indicator in oxidation/reduction reactions involving iodine as an oxidant or iodide as a reductant.
A starch solution containing a little triiodide or iodide ion can also function as a general redox indicator, as well.
In the presence of excess oxidizing agent, the concentration ratio of iodine to iodide is high, giving a blue color to the solution. With excess reducing agent, on the other hand, iodide ion predominates, and the blue color is absent.
Thus, the indicator system changes from colorless to blue in the titration of many reducing agents with various oxidizing agents. This color change is quite independent of the chemical composition of the reactants, depending only upon the potential of the system at the equivalence point.
Let me point out some other practices discussed in the chapter. Some analytical methods involve adjusting the redox state of the analytes before titrating. An example from the book is converting Mn2+ to permanganante before titrating to convert an analyte that is difficult to analyze into one that is easily titrated.
This is discussed in the book as preoxidation or prereduction.
Another common practice is to do redox back titrations. An analyte may be oxidized with an excess of a strong oxidizing agent and then the remaining oxidizing agent reduced with a titrant.
These procedures are used to get titrations that have better end-points, or when the analytes thens to react slowly, or in cases where we have mixed species such as iron(II) and iron(III) and we want to get total iron ion in solution.
Finally the chapter describes some of the substances found to make the best titrants. Obviously having high or low standard potential helps. We also want rapid and complete reaction. And a good color change helps.
Now let’s take the last few minutes and work on the homework assignment.