Experiment 19:  Titration of Phosphoric Acid

Objective

Solutions of pure phosphoric acid and of phosphoric acid mixed with its conjugate base, dihydrogen phosphate, will be titrated with a strong base. The data from the titration of the pure phosphoric acid will be used to determine the concentration of the acid. The titration of the mixture will be done to illustrate the effect of the conjugate base on the titration curve.

Introduction

Acids that contain more than one acidic (ionizable) hydrogen (proton) are called polyprotic or polybasic acids. The dissociation of polyprotic acids occurs in a stepwise fashion, one proton lost at a time. For example, the generic triprotic acid will dissociate as shown in Reactions (1) through (3). The equilibrium constants for these reactions are symbolized by Ka. The trailing subscript "a" indicates that the equilibrium constant describes an acid dissociation reaction. The trailing subscript "n" is written as a number and indicates which proton is being dissociated.

Reactions such as those shown in Reactions (4) and (5) are sometimes used as the basis of chemical calculations, but these reactions are generally not considered to be representative of what is actually occurring in solution. These reactions can be useful at times even though they are not rigorously correct chemically. The equilibrium constant for Reaction (4) is the product of Ka1 and Ka2 while the equilibrium constant for Reaction (5) is the product of Ka1, Ka2, and Ka3. Prove this to yourself.

Remember that the numerical value of an equilibrium constant is an indication of how far to the right a reaction proceeds. The greater the magnitude of the equilibrium constant, the more complete the reaction. Generally the numerical value of Ka1 is larger than that of Ka2, which is larger than Ka3 This is reasonable when one considers that successive protons are removed from species with progressively higher negative charges.

Polyprotic acids are called polybasic because they have more than one conjugate base. A conjugate base is a species that is produced when an acid loses a proton. For example, the species H2A-, HA2-, and A3- are all conjugate bases of H3A. The completely deprotonated acid, A3-, is a weak base. The other two conjugate bases are also weak bases, but in addition they have one or more acidic protons. As a result these species are amphiprotic or amphoteric, which means that they can act as either an acid or a base. Molecules that are partially deprotonated polyprotic acids are called acid salts. A common acid salt is sodium bicarbonate, NaHCO3, which is found in baking soda.

When a strong base is added to a solution of a polyprotic acid, the protons of the acid are neutralized in a stepwise fashion. That is, Reaction (6) will occur first until all of the H3A is used up. Then Reaction (7) will begin and will continue until all of the H2A- is gone. Then Reaction (8) will occur until all of the HA2- is gone. This will only be true when the successive dissociation constants are different by a large enough factor and when all of the acidic species are strong enough. For example, phosphoric acid has Ka values that are different by a large enough factor to allow it to react with a strong base in a stepwise fashion, however, the value of Ka3 for phosphoric acid is so small that the last proton of phosphoric acid is extremely difficult to remove, and the reaction of phosphoric acid that is analogous to Reaction (8) essentially will not occur in aqueous solution.

The titration curve for the titration of a polyprotic acid such as phosphoric acid will have the form shown in Figure 1. This curve is a plot of pH (-log[H30+]) versus the volume of base added. The first point on the curve corresponds to a solution of phosphoric acid only. The pH at this point is due solely to the phosphoric acid in the solution. As soon as some base is added, some H2PO4- is produced. The solution now contains both phosphoric acid (a weak acid) and its conjugate base dihydrogen phosphate, and thus it is a buffer. A buffer is a solution that is resistant to change in pH upon dilution and addition of acid and base. This will be the situation from the initial point to the first equivalence point, and therefore this region of the curve is called the first buffer zone. The pH of the point midway between the first and second equivalence points is equal to the negative logarithm of Ka1, pKa1. At the first equivalence point, all of the H3PO4 has been neutralized and only H2P04- is present in the solution. When more base is added, some of the H2P04- is neutralized and some HP042- is produced. This solution contains both dihydrogen phosphate (a weak acid) and its conjugate base hydrogen phosphate, and thus is a buffer. At all points between the first and second equivalence points, the solution will contain these two species, and therefore this portion of the curve is called the second buffer zone. The pH of the solution at the point halfway between the second and third equivalence points is equal to pKa2. At the second equivalence point the only species in the solution is HPO42-. The region between the second and third equivalence points is called the third buffer zone because the solution contains both the weak acid HPO42- and its conjugate base PO43-. Halfway between the second and third equivalence points the pH of the solution is equal to pKa3. At the third equivalence point, only the weak base PO43- is in the solution. After the third equivalence point, the solution contains phosphate ion and excess unreacted OH-.

Figure 1. Titration curve for titration of phosphoric acid with sodium hydroxide. The point marked "a" is the initial point. The pH of the solution equals pKa1, pKa2, and pKa3 at points b, d, and f, respectively. Points c, e, and g are the first, second, and third equivalence points, respectively. The points between a and c, between c and e, and between e and g are the first, second, and third buffer zones, respectively.
Changes in the pH during the titrations you will do in this experiment will be monitored with a glass pH electrode (probe). This electrode will generate a potential in proportion to the hydronium ion concentration in the solution. The pH meter will electronically convert this potential to pH. Titrations monitored with electrodes, such as glass electrodes, that measure a potential are called potentiometric titrations.

In this experiment you will titrate a solution containing only phosphoric acid. The curve from this titration will be used to calculate the concentration of the phosphoric acid and to calculate the Ka1 and Ka2 values of phosphoric acid. You will also titrate a mixture of phosphoric acid and potassium dihydrogen phosphate to discover the effect the added species has on the titration curve of phosphoric acid.

More information on Acid-Base Equilibria can be found at http://www.chem.vt.edu/RVGS/APChem/notes/Acid-Base_Equilibrium.html

Procedure

1. Titration of H3PO4

Set up the LabPro and pH electrode on a computer. Set the data collection to Event with Entry. Make sure that the y-axis (the pH) goes from 0 to 14.

Next fill a 50.00 mL buret to the 0.00 mL level with standard 1 M NaOH. Then pipet 20.00 mL of the phosphoric acid solution into a 100 mL beaker. Place the pH probe in the acid letting the pH value equilibrate, then begin adding the NaOH in 0.50 mL increments for each entry while carefully stirring with the probe. Watch the computer screen as the titration curve develops and continue adding NaOH until the curve has peaked and leveled off. You do not need to record the final level off the buret because you have passed the equivalence point by several milliliters.

Save the data and graph. Then repeat the procedure two more times using the same amount of acid for each trial. Adjust the x-axis if necessary. Be sure to also save the data from these two trials.

2. Effect of KH2PO4 on the titration curve:

Add 20 mL of the phosphoric acid to a 100 L beaker and then mix in 20 mL of distilled water. Titrate as before. Repeat with another 20 mL of phosphoric acid but this time mix in 20 mL of 0.3 M KH2PO4 solution. Titrate as before.

Analysis:

1. Titration of H3PO4

Place a small "x" at both equivalence points (label as 1 and 2) and an "x" at the location you think represents the pKa1 and pKa2 values. Calculate the values of Ka1 and Ka2.

Repeat the previous two paragraphs with the second and third trials. Then take an average of the values of Ka1 and Ka2, and the average deviation for each. Look up the literature values of Ka1 and Ka2 for phosphoric acid and calculate your error.

Explain why you selected the locations you marked with an "x" as being the equivalence points and as representing pKa1 and pKa2. What could have been contributing factors in any error you got, especially if you were off by more than 10%? DO NOT use "human error" as a factor!

2. Effect of KH2PO4 on the titration curve:

Compare the two curves. Describe and explain the differences you see in these two titration curves.