REDOX Titrations

REDOX Titrations

Redox titration – A titration in which the reaction between the analyte and titrant is an oxidation/reduction reaction. Oxidation-reduction titration is a volumetric analysis that relies on a net change in the oxidation number of one or more species. The titrant is a commonly an oxidising agent although reducing titrants can be used.

Redox titrations were introduced shortly after the development of acid–base titrimetry. The earliest methods took advantage of the oxidizing power of chlorine. In 1787, Claude Berthollet introduced a method for the quantitative analysis of chlorine water (a mixture of Cl₂, HCl, and HOCl) based on its ability to oxidize solutions of the dye indigo (indigo is colorless in its oxidized state). In 1814, Joseph Louis Gay-Lussac (1778–1850), developed a similar method for chlorine in bleaching powder. In both methods the end point was signaled visually. Before the equivalence point, the solution remains clear due to the oxidation of indigo. After the equivalence point, however, unreacted indigo imparts a permanent color to the solution.

The number of redox titrimetric methods increased in the mid-1800s with the introduction of MnO₄^–, Cr₂O₇^2– and I₂ as oxidizing titrants, and Fe²⁺ and S₂O₃^2– as reducing titrants. Even with the availability of these new titrants, however, the routine application of redox titrimetry to a wide range of samples was limited by the lack of suitable indicators. Titrants whose oxidized and reduced forms differ significantly in color could be used as their own indicator. For example, the intensely purple MnO₄^– ion serves as its own indicator since its reduced form, Mn²⁺, is almost colorless. The utility of other titrants, however, required a visual indicator that could be added to the solution. The first such indicator was diphenylamine, which was introduced in the 1920s. Other redox indicators soon followed, increasing the applicability of redox titrimetry.

         The equivalent weight of a participant in an oxidation reaction is that amount that directly or indirectly produces or consumes 1 mole of electrons.

In a redox titration we monitor electrochemical potential. The Nernst equation relates the electrochemical potential to the concentrations of reactants and products participating in a redox reaction. The Nernst expression for electrode potential of redox reaction (aA + bB « cC + dD) participants is

E = =

n – total number of electrons gained in the reaction

This expression is valid for simple redox expressions.

Consider, for example, a titration in which the analyte in a reduced state, A_red, is titrated with a titrant in an oxidized state, T_ox. The titration reaction is

A_red + T_ox « T_red + A_ox

The electrochemical potential for the reaction is the difference between the reduction potentials for the reduction and oxidation half-reactions; thus,

E_rxn = E_Tox/_Tred – E_Aox /_Ared

After each addition of titrant, the reaction between the analyte and titrant reaches a state of equilibrium. The reaction’s electrochemical potential, Erxn, therefore, is zero, and

E_Tox/_Tred = E_Aox /_Ared

Consequently, the potential for either half-reaction may be used to monitor the titration’s progress.

Before the equivalence point the titration mixture consists of appreciable quantities of both the oxidized and reduced forms of the analyte, but very little unreacted titrant. The potential, therefore, is best calculated using the Nernst equation for the analyte’s half-reaction

Although E°_Aox /_Ared is the standard-state potential for the analyte’s half-reaction, a matrix-dependent formal potential is used in its place. After the equivalence point, the potential is easiest to calculate using the Nernst equation for the titrant’s half-reaction, since significant quantities of its oxidized and reduced forms are present.

Formal potential – The potential of a redox reaction for a specific set of solution conditions, such as pH and ionic composition.

 

Calculating the Titration Curve

As an example, calculate of the titration curve for the titration of 50.0 mL of 0.100 M Fe²⁺ with 0.100 M Ce⁴⁺ in a matrix of 1 M HClO₄. The reaction in this case is

Fe²⁺ + Ce⁴⁺ « Ce³⁺ + Fe³⁺                                            (1)

The equilibrium constant for this reaction is quite large (it is approximately 6 ´ 10¹⁵), so we may assume that the analyte and titrant react completely.

The first task is to calculate the volume of Ce⁴⁺ needed to reach the equivalence point. From the stoichiometry of the reaction we know

Moles Fe²⁺ = moles Ce⁴⁺

or

M_FeV_Fe = M_CeV_Ce

Solving for the volume of Ce⁴⁺

V_Ce =  = 50.0 mL

gives the equivalence point volume as 50.0 mL.

Before the equivalence point the concentration of unreacted Fe²⁺ and the concentration of Fe³⁺ produced by reaction 9.16 are easy to calculate. For this reason we find the potential using the Nernst equation for the analyte’s half-reaction

                                           (2)

The concentrations of Fe²⁺ and Fe³⁺ after adding 5.0 mL of titrant are

Substituting these concentrations into equation 9.17 along with the formal potential for the Fe³⁺/Fe²⁺ half-reaction, we find that the potential is

At the equivalence point, the moles of Fe²⁺ initially present and the moles of Ce⁴⁺ added are equal. Because the equilibrium constant for reaction 9.16 is large, the concentrations of Fe²⁺ and Ce⁴⁺ are exceedingly small and difficult to calculate without resorting to a complex equilibrium problem. Consequently, we cannot calculate the potential at the equivalence point, Eeq, using just the Nernst equation for the analyte’s half-reaction or the titrant’s half-reaction. We can, however, calculate Eeq by combining the two Nernst equations. To do so we recognize that the potentials for the two half-reactions are the same; thus,

Adding together these two Nernst equations leaves us with

                (3)

At the equivalence point, the titration reaction’s stoichiometry requires that

[Fe²⁺] = [Ce⁴⁺]

[Fe³⁺] = [Ce³⁺]

The ratio in the log term of equation 9.18, therefore, equals one and the log term is zero. Equation 9.18 simplifies to

 

After the equivalence point, the concentrations of Ce³⁺ and excess Ce⁴⁺ are easy to calculate. The potential, therefore, is best calculated using the Nernst equation for the titrant’s half-reaction.

                                    (4)

For example, after adding 60.0 mL of titrant, the concentrations of Ce³⁺ and Ce⁴⁺ are

Substituting these concentrations into equation 9.19 gives the potential as

Additional results for this titration curve are shown in Table 1 and Figure 1.

 

Table 1. Data for Titration of 50.0 mL of 0.100 M Fe²⁺ with 0.100 M Ce⁴⁺

 

Volume Ce4+(mL)	E (V)	Volume Ce4+ (mL)	E (V)
5.00	0.711	55.00	1.64
10.00	0.731	60.00	1.66
15.00	0.745	65.00	1.67
20.00	0.757	70.00	1.68
25.00	0.767	75.00	1.68
30.00	0.777	80.00	1.69
35.00	0.789	85.00	1.69
40.00	0.803	90.00	1.69
45.00	0.823	95.00	1.70
50.00	1.23	100.00	1.70

 

 

Figure 1. Redox titration curve for 50.0 mL of 0.100 M Fe²⁺ with 0.100 M Ce⁴⁺ in 1M HClO₄.

As another titration methods, we can get either to the following types of curves, based on the type of reaction:

 

 

The vertical axis on oxidation/reduction titration curves is generally an electrode potential instead logarithmic p-functions that were used for all titration methods curves (precipitation, complex-formation, neutralisation). There is a logarithmic relationship between electrode potential and concentration of the analyte or titrant.

At equilibrium the redox potential of system is E_eq = .

The equilibrium constant is determined from lgK_eq = .

Selecting and Evaluating the End Point

The equivalence point of a redox titration occurs when stoichiometrically equivalent amounts of analyte and titrant react. As with other titrations, any difference between the equivalence point and the end point is a determinate source of error.

The equivalence point is almost identical with the inflection point located in the sharply rising part of the titration curve. When the stoichiometry of a redox titration is symmetrical (one mole analyte per mole of titrant), then the equivalence point also is symmetrical. If the stoichiometry is not symmetrical, then the equivalence point will lie closer to the top or bottom of the titration curve’s sharp rise. In this case the equivalence point is said to be asymmetrical.

Finding the End Point with a Visual Indicator. Three types of visual indicators are used to signal the end point in a redox titration.

– A few titrants, such as MnO₄^–, have oxidized and reduced forms whose colors in solution are significantly different. Solutions of MnO₄– are intensely purple. In acidic solutions, however, permanganate’s reduced form, Mn²⁺, is nearly colorless. When MnO₄^– is used as an oxidizing titrant, the solution remains colorless until the first drop of excess MnO₄^– is added. The first permanent tinge of purple signals the end point.

– A few substances indicate the presence of a specific oxidized or reduced species. Starch, for example, forms a dark blue complex with I₃^– and can be used to signal the presence of excess I₃^– (color change: colorless to blue), or the completion of a reaction in which I₃^– is consumed (color change: blue to colorless). Another example of a specific indicator is thiocyanate, which forms a soluble red-colored complex, Fe(SCN)²⁺, with Fe³⁺.

– The most important class of redox indicators, however, are substances that do not participate in the redox titration, but whose oxidized and reduced forms differ in color. When added to a solution containing the analyte, the indicator imparts a color that depends on the solution’s electrochemical potential. Since the indicator changes color in response to the electrochemical potential, and not to the presence or absence of a specific species, these compounds are called general redox indicators.

Classes of the redox indicators:

1)  Metal [more frequently – iron(II)] complexes of o-phenanthrolines;

2)  Diphenylamine and its derivatives.

The relationship between a redox indicator’s change in color and the solution’s electrochemical potential is easily derived by considering the half-reaction for the indicator

In_ox + ne^– « In_red

Typically, a change from the colour of the oxidised form of the indicator (colour 1) to the colour of the reduced form (colour 2) requires a change of about 100 in the ratio of reactants concentrations:

(colour 1) In_Ox + ne « In_Red (colour 2)

Therefore, the redox indicators transition interval (pT) is     pT =

where In_ox and In_red are, respectively, the indicator’s oxidized and reduced forms. The Nernst equation for this reaction is

If we assume that the indicator’s color in solution changes from that of In_ox to that of In_red when the ratio [In_red]/[In_ox] changes from 0.1 to 10, then the end point occurs when the solution’s electrochemical potential is within the range

 

A partial list of general redox indicators is shown in Table 2.

 

Table 2. Selected General Redox Indicators

 

Indicator	Oxidized Colour	Reduced Colour	E° (V)
indigo tetrasulfonate	blue	colorless	0.36
methylene blue	blue	colorless	0.53
diphenylamine	violet	colorless	0.75
diphenylamine sulfonic acid	red-violet	colorless	0.85
tris(2,2’-bipyridine)iron	pale blue	red	1.120
ferroin	pale blue	red	1.147
tris(5-nitro-1,10-phenanthroline)iron	pale blue	red-violet	1.25

 

Examples of appropriate and inappropriate indicators for the titration of Fe²⁺ with Ce⁴⁺ are shown in Figure 2.

 

 

Figure 2. Titration curve for 50.00 mL of 0.0500 M Fe²⁺ with 0.0500 M Ce⁴⁺ showing the range of E and volume of titrant over which the indicators ferroin and diphenylamine sulfonic acid are expected to change color.

Finding the End Point Potentiometrically. Another method for locating the end point of a redox titration is to use an appropriate electrode to monitor the change in electrochemical potential as titrant is added to a solution of analyte. The end point can then be found from a visual inspection of the titration curve. The simplest experimental design (Figure 3) consists of a Pt indicator electrode whose potential is governed by the analyte’s or titrant’s redox half-reaction, and a reference electrode that has a fixed potential.

Figure 3. Experimental arrangement for recording a potentiometric redox titration curve.

Selecting and Standardizing a Titrant In quantitative work the titrant’s concentration must remain stable during the analysis. Since titrants in a reduced state are susceptible to air oxidation, most redox titrations are carried out using an oxidizing agent as the titrant. The choice of which of several common oxidizing titrants is best for a particular analysis depends on the ease with which the analyte can be oxidized. Analytes that are strong reducing agents can be successfully titrated with a relatively weak oxidizing titrant, whereas a strong oxidizing titrant is required for the analysis of analytes that are weak reducing agents.

The two strongest oxidizing titrants are MnO₄^– and Ce⁴⁺, for which the reduction half-reactions are

MnO₄^– + 8H⁺ + 5e^– ® Mn²⁺ + 12H₂O

Ce⁴⁺ + e^– ® Ce³⁺

Solutions of Ce⁴⁺ are prepared from the primary standard cerium ammonium nitrate, Ce(NO₃)₄ ´ 2NH₄NO₃, in 1 M H₂SO₄. When prepared from reagent grade materials, such as Ce(OH)₄, the solution must be standardized against a primary standard reducing agent such as Na₂C₂O₄ or Fe²⁺ (prepared using Fe wire). Ferroin is a suitable indicator when standardizing against Fe²⁺ (Table 3). Despite its availability as a primary standard and its ease of preparation, Ce⁴⁺ is not as frequently used as MnO₄^– because of its greater expense.

Solutions of MnO₄^– are prepared from KMnO₄, which is not available as a primary standard. Aqueous solutions of permanganate are thermodynamically unstable due to its ability to oxidize water.

4MnO₄^– + 2H₂O ® 4MnO₂¯ + 3O₂­ + 4OH^–

This reaction is catalyzed by the presence of MnO₂, Mn²⁺, heat, light, and the presence of acids and bases. Moderately stable solutions of permanganate can be prepared by boiling for an hour and filtering through a sintered glass filter to remove any solid MnO₂ that precipitates. Solutions prepared in this fashion are stable for 1–2 weeks, although the standardization should be rechecked periodically. Standardization may be accomplished using the same primary standard reducing agents that are used with Ce⁴⁺, using the pink color of MnO₄^– to signal the end point (Table 3).

Table 3. Standardization Reactions for Selected Redox Titrants

2Ce(SO₄)₂ + 2FeSO₄ ® Ce₂(SO₄)₃ + Fe₂(SO₄)₃

2Ce(SO₄)₂ + H₂C₂O₄ ® Ce₂(SO₄)₃ + 2CO₂ + H₂SO₄

2KMnO₄ + 10FeSO₄ + 16H₂SO₄ ® 2MnSO₄ + 5Fe₂(SO₄)₃ + K₂SO₄ + 8H₂O

2KMnO₄ + 5H₂C₂O₄ + 3H₂SO₄ ® 2MnSO₄ + 10CO₂ + K₂SO₄ + 8H₂O

I₂ + 2Na₂S₂O₃ ® 2NaI + Na₂S₄O₆

 

Potassium dichromate is a relatively strong oxidizing agent whose principal advantages are its availability as a primary standard and the long-term stability of its solutions. It is not, however, as strong an oxidizing agent as MnO₄^– or Ce⁴⁺, which prevents its application to the analysis of analytes that are weak reducing agents. Its reduction half-reaction is

Cr²O₇^2– + 14H⁺ + 6e– ® 2Cr³⁺ + 21H₂O

Although solutions of Cr₂O₇^2– are orange and those of Cr³⁺ are green, neither color is intense enough to serve as a useful indicator. Diphenylamine sulfonic acid, whose oxidized form is purple and reduced form is colorless, gives a very distinct end point signal with Cr₂O₇^2–.

Iodine is another commonly encountered oxidizing titrant. In comparison with MnO₄^–, Ce⁴⁺, and Cr₂O₇^2–, it is a weak oxidizing agent and is useful only for the analysis of analytes that are strong reducing agents. This apparent limitation, however, makes I₂ a more selective titrant for the analysis of a strong reducing agent in the presence of weaker reducing agents. The reduction half-reaction for I₂ is

I₂ + 2e^– ® 2I^–

Because of iodine’s poor solubility, solutions are prepared by adding an excess of I^–. The complexation reaction

I₂ + I^– ® I₃^–

increases the solubility of I₂ by forming the more soluble triiodide ion, I₃^–. Even though iodine is present as I₃^– instead of I₂, the number of electrons in the reduction half-reaction is unaffected.

I₃^– + 2e^– ® 3I^–

Solutions of I₃^– are normally standardized against Na₂S₂O₃ (see Table 3) using starch as a specific indicator for I₃^–.

Oxidizing titrants such as MnO₄^–, Ce⁴⁺, Cr₂O₇^2– and I₃^–, are used to titrate analytes that are in a reduced state. When the analyte is in an oxidized state, it can be reduced with an auxiliary reducing agent and titrated with an oxidizing titrant. Alternatively, the analyte can be titrated with a suitable reducing titrant. Iodide is a relatively strong reducing agent that potentially could be used for the analysis of analytes in higher oxidation states. Unfortunately, solutions of I^– cannot be used as a direct titrant because they are subject to the air oxidation of I^– to I₃^–.

3I^– ® I₃^– + 2e^–

Instead, an excess of KI is added, reducing the analyte and liberating a stoichiometric amount of I₃^–. The amount of I₃^– produced is then determined by a back titration using Na₂S₂O₃ as a reducing titrant.

2S₂O₃^2– ® S₄O₆^2– + 2e^–

Solutions of Na₂S₂O₃ are prepared from the pentahydrate and must be standardized before use. Standardization is accomplished by dissolving a carefully weighed portion of the primary standard KIO₃ in an acidic solution containing an excess of KI. When acidified, the reaction between IO₃^– and I^–

IO₃^– + 8I^– + 6H⁺ ® 3I₃^– + 9H₂O

liberates a stoichiometric amount of I₃^–. Titrating I₃^– using starch as a visual indicator allows the determination of the titrant’s concentration.

Although thiosulfate is one of the few reducing titrants not readily oxidized by contact with air, it is subject to a slow decomposition to bisulfite and elemental sulfur. When used over a period of several weeks, a solution of thiosulfate should be restandardized periodically. Several forms of bacteria are able to metabolize thiosulfate, which also can lead to a change in its concentration. This problem can be minimized by adding a preservative such as HgI₂ to the solution.

Another reducing titrant is ferrous ammonium sulfate, Fe(NH₄)₂(SO₄)₂ ´ 6H₂O, in which iron is present in the +2 oxidation state. Solutions of Fe²⁺ are normally very susceptible to air oxidation, but when prepared in 0.5 M H₂SO₄ the solution may remain stable for as long as a month. Periodic restandardization with K₂Cr₂O₇ is advisable. The titrant can be used in either a direct titration in which the Fe²⁺ is oxidized to Fe³⁺, or an excess of the solution can be added and the quantity of Fe³⁺ produced determined by a back titration using a standard solution of Ce⁴⁺ or Cr₂O₇^2–.

There are some techniques of redox reaction rate rising:

1.     Temperature increasing.

2.     The pH value and reactants concentration change.

3.     Catalyst addition.

4.     Inducted reactions running.

 

 

The redox titration divides on titration with reducing agents – for oxidisers determination, and titration with oxidisers – for reducing agents determination. Common standard titrants are named below: