Exercise 4-3 Titration of Weak Acids EXERCISE OBJECTIVE Titrate both a weak acid solution and a weak polyprotic acid solution with a strong base solution. Plot a graph using the titration data, analyze the titration curves, and calculate the ph of a weak acid solution. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: The 5% rule Weak acids Calculation of the ph of a weak acid solution First method (5% rule approximation). Second method (the long one). Weak bases Calculation of the ph of a weak base solution DISCUSSION The 5% rule The measurement and calculation of ph involves concentrations covering up to 14 orders of magnitude. Within this wide range of concentrations, smaller values that are added to a value that is greater by 2 or 3 orders of magnitude often lead to no significant difference in ph value. Furthermore, having a very precise theoretical ph value is often useless because most ph measurement devices are not accurate to the hundredths of a ph unit, whatever is claimed by the manufacturers. Even when using high quality probes, temperature and calibration have an important influence on the measured ph value. To simplify matters when calculating the theoretical ph of a weak solution, the 5% rule can be used. The 5% rule states that "an approximation leading to a 5% variation in the hydronium concentration (or less) can be used if it simplifies the calculation, since it has little influence on the final ph value." Because it has only a small influence on the ph value of an aqueous solution, the contribution of the selfionization of water to the ph of a strong acid or strong base solution is often neglected in the calculation. The 5% rule is important when calculating the ph of a weak acid or a weak base solution because it can save time by simplifying the calculation. If the change in the concentration of the undissociated weak acid (or weak base) is less than 5%, then you can approximate and avoid solving a quadratic equation. To apply the 5% rule for a weak acid, the following inequality must be true: (4-42) Similarly, for a weak base, the following inequality must be true: (4-43) Festo Didactic 86013-00 83
Ex. 4-3 Titration of Weak Acids Discussion Weak acids While strong acids completely dissociate in solution, weak acids usually have a percentage of dissociation between 1% and 5%. Figure 4-39 shows the proportion of the different chemical species in a solution before and after dissociation (at equilibrium). Before dissociation After dissociation Proportion of the chemical species Proportion of the chemical species Figure 4-39. Proportion of the chemical species before and after dissociation. In the solution, there is equilibrium between the undissociated acid and its dissociated ions. This equilibrium is governed by the dissociation constant,, which is a function of the concentration of dissociated ions and the concentration of undissociated acid molecules. Taking the following equilibrium equation as an example: The equilibrium constant is given by: Figure 4-40. Phosphoric acid (2D). The molarity of pure water at a temperature of 25 C (77 F) is a constant and is equal to 55.5 mol/l. This constant can be moved to the left side of the equation, which gives the acid dissociation constant definition given earlier: Figure 4-41. Phosphoric acid (3D). Polyprotic acids have more than one dissociation constant since they can ionize more than once. For example, phosphoric acid,, has three ionization stages. In the first stage of ionization ( ), the acid dissociation constant is ; in the second stage of ionization ( ), the acid dissociation constant is ; and, finally, in the third stage of ionization ( ), the acid dissociation constant is 84 Festo Didactic 86013-00
Ex. 4-3 Titration of Weak Acids Discussion If is much larger than (and ), one can assume that the hydronium ions come mainly from the first dissociation and use only to calculate the ph of the polyprotic acid solution. Calculation of the ph of a weak acid solution Unlike the ph value of strong acids, which can easily be calculated using the acid concentration, the ph of a weak acid requires a little more work. Because of the partial dissociation of weak acids, their dissociation constants are required for the calculation. In most cases, the 5% rule approximation, a simplified method of calculation, can be used to find the ph of a weak acid. However, in some cases, a more tedious calculation is required. Two methods of calculating the ph of a weak acid solution are presented in this section. The first one shows how to calculate the ph when an approximation is possible, and the second method explains in detail how to calculate the ph of a weak acid solution when the 5% rule approximation cannot be applied. First method (5% rule approximation) To illustrate this first method, the ph of a 0.1 mol/l solution of acetic acid is calculated. 1. Write the equation of dissociation of the weak acid at equilibrium: 2. Write the initial concentration of the weak acid: 3. Write the dissociation constant equation: Figure 4-42. Acetic acid (2D). a The of common weak acids can be found in Table 4-4. 4. There is (are) mole(s) of weak acid per liter that dissociate(s), therefore the concentration of hydronium is. Consequently the concentration of conjugate base is. 5. We presume that is small compared to the concentration of the weak acid: Figure 4-43. Acetic acid (3D). Consequently we can approximate that: Festo Didactic 86013-00 85
Ex. 4-3 Titration of Weak Acids Discussion 6. Using all those information, the dissociation constant equation can be rewritten as follows: 7. Therefore, the hydronium concentration is: 8. Always check the validity of the approximation using the 5% rule: 9. If the approximation is valid (as in the present case), calculate the ph of the weak acid solution: Second method (the long one) If, after using the approximate method, it is found at step 8 that the second method must be used., To illustrate this method, a 0.001 mol/l solution of acetic acid is used. Trying the first method to find the ph of this acetic acid solution and checking the 5% rule gives the following results: The 5% rule is not valid because. That is, Consequently, the long method must be used: 1. As in the first method, write the equation of dissociation of the weak acid at equilibrium: 2. Write the initial concentration of the weak acid: 86 Festo Didactic 86013-00
Ex. 4-3 Titration of Weak Acids Discussion 3. Write the dissociation constant equation: 4. There is (are) mole(s) of weak acid per liter that dissociate(s), therefore the concentration of hydronium is. Consequently the concentration of conjugate base is. 5. Using all information, the dissociation constant equation can be rewritten as follows (without approximation): Therefore, 6. This quadratic equation must be solved to calculate the hydronium concentration at equilibrium. The roots of this quadratic equation can be found using the following equation: (4-44) For the quadratic equation presented in step 5, the values for a, b, and c are: Therefore, the roots of the quadratic equation are: Since the concentration cannot be negative, the second root ( ) must be discarded and the positive root ( ) is the only possible solution. Consequently, the hydronium concentration is: 7. The hydronium concentration can then be used to calculate the ph of the weak acid solution: Festo Didactic 86013-00 87
Outline Comparing the ph value found here with the value obtained with the first method (ph = 3.87) demonstrates that, with an error on the hydronium concentration of about 7%, the error on the ph value is still small (about 0.8%) because of the logarithmic nature of ph. Nevertheless, this error cannot be neglected and the long method must be used. Weak bases Like weak acids, weak bases do not dissociate completely and the equilibrium is governed by their small dissociation constant. The reasoning is similar to the one for weak acids (the molar concentration of pure water is included in the base dissociation constant): Calculation of the ph of a weak base solution To calculate the ph of a weak base solution, the two methods presented for weak acids can be used; but the hydroxyl concentration must be found instead of the hydronium concentration. Once the hydroxyl concentration is found, the poh can be calculated and used to deduce the ph using the following relationship: PROCEDURE OUTLINE The Procedure is divided into the following sections: Set up and connections Titration of phosphoric acid Neutralizing the process water Titration of acetic acid Neutralizing the process water Titration curve analysis PROCEDURE Set up and connections Before using ANY of the chemicals provided with the ph Process Control Training System, read the chemical MSDS and wear the appropriate personal protective equipment. 1. Connect the equipment as the piping and instrumentation diagram (P&ID) in Figure 4-44 shows. Use Figure 4-45 to position the equipment correctly on the frame of the training system from the 3532 series or use Figure 4-46 to position the equipment on the frame from the 3531 series. Use the basic setup presented in the Familiarization with the Training System manual. Table 4-14 lists the equipment you must add to the basic setup in order to set 88 Festo Didactic 86013-00
up your system for this exercise. This setup is exactly the same as for Ex. 4-2, only the chemicals used are different. Table 4-14. Equipment required for this exercise. Name Part number Identification Volumetric flask 38406 Scopulla 38442 Sodium hydroxide solution 1.0 N 38444 Phenol red 38446 Graduated cylinder 38447 Phosphoric acid solution 1.0 N 38481 Latex gloves 40331-54 Pipette 40331-65 Safety glasses 40348 ph transmitter 46945 AIT Metering pumps 46956 Paperless recorder 46972 UR Water analyzer 46989 Chemical tanks 46994 Acetic acid 5% (v/v)(vinegar) 76764 Festo Didactic 86013-00 89
Figure 4-44. P&ID. 90 Festo Didactic 86013-00
Figure 4-45. Setup (series 3532). Festo Didactic 86013-00 91
Figure 4-46. Setup (series 3531). 2. Wire the emergency push-button so that you can cut power in case of an emergency. The Familiarization with the Training System manual covers the security issues related to the use of electricity with the system as well, as the wiring of the emergency push-button. 3. Wire the paperless recorder to record the output of the ph transmitter. 92 Festo Didactic 86013-00
4. Do not power up the instrumentation workstation yet. Do not turn the electrical panel on before your instructor has validated your setup that is not before step 9. Sodium hydroxide is corrosive and harmful if swallowed. Do not breathe vapor. Avoid eye and skin contact. Avoid prolonged or repeated exposure. When handling, wear chemical-resistant gloves, chemical safety goggles, and a lab coat. Refer to the MSDS for more details on this product. Phosphoric acid is corrosive and harmful if swallowed. Do not breathe vapor. Avoid eye and skin contact. Avoid prolonged or repeated exposure. When handling, wear chemical-resistant gloves, chemical safety goggles, and a lab coat. Refer to the MSDS for more details on this product. 5. To titrate a phosphoric acid solution with a strong base, one of the chemical tanks must be filled with a solution of 0.08 mol/l of sodium hydroxide and the other chemical tank with a solution of 0.08 mol/l of phosphoric acid. If you have only two chemical tanks available, empty the chemical tank containing hydrochloric acid, rinse it, and fill it with the phosphoric acid solution (see caution below). Be sure to drain the metering pump tubing as well. Refer to the Familiarization with the Training System manual for instructions to drain the metering pump tubing. Dispose of all solutions according to local environmental regulation. 6. Make sure there is enough alkaline solution left in the other tank and follow the procedure of Ex. 3-1 to prepare the diluted phosphoric acid solution. 7. Before proceeding further, complete the following checklist to make sure you have set up the system properly. The points on this checklist are crucial elements for the proper completion of this exercise. This checklist is not exhaustive. Be sure to follow the instructions in the Familiarization with the Training System manual as well. f All unused male adapters on the column are capped and the flange is properly tightened. The hand valves are in the positions shown in the P&ID. The chemical tanks are filled with the appropriate solutions and are carefully labeled. You are wearing the appropriate PPE. Festo Didactic 86013-00 93
The vent tube is properly installed. The paperless recorder is set up and configured to record the output of the ph transmitter. 8. Ask your instructor to check and approve your setup. Titration of phosphoric acid a Tap water usually contains salts that can act as a buffer solution. Therefore, a titration curve obtained using tap water may have a shape different from a standard titration curve. The shape of the curve strongly depends on the type of tap water used. To obtain a titration curve similar to a standard titration curve for the acids in this exercise, use the setup and procedure of Appendix F to filter the process water before proceeding to the titration exercise. This setup requires the optional conductivity process add-on. 9. Power up the electrical unit. This starts all electrical devices. 10. Make sure the ph probe is properly inserted into the connection port on the process workstation. 11. Test your system for leaks. Use the drive to make the pump run at low speed in order to produce a small flow rate. Gradually increase the flow rate up to 50% of the maximum flow rate the pumping unit can deliver (i.e., set the drive speed to 30 Hz). Repair all leaks. 12. Start the pump and set the drive speed to 30 Hz. This setup uses a telescopic pipe, which can extend if the pump runs at an excessive speed. Be sure to set the drive speed to a maximum of 30 Hz and secure the tubing with as much attach brackets, Model 85444, as possible. 13. Fill the column up to 25 cm of water. Then, close HV1 and open HV6 to put the process workstation into recirculation mode. 14. Remove one of the caps from the top of the column and, using a funnel, add about 20 ml of phenol red to the process water. 15. Using the metering pump connected to the chemical tank containing the solution of 0.08 mol/l of phosphoric acid, start injecting acid solution into the process water. The purpose of this operation is to drop the ph of the process 94 Festo Didactic 86013-00
water down to a value around 3.5. Set the metering pump to 50% of its maximum delivery rate. 16. Closely monitor the ph of the process water on the transmitter. Once the ph of the process water has dropped to a value of 3.5, stop the metering pump injecting the acid solution and wait two minutes to make sure the process water is perfectly mixed. 17. Once the ph value is stable, inject alkaline solution into the process water using the second metering pump. Set the metering pump delivery rate at around 50%. This stretches the titration process and provides more data for analysis. 18. Make sure the paperless recorder is recording the output of the ph transmitter. 19. Watch the titration process by observing both the tint of the process water given by the phenol red and the ph value measured by the paperless recorder. 20. Wait until the ph of the process water has increased to a value of 10.0 and stop the metering pump injecting the alkaline solution. The titration of a weak acid solution (phosphoric acid) with a strong base (sodium hydroxide) is completed. 21. Follow the procedure in the Familiarization with the Training System manual to transfer the data of the titration of phosphoric acid from the paperless recorder to a computer. Neutralizing the process water 22. The process water now contains a strong base solution. Hence, it is very important that you neutralize the process water before proceeding to the next steps. 23. Use the metering pump connected to the chemical tank containing the solution of 0.08 mol/l of phosphoric acid to decrease the ph of the process water. If necessary, reduce the delivery rate to avoid injecting too much acid solution. 24. When the ph gets close to 7.5, stop the metering pump and wait about one minute for the ph reading to stabilize. 25. If the ph is not between 6.5 and 7.5 after one minute, inject more acid and base until the ph is within the desired range. Festo Didactic 86013-00 95
Titration of acetic acid 26. Using the information provided in Unit 3, calculate (and record below) the volume of vinegar required to make 2 L of a 0.08 mol/l solution of acetic acid. 27. To titrate an acetic acid solution with a strong base, one of the chemical tanks must be filled with a solution of 0.08 mol/l of sodium hydroxide and the other chemical tank with a solution of 0.08 mol/l of acetic acid. If you have only two chemical tanks available, empty the chemical tank containing phosphoric acid, rinse it, and fill it with the acetic acid solution (see caution below). Be sure to drain the metering pump tubing as well. Refer to the Familiarization with the Training System manual for instructions to drain the metering pump tubing. Dispose of all solutions according to local environmental regulation. 28. Make sure there is enough alkaline solution left in the other tank and follow the procedure of Ex. 3-1 to prepare the diluted acetic acid solutions used the required volume of vinegar calculated at step 26. 29. Using the metering pump connected to the chemical tank containing the solution of 0.08 mol/l of acetic acid, start injecting acid solution into the process water. The purpose of this operation is to drop the ph of the process water down to a value around 4.0. Set the metering pump to 50% of its maximum delivery rate. 30. Closely monitor the ph of the process water on the transmitter. Once the ph of the process water has dropped to a value of 4.0, stop the metering pump injecting the acid solution and wait two minutes to make sure the process water is perfectly mixed. 31. Once the ph value is stable, inject alkaline solution into the process water using the second metering pump. Set the metering pump delivery rate at around 50%. This stretches the titration process and provides more data for analysis. 32. Watch the titration process by both observing the tint of the process water given by the phenol red and the ph value measured by the paperless recorder. 33. Wait until the ph of the process water has increased to a value of 10.0 and stop the metering pump injecting the alkaline solution. The titration of a weak 96 Festo Didactic 86013-00
acid solution (acetic acid) with a strong base (sodium hydroxide) is completed. 34. Follow the procedure in the Familiarization with the Training System manual to transfer the data of the titration of acetic acid from the paperless recorder to a computer. Neutralizing the process water 35. The process water now contains a strong base solution. Hence, it is very important that you neutralize the process water before draining the system. 36. Use the metering pump connected to the chemical tank containing the solution of 0.08 mol/l of acetic acid to decrease the ph of the process water. If necessary, reduce the delivery rate to avoid injecting too much acid solution. 37. When the ph gets close to 7.5, stop the metering pump and wait about one minute for the ph reading to stabilize. 38. If, after one minute, the ph is between 6.5 and 7.5, it is safe to drain the water in the column into the main tank of the process workstation. Open HV4 and HV5 to do so. 39. If the ph is not between 6.5 and 7.5, inject more acid and base until the ph is within the desired range. Then, drain the column. 40. Stop the system, turn off the power, and store the equipment. Do not forget to rinse the ph probe and store it in a storage solution as described in the Familiarization with the Training System manual. Titration curve analysis 41. Plot the data using spreadsheet software. 42. Compare the phosphoric acid titration curve with the typical curve for the titration of a weak acid by a strong base (Figure 4-11). List the similarities and the differences between the two curves below. Festo Didactic 86013-00 97
Ex. 4-3 Titration of Weak Acids Conclusion 43. Compare the acetic acid titration curve you obtained with the typical curve for the titration of a weak acid by a strong base. List the similarities and the differences between the two curves below. 44. Compare the phosphoric acid titration and the acetic acid titration curves, and list the similarities and the differences between the two curves below. CONCLUSION You learned how to titrate weak acid solutions with a strong base solution. You analyzed and compared the titration curves obtained for both acetic acid and phosphoric acid. You also learned how to calculate the ph of a weak acid solution and the ph of a weak base solution. REVIEW QUESTIONS 1. What is the 5% rule approximation? 2. Given that the density of water is 983.24 g/l at 60 C (140 F), what is the molarity of pure water at this temperature. 3. What is the equilibrium constant of the dissociation equation of formic acid? 98 Festo Didactic 86013-00
Ex. 4-3 Titration of Weak Acids Review Questions 4. Is it possible for a polyprotic acid to be a strong acid for the first ionization and then a weak acid for the second ionization? 5. Can you always use the long method instead of the 5% rule to calculate the ph of weak acid? Festo Didactic 86013-00 99