Identifying an Unknown
A diprotic acid is an acid that yields two H^{+} ions per acid molecule. Examples of diprotic acids are sulfuric acid, H_{2}SO_{4}, and carbonic acid, H_{2}CO_{3}. A diprotic acid dissociates in water in two stages:
(1) H_{2}X(aq) H^{+}_{(aq)} + HX^{}_{(aq)}
(2) HX^{}_{(aq)} H^{+}_{(aq)} + X^{2}_{(aq)}
Because of the successive dissociations, titration curves of diprotic acids have two equivalence points, as shown in Figure 1. The equations for the acidbase reactions occurring between a diprotic acid, H_{2}X, and sodium hydroxide base, NaOH, are:
(3) H_{2}X + NaOH NaHX + H_{2}O
from the beginning to the first equivalence point:
from the first to the second equivalence point:
(4) NaHX + NaOH Na_{2}X + H_{2}O
from the beginning of the reaction through the second equivalence
point (net reaction):
(5) H_{2}X + 2 NaOH Na_{2}X + 2
H_{2}O
At the first equivalence point, all H^{+} ions from the first
dissociation have reacted with NaOH base. At the second equivalence
point, all H+ ions from both reactions have reacted (twice as many as
at the first equivalence point). Therefore, the volume of NaOH added
at the second equivalence point is exactly twice that of the first
equivalence point (see Equations 3 and 5).
The primary purpose of this experiment is to identify an unknown diprotic acid by finding its molecular weight. A diprotic acid is titrated with NaOH solution of known concentration. Molecular weight (or molar mass) is found in g/mole of the diprotic acid. Weighing the original sample of acid will tell you its mass in grams. Moles can be determined from the volume of NaOH titrant needed to reach the first equivalence point. The volume and the concentration of NaOH titrant are used to calculate moles of NaOH. Moles of unknown acid equal moles of NaOH at the first equivalence point (see Equation 3). Once grams and moles of the diprotic acid are known, molecular weight can be calculated, in g/mole. Molecular weight determination is a common way of identifying an unknown substance in chemistry.
You may use either the first or second equivalence point to calculate molecular weight. The first is somewhat easier, because moles of NaOH are equal to moles of H_{2}X (see Equation 3). If the second equivalence point is more clearly defined on the titration curve, however, simply divide its NaOH volume by 2 to confirm the first equivalence point; or from Equation 5, use the ratio:
1 mole H_{2}X / 2 mol NaOH
MATERIALS
CBL System
TI8X Graphing Calculator
Vernier pH Amplifier
Vernier pH Electrode
Vernier adapter cable
TIGraph Link
unknown diprotic acid, 0.120 g
milligram balance
~0.1 M NaOH solution (standardized)
magnetic stirrer (if available)
stirring bar
ring stand
2 utility clamps
250mL beaker
wash bottle
distilled water
PROCEDURE
1. Obtain and wear goggles.
2. Weigh out about 0.120 g of the unknown diprotic acid on a piece of weighing paper. Record the mass to the nearest 0.001 g in the Data and Calculations table. Transfer the unknown acid to a 250mL beaker and dissolve in 100 mL of distilled water.
3. Place the beaker on a magnetic stirrer and add a stirring bar. If no magnetic stirrer is available, you need to stir with a stirring rod during the titration.
4. Prepare the pH system for data collection.
5. Use a utility clamp to suspend a pH electrode on a ring stand as shown in Figure 2. Position the pH electrode in the HCl solution and adjust its position toward the outside of the beaker so that it is not struck by the stirring bar.
6. Obtain a 50mL buret and rinse the buret with a few mL of the ~0.1 M NaOH solution. Record the precise concentration of the NaOH solution in the Data and Calculations table. Use a utility clamp to attach the buret to the ring stand as shown in Figure 2. Fill the buret a little above the 0.00mL level of the buret. Drain a small amount of NaOH solution so it fills the buret tip and leaves the NaOH at the 0.00mL level of the buret. Dispose of the waste solution in this step as directed by your teacher.
7. Turn on the CBL unit and the TI8X calculator. Press PRGM and select CHEMBIO. Press ENTER, then press ENTER again to go to the CHEM MAIN MENU.
8. Set up the calculator and CBL for pH measurement.
9. Set up the calculator and CBL for data collection.
10. You are now ready to begin the titration. This process goes faster if one person manipulates and reads the buret while another person operates the calculator and enters buret readings.
11. STOP AND GRAPH from the DATA COLLECTION menu when you have finished collecting data. Use RIGHT ARROW to examine the data points along the displayed graph of pH vs. NaOH volume. As you move the cursor right or left, the volume (X) and pH (Y) are displayed below the graph.
One of the two equivalence points is usually more clearly defined than the other; the twodrop increments near the equivalence points frequently result in larger increases in pH (a steeper slope) at one equivalence point than the other. Indicate the more clearly defined equivalence point (first or second) in Box 1 of the Data and Calculations table. Determine the volume of NaOH titrant used for the equivalence point you selected. To do so, examine the data to find the largest increase in pH values during the 2drop additions of NaOH. Find the NaOH volume just before this jump. Then find the NaOH volume after the largest pH jump. Record these values in Box 2 of your data table.
For the alternate equivalence point (the one you did not use in the previous step), examine the data points on your graph to find the largest increase in pH values during the 2 drop additions of NaOH. Find the NaOH volume just before and after this jump. Record these values in Box 10 of your data table.
12. Dispose of the beaker and buret contents as directed by your teacher. Rinse the pH electrode with distilled water and return it to the storage solution.
13. To obtain a printed graph of pH vs. volume and a printed copy of the data:
PROCESSING THE DATA
1. Use your graph and data table to confirm the volumes you recorded in Box 2 of the Data and Calculations table (volumes of NaOH titrant before and after the largest increase in pH values). Underline both of these data pairs on the printed data table.
2. Determine the volume of NaOH added at the equivalence point you selected in Step 1. To do this, add the two NaOH volumes determined in Step 1, and divide by two.
3. Calculate the number of moles of NaOH used at the equivalence point you selected in Step 1.
4. Determine the number of moles of the diprotic acid, H_{2}X. Use Equation 3 or Equation 5 to obtain the ratio of moles of H_{2}X to moles of NaOH, depending on which equivalence point you selected in Step 1.
5. Using the mass of diprotic acid you measured in Step 1 of the procedure, calculate the molecular weight of the diprotic acid, in g/mol.
6. From the following list of five diprotic acids, identify your unknown diprotic acid.

Diprotic Acid 
Formula 
Molecular weight 



Oxalic Acid 
H_{2}C_{2}O_{4} 
90 


Malonic Acid 
H_{2}C_{3}H_{2}O_{4} 
104 


Maleic Acid 
H_{2}C_{4}H_{2}O_{4} 
116 


Malic Acid 
H_{2}C_{4}H_{4}O_{5} 
134 


Tartaric Acid 
H_{2}C_{4}H_{4}O_{6} 
150 

7. Determine the percent error for your molecular weight value in Step 5.
8. Use your graph and data table to confirm the volumes you recorded in Box 10 of the Data and Calculations table (volumes of NaOH titrant before and after the largest increase in pH values at the alternate equivalence point). Underline both of these data pairs on the printed data table. Note: Dividing or multiplying the other equivalence point volume by two may help you confirm that you have selected the correct two data pairs in this step.
9. Determine the volume of NaOH added at the alternative equivalence point, using the same method you used in Step 2 of Processing the Data.
10. On your printed graph, clearly specify the position of the equivalence point volumes you determined in Steps 2 and 9, using dotted reference lines like those in Figure 1. Specify the NaOH volume of each equivalence point on the horizontal axis of the graph.
EXTENSION
Using a halftitration method, it is possible to determine the acid dissociation constants, K_{a1} and K_{a2}, for the two dissociations of the diprotic acid in this experiment. The Ka expressions for the first and second dissociations, from Equations 1 and 2, are:
The first halftitration point occurs when onehalf of the H^{+} ions in the first dissociation have been titrated with NaOH, so that [H_{2}X] = [HX^{}]. Similarly, the second halftitration point occurs when onehalf of the H^{+} ions in the second dissociation have been titrated with NaOH, so that [HX^{}] = [X^{2}]. Substituting [H_{2}X] for [HX^{}] in the K_{a1} expression, and [HX^{}] for [X^{2}] in the K_{a2} expressions, the following are obtained:
K_{a1} = [H^{+}] K_{a2} = [H^{+}] Taking the baseten log of both sides of each equation,
logK_{a1} = log[H^{+}]; logK_{a2} = log[H^{+}]
the following expressions are obtained:
pK_{a1} = pH; pK_{a2} = pH
Thus, the pH value at the first halftitration volume,
Point 1 in Figure 3, is equal to the pK_{a1} value. The first
halftitration point volume can be found by dividing the first
equivalence point volume by two.
Similarly, the pH value at the second titration point, is equal to
the pK_{a2} value. The second halftitration volume (Point 2
in Figure 3) is midway between the first and second equivalence point
volumes (1st EP and 2nd EP). Use the method described below to
determine the K_{a1} and K_{a2} values for the
diprotic acid you identified in this experiment.
1. Determine the precise NaOH volume for the first halftitration
point using onehalf of the first equivalence point volume
(determined in Step 2 or Step 9 of Processing the Data). Then
determine the precise NaOH volume of the second half titration point
halfway between the first and second equivalence points.
2. On your graph of the titration curve, draw reference lines similar to those shown in Figure 3. Start with the first halftitration point volume (Point 1) and the second halftitration point volume (Point 2). Determine the pH values on the vertical axis that correspond to each of these volumes. Estimate these two pH values to the nearest 0.1 pH unit. These values are the pK_{a1} and pK_{a2} values, respectively. (Note: See if there are volume values in your data table similar to either of the halftitration volumes in Step 1. If so, use their pH values to confirm your estimates of pK_{a1} and pK_{a2} from the graph.)
3. From the pK_{a1} and pK_{a2} values you obtained in the previous step, calculate the K_{a1} and K_{a2} values for the two dissociations of the diprotic acid.