Titration Curves

Objective

To make pH versus volume curves for three combinations of strong and weak acids and bases, including a diprotic acid

Concepts

Strong and weak acids and bases, pH curves, buffer systems, hydrolysis of ions

Introduction

Acid-base reactions involving strong acids and strong bases are often referred to as neutralization reactions. The term is valid because at the equivalence point the numbers of moles of hydrogen ion, and hydroxide ion are equal, and the system is neutral, with a pH of 7. Such is not the case for titrations involving weak acids and/or weak bases.

To review, the terms strong and weak, as they apply to acids and bases, indeed to electrolytes in general, refer to the degree to which the acid or base is present as ions. Strong acids and bases are
assumed to be 100% ionized (dissociated), so a 1.0 M solution of HN0₃ would be 1.0 molar in hydrogen ion (1.0 M H⁺) and 1.0 molar in nitrate ion (1.0 M NO₃^-), and would contain no molecules of undissociated nitric acid (0.0 M HN0₃). Likewise, a 1.0 M solution of potassium hydroxide would have 1.0 mole K⁺ and 1.0 mol OH^- per liter of solution, with no KOH molecules present in solution.

The percentage ionization for weak acids, such as acetic acid, CH₃COOH, is quite low. A 1.0 molar solution of acetic acid is only 0.4 ionized, so 99.6% of the acid is present as CH₃COOH molecules, with only 0.4% as H⁺ and CH₃COO^- ions. The same situation arises with weak bases, such as aqueous ammonia, NH₃( aq); the solution contains mostly ammonia molecules, with very little NH₄⁺ or OH^- present.

As you know, the conjugate of a weak acid is itself a base, and the weaker the acid, the more strongly basic its conjugate will be. Acetate ion, the conjugate of acetic acid, will act as a base in the presence of water. This process is referred to as hydrolysis, and is illustrated in Equation 22-1.

In this experiment, you will carry out three titrations, all following the same basic sequence of steps. In the first two, you will verify the predictions of the preceding paragraphs by titrating 1.0 M HNO₃ and 1.0 M CH₃COOH with 1.0 M KOH, and 1.0 M sodium acetate, NaC₂H₃0₂, with 1.0 M HN0_3. Sodium acetate is a source of the weak base acetate ion, C₂H₃O₂-(aq). This third titration will differ from the first two in that you will be adding acid from a buret to a measured quantity of the base. Because you are starting with a basic solution, the pH will start high, then decrease as more and more acid is added. In each case you will monitor the pH of the system as a function of the volume of titrant added.

At your teacher's discretion, an optional fourth titration may be carried out using 0.50 MH₂S0₄ and 1.0M KOH.

If you did Experiment 4, Analysis of Vinegar, you recall that it was necessary to standardize the base (KOH, in that experiment) against a primary standard, potassium hydrogen phthalate, KHP for short. In the present experiment, we are interested primarily in the shapes of the curves of pH versus volume of titrant, so standardization is not as necessary. This means, however, that the equivalence point for each titration may not occur at exactly the predicted volume ratio of titrant to analyte.

Prelaboratory Assignment

1. Read the entire experiment before coming to the laboratory.

2. Prepare data tables for each of the three titrations. In each case, you will be starting with 50.00 mL of the species to be titrated. You will need lines for the pH reading following each addition of the base, starting with 0.00 mL. If your teacher directs you to include the optional fourth titration, sulfuric acid with KOH, you will need a data table for it, as well.

Prelaboratory Questions

1. The value of K; for acetic acid is 1.8 x 10-⁵. Use this value to verify the percent ionization for 1.0 M CH₃COOH as given in the Introduction. Repeat for 0.10 M and 0.010 M CH₃COOH.

2. Determine the volume of titrant that you expect to need to reach the equivalence point in each of your titrations. (If you are to carry out the H₂SO₄- KOH titration, remember that there are two equivalence points for that one.)

3. Suggest an explanation for the fact that the concentration of sulfuric acid in the optional fourth titration is 0.50 M, while the concentrations of all other acids and bases are 1.0 M

Safety Precautions

1. Chemical splash-protective eyewear must be worn at all times in the laboratory.

2. The solutions used in this experiment are corrosive to skin and clothing. Wipe up any and all spills with large volumes of water.

3. Aqueous ammonia has a harsh, unpleasant odor. The ammonia solution will readily release ammonia gas into the air. This not only exposes you and others to that odor, it also means that the concentration of the solution will slowly diminish over time. Keep containers of aqueous ammonia tightly closed when not in actual use.

Materials

Apparatus

buret,50-mL

pH meter with pH electrode or other interface with pH probe
beaker, 150-mL (3 or 4)¹

magnetic stirrer and stirring bar(s) (optional)
400-mL (or larger) beaker for rinsing, waste

Reagents

nitric acid, HNO₃(aq), 1.0 M

potassium hydroxide, KOH(aq), 1.0 M
acetic acid, HC₂H₃O₂(aq), 1.0 M

sodium acetate, NaC₂H₃O₂(aq), 1.0 M
distilled or deionized water (wash bottle)

Procedure

Set up your pH meter or interfaced pH probe as shown in Figure 21-1. Set up your apparatus as shown below or as your teacher directs, if you are using a different type of pH measuring device, such
as a calculator- or computer-interfaced probe.

A typical stand-alone pH meter.

The same basic procedure applies to all of your titrations. If you are to perform the optional titration, it should follow the titrations of nitric and acetic acids, since all use the same KOH Titrant.

Before your first titration, rinse the buret twice with distilled water, then rinse it twice with 1.0 M KOH. Be sure you rinse the tip of the buret as well as its barrel. Use your large beaker to collect all rinsings.

Fill the buret, including the tip, with 1.0 M KOH. Fill it past the 0.0-mL mark, then carefully run the volume down to 0.0. You are now ready for Part A.

1 Assumes a fresh beaker for each titration, but beakers can be washed between trials. If they are, they should be rinsed with distilled water and dried before the next titration.

2 If you do not have a magnetic stirrer, you will need to swirl the beaker after each addition of titrant, or use a stirring rod to stir the contents.

1. Place 30.0 mL of 1.0 M HN0₃ in a clean lS0-mL beaker. Place the beaker on the magnetic stirrer, add the stirring bar, and begin the stirrer. Carefully lower the pH probe into the solution, taking care to position it so that the tip is not struck by the stirring bar. When the pH reading is stable, note and record the pH of the system for 0.00 mL of base added.

2. Add 10.00 mL of 1.0 M KOH from the buret and allow the solutions to mix thoroughly. When the pH is steady, record the volume of base added and the pH of the mixture.

3. Add 5.00-mL of the KOH solution. Allow the pH reading to become steady, then record the pH and the total volume of base added, 15.00 mL. Continue adding two more 5.00-mL samples of the KOH, recording the appropriate data after each addition, until a total of 25.0 mL has been added. After each addition, enter the total volume of base.

Now begin to add the base 1.0 mL at a time, recording the total volume of base and the pH after each addition, until the total amount of base added reaches 35.0 mL. Follow with one final 5.00- mL addition and record the final volume and pH.

4. Raise the pH probe or electrode out of the solution and use your distilled-water wash bottle to rinse it thoroughly, catching the rinsings in the beaker containing your titration products. If you need to reuse your 150-mL beaker, place the contents in your large beaker and reserve it for Disposal.

Part B: Titration of a Weak Acid with a Strong Base: HC₂H₃0₂ and KOH

5. Refill your buret, then repeat steps 1-4 starting with 30.0 mL of 1.0 M HC₂H₃O₂, in place of the HNO₃ used previously. Use the same volumes of base as before, recording the pH as a function of the total volume of base added.

Note: If you are going to do the optional fourth titration, H₂SO₄ and KOH, refill your buret and repeat steps 1-4 starting with 30.0 mL of 0.50 M H₂S0₄ in place of the HNO_3. Use the same volumes of KOH as before, recording the pH as a function of the total volume of base added.

Part C: Titration of a Weak Base with a Strong Acid: NaC₂H₃O₂ and HNO₃

6. Empty your buret into your waste beaker. Wash it thoroughly with soap and water and rinse it with tap water, and then twice with distilled water, being sure to rinse the tip as well as the barrel of the buret. Rinse twice with 5-10 mL portions of 1.0 M nitric acid, then fill the buret with 1.0 M HN0₃ and adjust the level to 0.0 mL. CAUTION: Nitric acid may stain skin and clothes.

7. Place 30.0 mL of 1.0 MNaC₂H₃O₂ in a clean 150-mL beaker. Place the beaker on the magnetic stirrer, add the stirring bar, and begin the stirrer. Carefully lower the pH probe into the solution, taking care to position it so that the tip is not struck by the stirring bar. When the pH reading is stable, note and record the pH of the system for 0.00 mL of acid added.

8. Add 10.00 mL of 1.0 M HN0₃ from the buret, and allow the solutions to mix thoroughly. When the pH is steady, record the volume of base added and the pH of the mixture.

9. Add 5.00-mL ofthe-KOH solution. Allow the pH reading to become steady, then record the pH and the total volume of base added, 15.00 mL. Continue adding two more 5.00-mL samples of the HN0₃, recording the appropriate data after each addition, until a total of25.0 mL has been added. After each addition, enter the total volume of acid.

Now begin to add the acid 1.0 mL at a time, recording the total volume of base and the pH after each addition, until the total amount of base added reaches 35.0 mL. Follow with one final 5.00 mL addition and record the final volume and pH-=. ~

Disposal

1. As you have after each titration, raise the pH sensor out of the titration vessel and use your distilled-water wash bottle to rinse it, catching the rinsings in the beaker. After it has been cleaned, consult your teacher as to what you are to do with all electronic equipment.

2. Allow any remaining titrant to drain from your buret into the waste beaker. Since two of your three titrations wound up with an excess of KOH, it is likely (but not certain) that the contents of your waste beaker are basic. Test this by adding a few drops of an indicator such as bromothymol blue or phenolphthalein. If, as expected, the system is basic, add small amounts ofHN0₃ (or another acid, such as vinegar) until-the color of the indicator changes. The resulting mixture may be rinsed down the drain with large amounts of water. If the solution is not basic, check using pH paper to see if it is acidic. If acidic, neutralize by adding solid sodium bicarbonate until no bubbles are produced upon further addition of NaHCO₃, and then rinse down the drain with large amounts of water.

3. Wash your buret with soap and water, then rinse first with tap water and then with two 5-10 mL portions of distilled water. Clamp the buret, with the stopcock open, in an inverted (tip up)
position and allow it to drain dry.

Processing the Data

For each of the titrations, you are to make a separate plot of pH (vertical axis) versus Volume of Titrant (mL) (horizontal axis). In each case, identify the equivalence point for the titration by making a mark on the curve. The equivalence point in each case is the point of inflection. For those cases in which base was being added to acid, it will be where the slope of the graph stops increasing and begins to decrease. For the titration involving sodium acetate and nitric acid, the reverse is true. Consult your text for examples.

If you are using a computer-interfaced or calculator-interfaced pH probe, you may have software that will make the plots and identify the equivalence points for you. The same is true if you are using more stand-alone devices, such as Lab Quest or PasPort.

If you are making your own graphs, draw the best-fit smooth curve that you can through the data points. A device known as a French curve may be useful for this.

Analysis and Conclusions

1. Make and complete a table with the headings shown below. By "half-equivalence" is meant the point at which you had added half the volume of titrant that was needed to reach equivalence.

	HNO₃/KOH	HC₂H₃O₂/KOH	NaC₂H₃0₂/HNO₃
pH at equivalence
vol. of titrant needed to
reach equivalence
pH at half-equivalence
vol. of titrant needed to
reach half-equivalence

2. Write the net ionic equations for each of the three titration reactions that you conducted: HNO₃/KOH, HC₂H₃O₂/KOH, and NaC₂H₃O₂/HNO₃. (Hint: Consider the species that were present in the sodium acetate solution before you began addition of nitric acid.)

3. Use the pH values that you recorded to determine the concentration of all ions present initially, at half-equivalence, and at equivalence for the titration of nitric acid with KOH.

4. Repeat the calculations of question 2 for: (a) the titration of acetic acid by KOH, and (b) the titration of sodium acetate by HN0₃.

5. The Henderson-Hasselbalch equation was originally derived for use with buffer systems such as arise in biochemistry so often, but it also describes the effect of concentration on the relationship between pH and pKa for a weak acid being titrated with a strong base. It has the form:

pH = pK_a + log[A]/[HA]

where [HA] and [A-] represent the molar concentrations of a weak acid, HA, and its conjugate base, K. When your titration of acetic acid with KOH has reached the half-equivalence point, we
can assume that [HA] = [A^-]. Explain: (a) why this is a valid assumption, (b) what that means for pH and pKa, and (c) the extent to which your experimental result agrees with the predictions
made by the Henderson-Hasselbalch equation.

6. The Henderson-Hasselbalch equation can also be applied to titrations of a weak base with a strong acid, such as the reaction between acetate ion and nitric acid. In this case, at the half-
equivalence point the system contains equal amounts of acetate ion and acetic acid molecules, and the pH of the system should equal the value of pKa for acetic acid. Given that Ka for
HC₂H₃O₂ is l.8 X 10^-5, how well does your experimental result match the predictions of the Henderson-Hasselbalch equation?

7. In all probability, your experimental results will not exactly match prediction. Whether you got a close match or not, discuss the likely sources of variation from expected behavior that are present in this experiment.