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The history and development of redox titrations in analytical chemistry. It explains the use of redox reactions in titrations and the importance of suitable indicators. The document also covers the calculation of redox titration curves and the use of the Nernst equation to monitor the titration reaction's potential. It includes an example calculation of a redox titration curve and a method for sketching a redox titration curve. suitable for students studying analytical chemistry or related fields.
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Department of Chem. & Petrochemical Engineering 2 nd^. Stage / Analytical Chemistry
Titrations Based on Redox reactions Analytical titrations using redox reactions were introduced shortly after the development of acid–base titrimetry. The earliest Redox titration 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 Cl 2 , HCl, and HOCl) based on its ability to oxidize indigo, a dye that is colorless in its oxidized state. In 1814, Joseph Gay-Lussac developed a similar method for determining chlorine in bleaching powder. In both methods the end point is a change in color. Before the equivalence point the solution is colorless 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 MnO 4 – , Cr 2 O 72 – , and I 2 as oxidizing titrants, and of Fe2+^ and S 2 O 32 – as reducing titrants. Even with the availability of these new titrants, redox titrimetry was slow to develop due to the lack of suitable indicators. A titrant can serve as its own indicator if its oxidized and reduced forms differ significantly in color. For example, the intensely purple MnO 4 –^ ion serves as its own indicator since its reduced form, Mn2+, is almost colorless. Other titrants require a separate indicator. The first such indicator, diphenylamine, was introduced in the 1920s. Other redox indicators soon followed, increasing the applicability of redox titrimetry. Redox Titration Curves To evaluate a redox titration we need to know the shape of its titration curve. In an acid–base titration or a complexation titration, the titration curve shows how the concentration of H 3 O+^ (as pH) or Mn+^ (as pM) changes as we add titrant. For a redox titration it is convenient to monitor the titration reaction’s potential instead of the concentration of one species. You may recall from Chapter 6 that the Nernst equation relates a solution’s potential to the concentrations of reactants and products participating in the redox reaction. Consider, for example, a titration in which a titrand in a reduced state, A red, reacts with a titrant in an oxidized state, B ox. A red + Box ⇌ Bred + A ox where A ox is the titrand’s oxidized form, and B red is the titrant’s reduced form. The reaction’s potential, E rxn, is the difference between the reduction potentials for each half-reaction.
Department of Chem. & Petrochemical Engineering 2 nd^. Stage / Analytical Chemistry After each addition of titrant the reaction between the titrand and the titrant reaches a state of equilibrium. Because the potential at equilibrium is zero, the titrand’s and the titrant’s reduction potentials are identical.
This is an important observation because we can use either half-reaction to monitor the titration’s progress. Before the equivalence point the titration mixture consists of appreciable quantities of the titrand’s oxidized and reduced forms. The concentration of unreacted titrant, however, is very small. The potential, therefore, is easier to calculate if we use the Nernst equation for the titrand’s half-reaction Note : Although the Nernst equation is written in terms of the half-reaction’s standard state potential, a matrix-dependent formal potential often is used in its place. See Appendix 13 for the standard state potentials and formal potentials for selected half-reactions. After the equivalence point it is easier to calculate the potential using the Nernst equation for the titrant’s half-reaction. Calculating the Titration Curve Let’s calculate 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 HClO 4. The reaction in this case is
Note In 1 M HClO 4 , the formal potential for the reduction of Fe3+^ to Fe2+^ is +0.767 V, and the formal potential for the reduction of Ce4+^ to Ce3+is +1.70 V. Because the equilibrium constant for reaction 12.1 is very large—it is approximately 6 × 10^15 —we may assume that the analyte and titrant react completely. Note Step 1: Calculate the volume of titrant needed to reach the equivalence point.
Department of Chem. & Petrochemical Engineering 2 nd^. Stage / Analytical Chemistry Note Step 3: Calculate the potential after the equivalence point by determining the concentrations of the titrant’s oxidized and reduced forms, and using the Nernst equation for the titrant’s reduction half-reaction. After the equivalence point, the concentration of Ce3+^ and the concentration of excess Ce4+^ are easy to calculate. For this reason we find the potential using the Nernst equation for the Ce4+/Ce3+^ half-reaction.
For example, after adding 60.0 mL of titrant, the concentrations of Ce3+ and Ce4+ are Substituting these concentrations into equation 9.3 gives a potential of Note Step 4: Calculate the potential at the equivalence point. At the titration’s equivalence point, the potential, E eq, in equation 12.2 and equation 12 .3 are identical. Adding the equations together to gives Because [Fe2+] = [Ce4+] and [Ce3+] = [Fe3+] at the equivalence point, the log term has a value of zero and the equivalence point’s potential is
Department of Chem. & Petrochemical Engineering 2 nd^. Stage / Analytical Chemistry Additional results for this titration curve are shown in Table 12.1 and Figure 1. Table 12.1 Data for the Titration of 50.0 mL of 0.100 M Fe2+^ with 0.100 M Ce4+ Volume of Ce4+^ (mL) E (V) Volume Ce4+^ (mL) E (V) 10.0 0.731 60.0 1. 20.0 0.757 70.0 1. 30.0 0.777 80.0 1. 40.0 0.803 90.0 1. 50.0 1.23 100.0 1. Figure 1 Titration curve for the titration of 50.0 mL of 0.100 M Fe2+ with 0.100 M Ce4+. Theredpoints correspond to the data in Table12.1. Theblue line shows the complete titration curve. Practice Exercise 1 Calculate the titration curve for the titration of 50.0 mL of 0.0500 M Sn2+^ with 0. M Tl3+. Both the titrand and the titrant are 1.0 M in HCl. The titration reaction is Sn2+^ (aq) + Tl3+^ (aq) → Sn4+^ (aq) + Tl+^ (aq) Sketching a Redox Titration Curve To evaluate the relationship between a titration’s equivalence point and its end point we need to construct only a reasonable approximation of the exact titration curve. In this section we demonstrate a simple method for sketching a redox titration curve. Our goal is to sketch the titration curve quickly, using as few
Department of Chem. & Petrochemical Engineering 2 nd^. Stage / Analytical Chemistry Figure c shows the third step in our sketch. First, we add a ladder diagram for Ce4+, including its buffer range, using its E oCe4+/Ce3+value of 1.70 V. Next, we add points representing the potential at 110% of V eq (a value of 1.66 V at 55.0 mL) and at 200% of V eq (a value of 1.70 V at 100.0 mL). Note We used a similar approach when sketching the complexation titration curve for the titration of Mg2+^ with EDTA. Next, we draw a straight line through each pair of points, extending the line through the vertical line representing the equivalence point’s volume (Figure d). Finally, we complete our sketch by drawing a smooth curve that connects the three straight-line segments (Figure e). A comparison of our sketch to the exact titration curve (Figure f) shows that they are in close agreement.
Department of Chem. & Petrochemical Engineering 2 nd^. Stage / Analytical Chemistry Figure 2 Illustrations showing the steps in sketching an approximate titration curve for the titration of 50.0 mL of 0.100 M Fe2+^ with 0.100 M Ce4+^ in 1 M HClO 4 : (a) locating the equivalence point volume; (b) plotting two points before the equivalence point; (c) plotting two points after the equivalence point; (d) preliminary approximation of titration curve using straight-lines; (e) final approximation of titration curve using a smooth curve; (f) comparison of approximate titration curve (solid black line) and exact titration curve (dashed red line). See the text for additional details. Practice Exercise 2 Sketch the titration curve for the titration of 50.0 mL of 0.0500 M Sn4+^ with 0.100 M Tl+. Both the titrand and the titrant are 1.0 M in HCl. The titration reaction is
Compare your sketch to your calculated titration curve from Practice Exercise 1 Practice Exercise 1 The volume of Tl3+^ needed to reach the equivalence point is Before the equivalence point, the concentration of unreacted Sn2+^ and the concentration of Sn4+^ are easy to calculate. For this reason we find the potential using the Nernst equation for the Sn4+/Sn2+^ half-reaction.For example, the concentrations of Sn2+^ and Sn4+^ after adding 10.0 mL of titrant are