Lecture 13 - Acid-Base Titrations

Chem 321 Lecture 13 - Acid-Base Titrations Student Learning Objectives Indicators A common end point for acid-base titrations is the color change associated with an acid-base indicator. An acid-base indicator is usually an organic weak acid or base that has a different color in solution than its conjugate form. These substances strongly absorb light so that even a very small concentration in solution produces an obvious color. If the weak acid form of the indicator is taken as HIn, the acid dissociation process for this indicator is represented by: HIn + H2O Ka º H3O+ + In- At equilibrium, and This means that as [H3O+] changes, so do the relative amounts of the different colored conjugate species in solution. Thus, the indicator in solution will take on a specific color depending upon the solution pH. As an example, consider the acid-base indicator methyl orange indicator. The weak acid form is red in solution while the conjugate base form is yellow (that is, HIn = red and In- = yellow). In order to anticipate the pH range in which this indicator changes from yellow to red, or vice versa, assume that a 10-fold excess of one colored form over the other is needed to establish the color of one of the conjugate pairs. Thus, to see predominately yellow in solution, In a similar way it can be shown that the red color dominates when the solution pH is about equal to pKa - 1. Therefore, an indicator color change is expected in a pH range equal to pKa ± 1. The pKa for methyl orange is 3.46, so it should change from red to yellow as the pH increases from about 2.5 to 4.5. This is in substantial agreement with the pH transition range for methyl orange in the table below. Table of Common Acid-Base Indicators Transition range (pH) Acid color Base color Methyl violet 0.0 - 1.6 Yellow Violet Cresol red 0.2 - 1.8 Red Yellow Thymol blue 1.2 - 2.8 Red Yellow Cresol purple 1.2 - 2.8 Red Yellow Erthrosine disodium 2.2 - 3.6 Orange Red Methyl orange 3.1 - 4.4 Red Yellow Congo red 3.0 - 5.0 Violet Red Ethyl orange 3.4 - 4.8 Red Yellow Bromocresol green 3.8 - 5.4 Yellow Blue Methyl red 4.8 - 6.0 Red Yellow Chlorophenol red 4.8 - 6.4 Yellow Red Bromocresol purple 5.2 - 6.8 Yellow Purple p-Nitrophenol 5.6 - 7.6 Colorless Yellow Litmus 5.0 - 8.0 Red Blue Bromothymol blue 6.0 - 7.6 Yellow Blue Phenol red 6.4 - 8.0 Yellow Red Neutral red 6.8 - 8.0 Red Yellow Cresol red 7.2 - 8.8 Yellow Red α-Naphtholphthalein 7.3 - 8.7 Pink Green Cresol purple 7.6 - 9.2 Yellow Purple Thymol blue 8.0 - 9.6 Yellow Blue Phenolphthalein 8.0 - 9.6 Colorless Red Thymolphthalein 8.3 - 10.5 Colorless Blue Alizarin yellow 10.1 - 12.0 Yellow Orange-red Nitramine 10.8 - 13.0 Colorless Orange-brown Tropaeolin O 11.1 - 12.7 Yellow Orange Indicator Consequently, knowledge of the pH at the equivalence point allows one to select an indicator that will undergo a color change in a pH range that brackets the equivalence point pH. Check for Understanding 9.3 1. Solutions Which indicator would be suitable for the titration of: a) HC2H3O2 with NaOH? b) NH3 with HCl? See Example 9.1 and Check for Understanding 9.1 for estimates of the equivalence point pH for these titrations. Polyprotic Acid and Base Titrations The titration of a polyprotic acid or base is very similar to that for a monoprotic weak acid or base except that more than one equivalence point is observed. The maleic acid experiment in lab involves such a titration. The titration curve for the titration of 50.0 mL of 0.100 M Na2CO3 with 0.100 M HCl is shown in Figure 9.5. Since the analyte and titrant concentrations are the same, the first equivalence point occurs at 50 mL and the second one occurs at 100 mL. Figure 9.5 Curve for the titration of Na2CO3 with a HCl(aq) The titration reaction to the first equivalence point involves neutralization of the weak base carbonate. CO32- + H3O+ 6 HCO3- + H2O As this process occurs, a CO32-/HCO3- buffer is formed. The region before the first equivalence point where the pH is changing slowly with added titrant corresponds to this first buffer region. Throughout this portion of the titration pH ~ pKa and at the halfway point (25 mL), pH = pKa = 10.33. Note that the Ka is that for the weak acid in the buffer, that is, HCO3-, which corresponds to Ka2 for H2CO3. At the first equivalence point, all the CO32- has been converted to HCO3- and additional titrant starts neutralizing the bicarbonate. HCO3- + H3O+ 6 H2CO3 + H2O As this process occurs, a HCO3-/H2CO3 buffer is formed. The region between the first and second equivalence points where the pH is changing slowly with added titrant corresponds to this second buffer region. Throughout this portion of the titration pH ~ pKa and halfway between the first and second equivalence points (75 mL), pH = pKa = 6.35. Here Ka is that for the weak acid H2CO3 and is thus Ka1 for carbonic acid. An estimate of each equivalence point pH can be made as before by taking the average of the pH plateau values before and after the equivalence point. For the first equivalence point pH ~ (10.33 + 6.35)/2 = 8.3. Check for Understanding 9.4 Solutions 1. Estimate the pH at the second equivalence point in the carbonate titration. 2. Which indicators are suitable for use at the first and second equivalence points in the carbonate titration? Because the pH jump at either equivalence point in the carbonate titration is not very large, an indicator color change is not a very sharp end point. An indicator color match can be used instead as the end point. For this to be a valid end point, the indicator must have the same color in the comparison solution as it has in the titration solution at the second equivalence point. This is true only if the pH of the comparison solution is the same as the pH at the second equivalence point. Previously you have calculated, using activities, the pH of a CO32-/HCO3- buffer solution that is suitable for use as a comparison solution for the carbonate titration, and above you have estimated the pH at the second equivalence point. To make a more careful comparison of pH, make the following calculation of the second equivalence point pH. Check for Understanding 9.5 1. Solution What is the pH at the second equivalence point in the titration of Na2CO3 with 0.100 M HCl? Use activities and assume a 0.200-g sample of Na2CO3 is dissolved in 60.0 mL of deionized water and titrated. Gran Plots For the maleic acid experiment, you will use a graphical method known as a Gran plot to determine the second equivalence point in your titration. In this approach, the pH of your maleic acid solution is recorded as a function of the volume of added base (Vb) and a graph of Vb@10-pH versus Vb is made using data just before the equivalence point. Assuming that the ionic strength of the solution is constant, the xintercept of this linear plot is the equivalence point volume (Ve). An example of a Gran plot is shown below. Derivation of relationship used for Gran plot Figure 9.6 © 2011 W. H. Freeman and Company Gran plot for a weak acid-strong base titration The ionic strength of the maleic acid solution is fixed by adding a large amount of KCl to the titration solution. The key advantage of using a Gran plot is that the equivalence point can be determined by using only data before the equivalence point (typically the data between 0.9Ve and Ve). The slope of the Gran plot also allows one to determine the Ka of the weak acid (for a weak acid-strong base titration, slope = - KaγHA /γA-).