Department of Chemistry and Geosciences

Chem 1084 Honors Lab Lab 5 Spring 2001

The Determination of the pKa of a Weak Acid

 

Objective: Determination of the concentration of a weak acid solution by titration with a standardized solution of sodium hydroxide. The Ka of the acid is determined by plotting the titration curve of the acid against sodium hydroxide. The pH at the half-equivalence point will be equal to the pKa of the acid.

Textbook: Chapter 15.4 Titrations and pH Curves

Introduction

Weak acids and bases only partially ionize in aqueous solution according to the following reactions:

(1)

(2)

where HA is a generic Brønsted acid and B is a generic Brønsted base. Both reactions represent reversible reactions and are governed by equilibrium constants called ionization constants. For a weak acid, the equilibrium constant is referred to as an acid ionization constant, Ka, and is represented by the following expression:

(3)

For a weak base, the equilibrium constant is referred to as a base ionization constant, Kb, and is represented by the following expression:

(4)

The value of Ka and Kb depend on the strength of the acid or base. In general, the value of the Ka or Kb increases with the strength of the acid or base.

In aqueous solution, the acidity of a solution is based on the concentration of H+ or OH¯ in solution. Remember these two concentrations are related to each other by the autoionization constant for water:

Kw = [H+][OH¯] = 1.00 ´ 10-14 (at 25°C) (5)

In a neutral solution, the concentrations of H+ and OH¯ are equal. In acidic solution, the concentration of H+ is greater than the concentration of OH¯. In basic solution, the concentration of OH¯ is greater than the concentration of H+. The acidity of a solution is generally expressed in terms of the pH of solution. The pH of a solution is defined as:

pH = –log[H+] (6)

At 25°C, a neutral solution has a pH equal to 7.00, an acidic solution has a pH less than 7.00, and a basic solution has a pH greater than 7.00.

In today's experiment, you will perform a number of acid-base titrations of a sodium hydroxide solution against a weak acid solution. In the first set of titrations, you will accurately determine the concentration of the sodium hydroxide solution in a procedure called a standardization. Sodium hydroxide solutions are notoriously difficult to prepare to an accurate concentration. First of all, pure sodium hydroxide is very hygroscopic, which means it absorbs water readily from the atmosphere. As a result, it is quite hard to weigh a solid sample of sodium hydroxide accurately because as it absorbs water from the atmosphere, the weight of the sample will continuously increase as it sits on the scale. In fact, solid sodium hydroxide is generally sold as pellets to reduce the rate of absorption of water from the atmosphere. Even then, if you leave a pellet of solid sodium hydroxide on a countertop, within 15 minutes, you will have a puddle of sodium hydroxide solution from all the water that the sample absorbs from the atmosphere. Additionally, sodium hydroxide also reacts over time with carbon dioxide from the atmosphere to form sodium carbonate, Na2CO3. Older samples of sodium hydroxide tend to be contaminated with significant quantities of sodium carbonate. The problems with sodium hydroxide solutions also continue even after the solution is prepared. Over time, sodium hydroxide solutions react with carbon dioxide in the atmosphere. Therefore, the concentration of sodium hydroxide will decrease in the solution over time. Because of these problems, solutions of sodium hydroxide need to be standardized.

Standardization of NaOH solutions generally involve the titration of the solution against an acid that can be accurately weighed. The acid that is used in most cases is potassium hydrogen phthalate, KC8H6O4, generally known by the acronym KHP. A structural formula of KHP is shown on the next page. It is a potassium salt of the phthalate ion, C8H6O4¯, which is a weak acid. The reaction between C8H6O4¯ and NaOH is a typical acid-base neutralization reaction:

C8H6O4¯(aq) + NaOH(aq) ¾ ¾ ® C8H5O42-(aq) + Na+(aq) + H2O(l) (7)

In the standardization procedure, an accurately weighed sample of KHP is dissolved in water. The sodium hydroxide solution is added to the KHP solution via a buret until a phenolphthalein endpoint is reached. At the endpoint, the number of moles of NaOH contained in the added solution equals the number of moles of KHP neutralized. The volume of NaOH solution is read off the buret. Since the number of moles of NaOH and the volume of solution are known, the concentration of NaOH can be determined.

Figure 1 Structural Formula for KHP

In the second part of the experiment, you will be given a solution containing an unknown concentration of a monoprotic weak acid, referred to here as "HA". First, you will perform a titration against the standardized NaOH solution to a phenolphthalein endpoint to determine the concentration of the weak acid solution. Then you will construct a titration curve for the titration of NaOH versus this weak acid by performing a titration while monitoring the pH of the acid solution with a pH meter. A titration curve is a plot of pH (vertical axis) versus volume of titrant added. In the titration of a weak acid versus NaOH solution, a plot of pH versus volume of NaOH solution added will result in a titration curve that looks like this:

Figure 2 Typical Weak Acid-Strong Base titration curve

Before addition of any NaOH solution, the weak acid solution will have a fairly low pH. As you add sodium hydroxide solution, an acid-base neutralization reaction occurs:

HA(aq) + NaOH(aq) ¾ ¾ ®(aq) + Na+(aq) + H2O(l) (8)

As you add NaOH solution, since acid is being neutralized, the pH should increase. After initial addition of NaOH solution, you will have a solution in which there are significant concentrations of a weak acid, HA, and its conjugate base, A¯. This is the definition of a buffer solution. Remember that a buffer solution resists changes in pH. Therefore, the pH will not change very much upon addition of NaOH solution. This will result in the titration curve being fairly "flat" in this buffer region (from 5 mL to about 25 mL of NaOH added in Figure 2). Eventually, a point will be reached where most of the weak acid has been neutralized and the solution will no longer act as a buffer. At this point, the pH starts to increase rapidly as can be seen in figure 2. The equivalence point of a titration is the point at which all of the acid has been neutralized. At the equivalence point, the number of moles of NaOH added will be equal to the initial number of moles of HA. The equivalence point in a titration curve is the point in the curve with the steepest slope. It is also an inflection point in the curve. In figure 2, the equivalence point occurs just before a pH of 8. As more NaOH solution is added, the pH will continue to increase until it approaches the pH of the NaOH titrant, at which point, it will begin to level off.

In the buffer region of the titration curve, the pH can be determined using the Henderson-Hasselbach equation:

(9)

Notice when [A¯] = [HA], the pH = pKa for the weak acid HA. In a titration curve, [A¯] will be equal to [HA] when exactly half of the acid has been neutralized by the NaOH solution. This occurs at the half-equivalence point in the titration. The half-equivalence point is found by first determining where the equivalence point occurs by plotting the titration curve and finding the point with the steepest slope. Once the volume of the equivalence point is determined, divide this volume in half and find the pH associated with this half-volume on the titration curve. In figure 2 above, the volume of the equivalence point occurs at approximately 26.3 mL of NaOH added. Cutting this volume in half gives a volume of 13 mL for the half-equivalence point. The pH at a volume of about 13 mL is approximately 4.65.

 

Laboratory Procedure

Before mixing the solutions, the sodium hydroxide solution must be standardized in order to obtain a more accurate concentration of NaOH:

Standardization of approximately 0.1 M NaOH

1- Obtain a sample of dried potassium hydrogen phthalate, KHC8H4O4, from the instructor and accurately weight a 0.7-0.9 gram sample to the nearest 0.0001 g. Transfer to a 250 mL Erlenmeyer flask from your drawer.

2- Dissolve the sample in 50.0 mL of deionized water and add 2 drops of phenolphthalein.

3- Titrate with NaOH solution until you obtain the first pale pink color that persists for more than 30 seconds after addition of the last drop. The neutralization reaction is given by equation 7.

4- Record the volume of NaOH solution added to the nearest 0.01 mL.

5- Repeat steps 1-4 for a second sample of potassium hydrogen phthalate.

6- The concentration of the NaOH solution is determined by calculating the number of moles of NaOH contained in the added solution and dividing by the volume, in liters, of the added solution. At the endpoint, the number of moles of NaOH contained in the added solution will be equal to the initial number of moles of KHC8H4O4 weighed out:

moles of NaOH added = moles of KHC8H4O4 (10)

7- The concentration of NaOH will be equal to the moles of NaOH added divided by the volume, in liters, of the added solution for each titration:

[NaOH] = (11)

8- Average the two calculated concentrations to obtain the concentration of the standardized NaOH solution.

Determination of the concentration of the weak acid solution

9- Obtain a weak acid solution from the instructor. Write down the unknown number on your data sheet.

10- Transfer 25.00 mL of the weak acid solution using a 25 mL pipet to a 125 mL erlenmeyer flask. Add 2-3 drops of phenolphthalein to the solution.

11- Titrate with NaOH solution until you obtain the first pale pink color that persists for more than 30 seconds after addition of the last drop. Record the volume of added NaOH solution to the nearest 0.01 mL.

12- Calculate the number of moles of added NaOH solution from the volume of added solution and the concentration of NaOH solution calculated previously:

(12)

13- Since this is a monoprotic acid, the number of moles of NaOH added at the endpoint will be equal to the number of moles of acid contained in 25.00 mL of the weak acid solution.

Moles of NaOH = Moles of acid (13)

14- Calculate the concentration of the weak acid by dividing the number of moles of acid by the volume of the solution in liters (0.02500 L).

(14)

Construction of a titration curve for your weak acid

14- Calibrate the pH meter according to the instructions given to you in the pre-lab.

15- Transfer 25.00 mL of your weak acid solution to a 150 mL beaker. Place the electrode of the pH meter in the solution and record the pH of the solution.

16- Begin the titration by adding approximately 1 mL of NaOH solution to your weak acid solution. Record the volume added to the nearest .01 mL. Do not waste time trying to add exactly 1.00 mL of NaOH solution. Stir the solution in the beaker and record the pH of the solution.

17- Continue adding approximately 1 mL portions of NaOH solution then record the total volume of NaOH solution added and the pH of the solution until you come within 1.5 mL of the end point of the titration (determined in step 11). Don't forget to stir the solution before reading the pH. When you get within 1.5 mL of the endpoint, reduce the portion of added solution to about 0.1 mL then record the total volume of NaOH solution added and the pH of the solution. Continue with the 0.1 mL portions until the pH stops changing drastically (about a pH of 10).

18- Continue with at least 5 more approximately 1 mL portions of NaOH solutions. Remember to record the total volume of NaOH solution added and the pH of the solution at each stopping point.

19- Repeat steps 14 through 18 for one more titration.

20- Construct a titration curve for each titration by plotting pH (vertical axis) versus volume of NaOH solution added (horizontal axis).

21- For each titration curve, estimate the position of the equivalence point to the nearest 0.02 pH unit and the nearest 0.1 mL.

22- For each titration curve, estimate the pKa of your weak acid to the nearest 0.02 pH unit by finding the pH at the half-equivalence point. Average your two pKa values. Calculate the value of the Ka for the acid from your pKa value.

 

Preliminary Problem

 

Name: Section:

Answer the following problem to the best of your ability showing all work necessary to obtain the answer. The answer should be reported with the correct number of significant figures and with the appropriate units on it.

In a standardization procedure, it took 23.45 mL of NaOH solution to reach an endpoint when titrated against a solution prepared by dissolving 0.6432 g of KHP in 50 mL of water. Calculate the concentration of NaOH. The standardized NaOH solution was then titrated against 25.00 mL of a monoprotic weak acid solution to a phenolphthalein endpoint. If it took 17.76 mL of the NaOH to reach the endpoint, what is the concentration of the weak acid solution?