Acid-Base Titrations Using ph Measurements Introduction According to the Brønsted Lowry definition, an acid is a substance that donates a hydrogen ion and a base is a substance which will accept a hydrogen ion. Whether an acid is strong or weak is determined by how much they dissociate in water. When an acid is strong, the dissociation is virtually complete. When an acid is weak, the dissociation is much less. A strong acid exists mostly as ions and a weak acid exists mostly as molecules. The extent to which a weak acid will dissociate is indicated by the magnitude of its acid dissociation constant (K a ) which is the equilibrium constant for the dissociation reaction for that acid. For example, the dissociation of acetic acid in water is HC 2 H 3 O 2 + H 2 O H 3 O + + C 2 H 3 O 2 (1) Since acetic acid is a weak acid, the equilibrium will lie mostly to the left and have a small K a. When you titrate a weak acid with a strong base, such as NaOH, the reaction will go essentially to completion, giving an acidic solution until just before the equivalence point OH + HC 2 H 3 O 2 C 2 H 3 O 2 + H 2 O (2) At the equivalence point, the ph will not be 7. This is because the weak conjugate base, acetate ion, is the major species in solution. Acetate ion react with water to give a basic solution: C 2 H 3 O 2 + H 2 O OH + HC 2 H 3 O 2 (3) When you are titrating a weak acid with a strong base and you plot your data (ph vs ml), you will notice that the inflection point in your graph where the equivalence point is located does not show as pronounced a change in ph as that of a titration of a strong acid with a strong base. The size of the inflection point depends on the Ka of the acid. If the acid is too weak, this change becomes so small that it is not possible to identify an inflection point. Acetic acid is a monoprotic acid and so therefore, you will see only one inflection point on your graph. In the second part of this experiment, you will be titrating a solution of phosphoric acid. As you know, phosphoric acid is a weak triprotic acid. The dissociation of each of these protons (hydrogen ions) from the molecule will occur in steps. The first proton will dissociate more readily than the second proton, which will dissociate more readily than the third. When you plot your data (ph vs ml), you will see that the first equivalence point will be very clear, the second equivalence point will be harder to notice with the third probably not being evident. In order to find the equivalence points clearly for both parts of this experiment, you will have to treat your data appropriately so you can plot a first and second derivative plot. Instructions for the treatment of your data are located at the end of this experiment. 26
Procedure Part I Titration of Acetic Acid 1. Rinse a buret with a few milliliters of the provided standardized sodium hydroxide solution, fill and remove the air bubble from the tip. Make sure you record the molarity of this sodium hydroxide solution since you will need it to calculate the molarity of the acetic acid solution. 2. Obtain an acetic acid solution with an unknown concentration. Record the unknown letter. 3. Pipet 25.00 ml of the unknown solution into a 250-mL beaker. Add 25 ml of distilled water (graduated cylinder) and a teflon-coated stir bar. Place the beaker on the stir plate. The first titration you will perform will be a trial titration so you can get the approximate volume of sodium hydroxide that is required to reach the equivalence point. Add a few drops of phenolphthalein indicator to give help visualize the equilvalence point. 4. Place the ph electrode in the acetic acid solution and record the ph before any sodium hydroxide is added. Keep the electrode in the solution for the duration of the titration. 5. Record the initial volume of the buret to an accuracy of 0.01 ml. Start the stirrer. 6. Add approximately 1 ml of NaOH solution. Record the final volume to 0.01 ml. 7. Record the ph after the reading has stabilized. 8. Repeat steps 6 and 7 until you observe the equivalence point (you will notice a sharp increase in the ph of the solution). Go past the equivalence point in the same way until the ph reaches about 11 to 12. Now that you know approximately what volume of sodium hydroxide you need to reach the equivalence point, repeat the titration, but with more data recorded in the vicinity of the equivalence point. Sketching a rough plot in your notebook will help you find that point. 9. Pipet 25.00 ml of the unknown solution into a 250-mL beaker and add 25 ml of distilled water (graduated cylinder). Do not add phenolphthalein indicator. 10. Record the initial volume of the buret to 0.01 ml and the ph. 12. Add approximately 1 ml of NaOH solution. Record the final volume to 0.01 ml. 13. Mix the solutions thoroughly and record the ph. 27
14. Repeat 12 and 13. When you are within about 5 ml of the equivalence point (determined in the first titration), add the NaOH in increments of about 0.5 ml for the next 3 ml and then in increments of about 0.2 ml or less for the next 2 ml. Continue for 5 ml on the other side of the equivalence point in a mirror image (about 0.2, then 0.5 ml increments). Record all volumes to 0.01 ml accuracy. Part II Titration of Phosphoric Acid As in Part I, obtain a phosphoric acid solution of unknown concentration. Record the unknown designation. Add 3 drops of bromocresol green before you begin. This indicator will undergo a color change when you have reached the first equivalence point. Proceed as before with a trial titration. Record the volume, color and ph as you titrate. You will be able to clearly determine when you have reached the first equivalence point by a color change. You will not clearly see the second, but it will be approximately two times the first. You will not see the third equivalence point at all. Proceed as before (Part I) with a good titration. Do not add any indicator. Obtain good data points in the vicinity of the first and the second equivalence points. You can take longer intervals after the first and within about 5 ml of the second (which should be twice the first point). Record the volume, color and ph as you titrate. Question 1. Calculate the missing ph s in the following titration of 10.0 ml of 0.10 M weak acid, HA, (K a = 1.0 x 10 5 ) with 0.10 M NaOH solution. Tabulate and plot three graphs: the titration curve, the first derivative and the second derivative (see page 29). ml 0.10 M NaOH ph 0.00 3.00 1.00 4.05 2.50 4.52 5.00 5.00 7.50 5.48 8.75 5.85 9.50 6.28 9.75 6.59 9.90 7.00 10.00 8.85 10.10 10.70 10.25 11.09 10.50 11.39 12.75 12.08 15.00 12.30 28
Data Treatment and Discussion 1. Using a spreadsheet, tabulate the good titration data of the acetic acid and the phosphoric acid unknowns. Calculate the first and second derivatives. Show one sample calculation of the first and second derivative in your notebook. An example is shown below. v (ml NaOH) ph v ' (ml) f ' (ph/v) v'' (ml) f '' (f /v ) 20.50 11.59 20.75 0.02 21.00 0.04 21.00 11.60 21.25 0.04 21.50 0.16 21.50 11.62 21.75 0.12 21.00 0.08 22.00 11.68 22.25 0.08 22.50 11.72 v ' is the average of two consecutive volumes: 21.00 + 20.50 = 20.75 2 and f ' is calculated by taking the difference in ph and dividing by the difference in volume of NaOH. 11.60 11.59 0.01 = = 0.02 21.00 20.50 0.50 v '' is the average of consecutive v ': 21.25 + 20.75 = 21.00 2 and f '' is calculated by taking the difference in f ' and dividing it by the difference in v'. 0.04 0.02 0.02 = = 0.04 21.25 20.75 0.50 A spreadsheet to do this calculation for all your tabulated data looks like: A B C D E F 1 Volume ph v' (ml) f' ( ph/ v) v'' (ml) f'' ( ph 2 / 2 v) 2 A2 B2 =(A2+A3)/2 =(B3-B2)/(A3-A2) =(C2+C3)/2 =(D3-D2)/(C3-C2) 3 A3 B3 =(A3+A4)/2 =(B4-B3)/(A4-A3) =(C3+C4)/2 =(D4-D3)/(C4-C3) 4 A4 B4 =(A4+A5)/2 =(B5-B4)/(A5-A4) =(C4+C5)/2 =(D5-D4)/(C5-C4) 5 A5 B5 =(A5+A6)/2 =(B6-B5)/(A6-A5) =(C5+C6)/2 =(D6-D5)/(C6-C5) 6 A6 B6 =(A6+A7)/2 =(B7-B6)/(A7-A6) 7 A7 B7 Note: The last cell in C and D and the last two cells of E and F will contain no data. 29
2. For Part I, make a plot of ph vs ml of NaOH solution added, a first derivative plot and a second derivative plot. The plots are column B versus column A, column D versus column C, and column F versus column E. The equivalence point is found at the volume corresponding to the x-intercept of the second derivative curve. This point should be coincident with the inflection point (the point at which the curve changes direction) of the original data plot and the peak of the first derivative plot. Read the equivalence point volume, to 4 significant figures, off the graph. Expand the x axis to read it accurately. 3. For Part II, find the volume of sodium hydroxide at the first and the second equivalence points by plotting the first and second derivative of your good data as in #2 above. 4. Calculate the molarity of the original acetic acid solution using the equivalence point off the graph. The volume of the original solution was 25.00 ml. Do not include the 25 ml of water added from the graduated cylinder. You are still titrating moles. 5. Calculate the molarity of the original phosphoric acid solution using both equivalence points and give the average. Conclusion In order to calculate the molarity of the H 3 PO 4 solution, use the first equivalence point in a 1:1 reaction and use the difference between the second equivalence point and the first also in a 1:1 reaction. Take the average of the two molarities. Give the unknown number and the molarity of the acetic acid solution and the unknown number and the molarity of the phosphoric acid solution. Also address: In part II, are the first equivalence point and the difference from the second equivalence point identical? If not, suggest a reason. What is the advantage to using a ph electrode and meter to find the equivalence point versus a visual indicator? 30