ph Titration of H 3 PO 4 Mixtures Calculation of K 1, K 2, and K 3

Transcription

1 ph Titration of H 3 PO 4 Mixtures Calculation of K 1, K 2, and K 3 Purpose In this experiment the titration of pure H 3 PO 4 and H 3 PO 4 with HCl or NaH 2 PO 4 is followed by measuring the ph of the solution after each addition of NaOH titrant. From this data, K 1, K 2, and K 3 of H 3 PO 4 may be calculated. In addition the amount of HCl, H 3 PO 4, and NaH 2 PO 4 present in the sample may be determined. Apparatus Chemicals Theory ph meter Combination ph electrode Magnetic stirrer Beakers (2), 300 ml, tall form Graduated cylinder, 100 ml Volumetric flasks (2), 100 ml Buret, 50 ml Pipet, 25 ml M sodium hydroxide [NaOH], standard Sample 1: Approximately 0.1 M phosphoric acid [H 3 PO 4 ] diluted to mark in a 100-mL volumetric flask Sample 2: Approximately 0.1 M H 3 PO 4, plus hydrochloric acid [HCI] or sodium phosphate, monobasic [NaH 2 PO 4 ] diluted to mark in a 100-mL volumetric flask Buffers, for standardization of ph meter: ph 4.0 and ph 7.0 Chapter 22, Principles of Instrumental Analysis, 6 th ed., Skoog et. al. Procedure Set up a titration assembly using the 300-mL tallform beaker as the receptacle for the titrant. Turn on and standardize the ph meter, following the instructions supplied with the instrument. For more accurate results, it is preferable to standardize the meter using two buffers, one at ph 7, the other at ph 4. Rinse the electrodes with distilled water after using the buffer. Care must be taken to prevent rinse water or any other liquid from entering the filling hole of the reference electrode. Keep the electrodes immersed in distilled water until your sample is ready to titrate. Take a 25-mL aliquot of H 3 PO 4 solution (Sample 1) and dilute it with distilled water to 100 ml in a 300-mL tall-form beaker. Wash the electrodes (or the combination electrode) thoroughly with distilled water, and introduce them in such a way that they will not touch each other, the side or bottom of the beaker, or the stirring bar. Place the magnetic stirring bar in the beaker, taking care that the bar will clear the electrodes.

2 Keep the solution well stirred throughout the titration. Use of a water-driven stirrer is recommended. Record the ph of the solution before adding any of the titrant. The first titration can be a qualitative titration to help identify where the endpoints will be. For the first titration add titrant in approximately 2 ml increments, recording the actual volume added at this point, until you have reached a ph of about 12. Examine this data to determine where the larger changes in ph occurred (there should be 2). For your second titration concentrate on data that are close to the ½ way point to the approximate equivalence points (0.5 ml increments) and data that are close to the equivalence points (0.1 ml or less). Once you are past the second equivalence point get about 3-4 readings that would be about half the volume to the 3 rd equivalence point, again at 0.5 ml increments. Take a 25-mL aliquot of H 3 PO 4 plus HCl or NaH 2 PO 4 (Sample 2) and dilute it with distilled water to 100 ml in a 300-mL tall-form beaker or Erlenmeyer flask, and carry out a titration in the same manner as with Sample 1. Again, repeat the titration if necessary to obtain sufficient readings. Treatment of Data For each set of data, plot ph vs. milliliters of NaOH added on fineruled graph paper (ruling of 10 by 10 to the cm is desirable). Also, enter the data into a spreadsheet, and use the spreadsheet to calculate both a first- and second-derivative plot of the data to determine the endpoint. Calculate the molarity and the number of grams of H 3 PO 4 and HCl or NaH 2 PO 4 present in your samples. Calculate K 1, K 2, and K 3 from your data for the pure H 3 PO 4 (Sample 1). Be sure to take into account increased volumes when calculating concentrations at all points on the curve, remembering the initial aliquot volume. Calculation of K 1, K 2, and K 3 For these calculations, you will use the data from Sample 1. Stoichiometrically, the point halfway to the end point should give equal concentrations of H 2 PO 4 - and H 3 PO 4, in which case K 1 would equal the H +. However, because K 1 is relatively large, at the halfway point B (above), [H 2 PO 4 - ] > [H 3 PO 4 ], due to the ionization of H 3 PO 4 to H 2 PO 4 - and H +. Hence an indirect method must be used in calculating K 1. Starting at point A in the adjacent figure, determine the ph when you are ½ the volume required to reach the equivalence point (point B). At this point we know that the analytical concentration of H 3 PO 4 (C HA ) is equal to the analytical concentration of H 2 PO 4 - (C A -). The secondary reaction that occurs at B is the dissociation of H 3 PO 4 : H 3 PO 4 º H 2 PO H +

3 From the secondary equation, we can see that the analytical concentration of H 3 PO 4 is reduced by an amount equal to the concentration of the hydrogen ion, and the analytical concentration of H 2 PO 4 - is increased by the same amount. Mathematically: [H 3 PO 4 ] = C HA - [H + ] (1) [H 2 PO - 4 ] = C A - + [H + ] (2) For the dissociation of H 3 PO 4, K 1 = [H 2 PO 4 - ] * [H + ] / [H 3 PO 4 ] Substituting (1) and (2): K 1 = (C A - + [H + ]) * [H + ] / (C HA - [H + ]) The analytical concentrations of H 3 PO 4 and H 2 PO 4 - can be determined from the amount of your standard base required to reach point B, and [H + ] is calculated from the ph reading at point B. K 2 can be calculated as follows: H 2 PO 4 - º HPO H + K 2 = [HPO 4 2- ][H + ] / [H 2 PO 4 - ] Point C in Fig represents a mark halfway to the second end point. [HPO 4 2- ] = [H 2 PO 4 - ] K 2 = [H + ] Because there is no significant secondary reactions from H 2 PO 4 - or HPO 4 2-, K 2 may be determined directly from the ph value. The following describes the calculation of K 3 : HPO 4 2- º PO H + K 3 = [PO 4 3- ][H + ] / [HPO 4 2- ] (3) Because of the small value of K 3 and the secondary reaction of PO 4 3-, an indirect method must also be used in calculating its value. Calculate the amount of NaOH added from the end point D to any selected point E on the top, level part of the curve. A convenient value to use will be ½ way to the third equivalence point; however any value may be used. The analytical concentration for PO 4 3- (C A -) will be given by the millimoles of OH - added (from D to E), while the analytical concentration for HPO 4 2- (C HA ) will be determined by the initial moles of H 3 PO 4 present [calculated by the volume of OH - required to reach the 1 st equivalence point (A) OR the volume of OH - required to reach the second equivalence point (D - A)] minus C A -.

4 The secondary reaction we are concerned with is the reaction of PO 4 3- : PO H 2 O º OH - + HPO 4 2- As we did with the secondary reaction for the calculation of K 1, we can determine that: [PO 3-4 ] = C A - - [OH - ] (4) [ HPO 2-4 ] = C HA + [OH - ] (5) Remember, C A - is the analytical concentration of the conjugate base (in this case PO 4 3- ) and C HA is the conjugate acid (in this case HPO 4 2- ). The value for [H + ] and [OH - ] are determined from the graph (Remember, [H + ]*[OH - ] = K W ) We can then substitute the values from (4) and (5) into equation (3) and calculate K 3.

5 References 1. R. G. Bates, "Determination of ph," Wiley, New York, J. J. Lingane, "Electroanalytical Chemistry," 2nd ea., Interscience, New York, D. T. Sawyer and J. L. Roberts, Jr., "Electrochemistry for Chemists," Wiley- Interscience, New York, D. A. Skoog and D. M. West, "Fundamentals of Analytical Chemistry," 4th ea., Saunders, Philadelphia, 1982, chaps. 8, 9, and 16.