Titration Lab: Determination of a pk a for an Acid and for a Base Theory A Brønsted-Lowry acid is a substance that ionizes in solution (usually aqueous, but it doesn t have to be, ammonia is often used as a solvent) to yield a solvated hydrogen ion. Conversely, a Brønsted-Lowry base is a substance that accepts a hydrogen ion in solution. If the solvent is water this gives: Acid: HA + H 2 O A - + H 3 O + Base: B + H 2 O OH - + BH + The acid ionization constant, K a is simply: K a H + A HA We can rearrange the above to yield: pk a ph + log HA A - We can thus obtain the pk a for an acid from the ph of a solution and the concentrations of the acid and its conjugate base. Here is an example for acetic acid and for the ammonium ion: CH 3 CO 2 H CH 3 CO 2 - + H + K a NH 4 + NH 3 + H + K a H + - CH 3 CO 2 [ CH 3 CO 2 H] H + NH 3 + NH 4 The base ionization constant, K b, may be found as well: K b HB + OH - B [ B] or pk b poh + log HB + However, it is more common today to give K a or pk a values, so we use the relationship pk a + pk b 14 to interconvert between pk a and pk b values. For example, if we found the pk b of ammonia to be 4.64 at 20 C, the pk a for its conjugate acid, ammonium ion, is 14 4.64 9.36 at 20 C. If you look at acid ionization constant tables, many of them are for the conjugate acids of common bases. The problem is how to determine the K a or pk a for an acid or base. Although there are several methods, one of the easiest and most convenient is a potentiometric titration method. This is an acid-base titration. In this method, the acid (or base) is titrated with KOH or NaOH (or HCl) until the acid (or base) is neutralized. In addition, the ph of the sln is monitored with a ph electrode. As a ph electrode really measures the cell potential in the electrode in volts (but the ph meter converts voltage to ph), it really is an electrochemical cell measuring potential. Thus the name potentiometric titration. Chem 410 Titration Lab page 1
The point in the titration at which the acid and base have neutralized each other stoichiometrically is called the equivalence point. The half-equivalence point is when the concentrations of the acid and its conjugate base are equal to each other, and this is where the ph equals the pk a. If we graph the titration of a weak acid with KOH over time, here is a typical curve: HF + KOH KF + H 2 O Notice that the ph of the solution at the equivalence point will be over 7. The titration curve of a weak base with HCl would be reversed, and the ph at the equivalence point will be below 7. Although there are graphical techniques using calculus (i.e. 1 st and 2 nd derivatives) to find the pk a, there is also a simple mathematical way to find the pk a if certain conditions are met. The proper conditions for this type of mathematical determination of pk a are as follows: 1) the substance to be titrated is ideally at 0.01000 M; 2) the NaOH, KOH, or HCl titrant is at least 10x more concentrated, so 0.1000 M up to 1.000 M; 3) the expected pk a is between 2.5 and 11; and 4) the ph during titration remains between 4 and 10 (although a slight deviation from this at the very end or very beginning may be tolerated). If these conditions are met, then this simple equation may be used to calculate the pk a at equally spaced intervals throughout the titration: Eq 1) pk a ph + log HA A - The ph will be measured at the beginning and at 10 equally spaced intervals in the titration. The concentrations of the acid and its conjugate base could be calculated from simple ICE tables of the titrations but it is simplified because of the carefully picked concentrations. Because of the start concentrations of 0.01000 M for the acid, 1.000M for the titrant, and the 10 equally spaced titration additions, the ratio [HA]/[A-] is just a ratio of simple whole numbers, like 1/9, 2/8, 5/5, 9/1. The log of this simple ratio is taken, and then to the measured ph value. As 11 ph values were read (the Chem 410 Titration Lab page 2
beginning ph and the ph after the addition of 10 equal amounts of the base), we can obtain 9 pk a values. These 9 pk a values are averaged and the standard deviation is calculated. If the ph goes below 4, the concentrations of the acid and its conjugate base must be corrected for hydronium ion concentration as it is now too large to ignore. Likewise, if the ph goes above 10, the concentrations of the acid and its conjugate base must be corrected for hydroxide ion concentration as it is now too large to ignore. In this lab, we will ignore this correction, although there are tables that allow this correction to be made easily.* * This procedure is adapted from The Determination of Ionization Constants, A Lab Manual, 3 rd Ed., A. Albert & E.P. Serjeant. Chapman and Hall, New York, 1984 Materials ph meter and electrode waste beakers weigh paper 10 ml beakers, 5 100 ml volumetric flask 250 ml beaker stir plate stir bar spatula 300 µl pipetman pipet tips, 2 KimWipes Chemicals DI water 1.000 M HCl (standardized) 1.000 M NaOH (standardized) TRIS Boric Acid ph 4, 7, 10 buffer slns Precalculations 1A) Calculate the amount of boric acid required to make 100.00 ml of a 0.01000 M sln. Check with your instuctor. 1B) Calculate the amount of TRIS required to make 100.00 ml of a 0.01000 M sln. Check with your instuctor. Procedures Boric Acid Titrations 1A) Weigh out the required amount of boric acid on weigh paper. Put in the 100 ml volumetric flask. 2A) Using DI water, dilute to 100 ml. Mix well. 3A) Pour this boric sln into a clean and dry 250 ml beaker. Add the stir bar. 4A) Clean and dry a 10 ml beaker. Pour a few ml of the standardized NaOH sln into this beaker (6 ml is fine). 5A) Calibrate the ph electrode using the known buffer slns of ph 4, 7, and 10 or 4 and 10. 6A) Place the boric acid sln beaker onto the stir plate. Turn the stir plate on to a gentle but thorough stir rate. 7A) Put the ph electrode into the boric acid sln and place so the stir bar doesn t hit the tip of the electrode. 8A) Allow the ph reading to stabilize for a minute, then record the initial ph. 9A) Using a 300 µl pipetman and a clean, dry pipet tip, set the pipetman to 100 µl, and wet the pipet tip with the standardized NaOH sln in the beaker. 10A) Start the NaOH titration by adding 100 µl of the NaOH. Be careful not to touch the electrode or the beaker walls with the NaOH. Do not rinse down the walls of the beaker with DI water at any time! (This will affect the concentration and ionic strength.) 11A) Allow the ph reading to stabilize for 20 seconds or so, then record the ph. 12A) Add another 100 µl of the base. Allow the ph reading to stabilize, then record the ph. 13A) Repeat Step 12A) until 1000 µl (1.00 ml) of NaOH have been. Make sure to record the final ph. 14A) Repeat the entire titration 3 more times (or four total). Clean and dry the beaker thoroughly each time. Chem 410 Titration Lab page 3
TRIS Base Titrations 1B) Check the ph electrode with the ph 4, 7, and 10 buffers. Recalibrate if necessary. 2B) Conduct the titration using the base TRIS and using the 1.000 M HCl as the titrant. Make sure to thoroughly rinse the volumetric flask and 250 ml beaker. Dry the 250 ml beaker before pouring the TRIS sln into it. 3B) Use a clean, dry pipet tip and a clean, dry 10 ml beaker for the standardized HCl solution. 4B) Conduct the TRIS titration with 100 µl portions of the standardized HCl sln until 1000 µl has been. Repeat the titration of TRIS with HCl three more times. 5B) Clean up all equipment and the benchtop. Waste and all slns go into the waste container in the hood. Chem 410 Titration Lab page 4
Data Weight of Boric Acid Trial 1: Weight of Boric Acid Trial 3: Weight of Boric Acid Trial 2: Weight of Boric Acid Trial 4: Weight of TRIS Trial 1: Weight of TRIS Trial 2: Weight of TRIS Trial 3: Weight of TRIS Trial 4: Titration Data for Boric Acid Room Temperature: Electrode #: ph Meter #: 1 st Titration 2 nd Titration µl NaOH ph µl NaOH ph 3 rd Titration 4 th Titration µl NaOH ph µl NaOH ph Chem 410 Titration Lab page 5
Titration Data for TRIS Room Temperature: Electrode #: ph Meter #: 1 st Titration 2 nd Titration µl HCl ph µl HCl ph 3 rd Titration 4 th Titration µl HCl ph µl HCl ph Chem 410 Titration Lab page 6
Data Analysis (copy the below tables as need 4 tables for each) Table: pk a Determination for Boric Acid Titration Trial # µl NaOH ph HA i diminished by tenths HA i Column 3 Column 3 Column 4 Log of column 5 0..010.0000 --- --- --- 10.009.0010 9/1 20.008.0020 8/2 30.007.0030 7/3 40.006.0040 6/4 50.005.0050 5/5 60.004.0060 4/6 70.003.0070 3/7 80.002.0080 2/8 90.001.0090 1/9 100.000.0100 --- --- ---- Calculate the average pk a and Standard Deviation for pk a : Show calculations for both titrations. Note: Column 3 is [HA]; Column 4 is [A - ]; Column 6 is log([ha]/[a - ]). These are used in Eq 1). Table: pk a Determination for TRIS Base Titration Trial # µl HCl ph B i Column 4 B i diminished by tenths Column 3 Column 4 Log of column 5 0..000.0100 --- --- ---- 10.001.0090 20.002.0080 30.003.0070 40.004.0060 50.005.0050 60.006.0040 70.007.0030 80.008.0020 90.009.0010 100.010.0000 --- --- ---- pk a (columns 2 + 6) pk a (columns 2 + 6) Calculate the average pk a and Standard Deviation for pk a. Do use the Q Test to see if a data point may be discarded. Note: Column 4 is [B]; Column 3 is [HB + ]; Column 6 is log([hb + ]/[B]). These are used in Eq 1). Discussion/Errors: 1) Looking at your Columns 7 and your standard deviation, is there a large variation in pk a during the titrations of boric acid? 2) Look up the pk a of boric acid (pk a1 ) and compare to your average value. Calculate your %-Error. Do you think that this method of pk a determination is accurate enough for boric acid? 3) Looking at your Columns 7 and standard deviation, is there a large variation in pk a during the titrations of TRIS? 4) Look up the pk a of TRIS and compare to your average value. Calculate your %-Error. Do you think that this method of pk a determination is accurate enough for TRIS? Conclusion: Summarize your data and results, and any errors that were encountered. Chem 410 Titration Lab page 7