Anal. Chem. lQ83, 5 5 , 684-687
684
Kim, Y. S.; Zeitlln, H. Anal. Chem. 1971, 43, 1390. Chalne, F. E.; Zeitlln, H. Sep. Sci. 1974, 9 , 1. Hagadone, M.; Zeitlln, H. Anal. Chim. Acta 1976, 86, 289. Tzeng, J.; Zeitlln, H. Anal. Chlm. Acta 1978, 101, 71. Nakashlma, S. Anal. Chem. 1979, 51, 654. Nakashlma, S. Bull. Chem. SOC.Jpn. 1979, 52, 1844. Nakashlma, S. Fresenius' 2.Anal. Chem. 1980, 303, 10. Kim, Y. S.; Zeitlln, H. Sep. Sci. 1972, 7 , 1. Nakashlma, S. Analyst(London) 1978, 103, 1031. Leung, G.; Kim, Y. S.; Zeltlln, H. Anal. Chim. Acta 1972, 60, 229. HlraMe, M.; Yoshlda, Y.; Mlzulke, A. Anal. Chlm. Acta 1978, 61, 185. Mlzulke, A.; Hlralde, M.; Kanematsu, T. Bunseki Kagaku 1977, 26, 137. Chem. Abstr. 1978, 88, 8 3 0 4 9 ~ . (15) Hlrakie, M.; Ito, T.: Baba, M.: Kawaauchl, H.: Mlzulke. A. Anal. Chem. 1980, 52, 804. (18) Voyce, D.; Zeitlln, H. Anal. Chlm. Acta 1974, 69, 27. (17) Rothsteln, N.; Zeitlln, H. Anal. Lett. 1976, 9 , 481.
(3) (4) (5) (8) (7) (8) (9) (IO) (11) (12) (13) (14)
-
(18) Seklne, K. Mikrochlm. Acfa 1975, 313. (19) Kester, D. R.; Duedall, I. W.; Connor, D. N.; Pytkowlcz, R. M. Llmnol. Oceanogr. 1967, 12, 178. (20) DeCarlo, E. H.; Zeltlln, H.; Fernando, Q. Anal. Chem. 1981, 53, 1104. (21) Robberecht, H. J.; van Grleken, R. E. Anal. Chem. 1980, 52, 449. (22) Ryan, D. E.; Stuart, D. C.; Chattopadhyay, A. Anal. Chim. Acta 1978, 100, 87. (23) Holzbecher, J.; Ryan, D. E. Anal. Ch/m Acta 1980, 119, 405. (24) van der Sloot, H. A.; Das, H. A. J . Radloanal. Chem. 1977, 35, 139. (25) van der Sloot, H. A.; Wals, G. D.; Das, H. A. Anal. Chim. Acta 1977, 90, 193.
RECEIVED for review November 1, 1982. Accepted January 3,1983. This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
Raman Spectrometric Determination of Tribasic Sodium Phosphate Hydrolysis Quotient Allan 0. Mlller * Analytical Laboratorles, Rockwell Hanford Operatlons, Richland, Washington 99352
John W. Macklln Deparfment of Chemistry, Unlversity of Washington, Seattle, Washington 9 8 195
The hydrolysis quotient of tribasic sodium phosphate has been determined over the 0.001 to 0.4 M phosphate concentration range in order to establish hydroxide concentration limits for the quantltative determination of PO,a- in aqueous solutions by laser Raman spectrometry. Concentrations of phosphate species In the hydrolysis equilibrium were measured by laser Raman spectrometry and hydroxide concentrations were determined by both pH measurement and a titrimetric method. The hydrolysis quotient ranged from near 0.004 M at phosphate concentrations above 0.01 M to 0.014 M at infinite dilution. This corresponds to a thermodynamic equilibrium constant 7.1 X lo-'' M, for the third dissociation of phosphoric acid. These results are compared with those of the only previous Raman spectrometric investigation of the HPO:PO-: equilibrium.
Raman spectrometry is a suitable technique for quantifying orthophosphate as described previously (I). The application is, however, hindered by the spectral complications of more than one phosphate species resulting from phosphoric acid dissociation and dimerization equilibria ( 2 , 3 ) . Phosphate is essentially 100% Po43in the presence of greater than about 0.3 M hydroxide allowing direct spectrometric analysis. Below this hydroxide concentration, the analytical determination is complicated by the presence of protonated phosphate species. So that we can establish this lower hydroxide concentration limit better, the hydrolysis quotient, Qh, was measured for the 0.001 to 0.4 M PO-: concentration range, and consequently, K3, the third dissociation constant of phosphoric acid. Although the literature contains many values of K3 from which Qhcan be calculated ( 4 , 5 ) , they range over 2 orders of magnitude. Present address: United States Testing Laboratories, Richland,
WA 99352.
A determination of &h by Raman spectrometry is more direct than many methods and involves the same measurements as the Raman analytical method for Po43-(1). Other methods such as titrimetry are nonspecific and may suffer from difficulties such as the insensitivity of the pH electrode a t the high pH levels necessary. The Raman and infrared spectra of aqueous orthophosphate solutions have been studied and assigned (6, 7),and equilibrium investigations by Raman spectrometry have recently been reported by Preston and Adams (2, 3, 8). They also determined Qhfor the HP042--P043- equilibrium; however, their experimental procedure does not include carbon dioxide control or an internal standard. The work described here includes these controls along with independent measurements of each constituent in the hydrolysis equilibrium in order to establish Raman spectrometrically measured values of Qhthat can be confidently used in the quantitative determination of Po43-and to estimate the third dissociation constant, K 3 of phosphoric acid. EXPERIMENTAL SECTION Solutions. A 1.001M phosphate stock solution was prepared by dissolving undried, assayed NaH2P04.H20(Mallinkrodt, analyzed reagent) in distilled, deionized water. The phosphate solution was filtered through a Millipore BDWP 0.4-pm filter. Similarly filtered, distilled, and deionized water was used in all subsequent preparations. All vessels were rinsed with the filtered water. A 0.049 95 M dilution by weight of the stock solution was prepared. Solutions for Raman studies with the following approximate concentrations were prepared 0.4,0.1,0.05,0.02,0.01,0.005,0.002, 0.001, and 0.0005 M. Weighed aliquots of the appropriate phosphate solution and 1.00 mL of 2.50 M sodium nitrate internal standard solution were added to water in individual 25-mL volumetric flasks. Subsequent preparation steps for these test solutions were carried out in a gloved gas bag purged with nitrogen to provide a carbon dioxide free atmosphere. In addition,beakers containing dilute sodium hydroxide were kept in the gas bag for waste and as getters for C02. Calculated amounts of either 4.3 or 19.3 M NaOH were added to each solution to obtain approx-
6603-2700/83/0355-0884$01.50/00 1983 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 55, NO. 4, APRIL 1983 685
E'
r , 4
98 0
0.02
0.09
0.08
0.08
0.10
millimoles H,PO;
HPOi
Figure 2. Bias in LaPO, precipitation, reverse titration method for aqueous hydrogen ion.
z
zi 5
I
I
0.2,4 0.02.10 0.1.6
0.01.23
- 8
906
930
970 WAVENUMBER (cm ' )
1.010
Averaged spectra for soiutlons of varlous phosphate concentrations. Spectra are identified by total phosphate molarity and number of spectra averaged, respectively.
Figure 1.
imately equal concentrations of HP02- and Po43-(around pH 12.3). The solutions were diluted to 25 mL and stirred before pH measurements were performed within in the gas bag with a Beckman 0-14 pH electrode and an Orion Model 901 "Ionalyzer" pH meter. Reference pH solutions were 1.00 and 0.1 M NaOH and Beckman pH 10 buffer. Raman Spectra. Spectra were taken at 2 to 2.5 W of 514.5-nm radiation from a CR-6, Coherent Radiation argon laser. The spectrometer system is a Spex Industries Ramalog-5 equipped with 1800 grove/mm holographic gratings, a photon counting system, and slits set to provide a spectral band-pass of 6 cm-*. Spectra were accumulated in 1-cm-' increments with 1-s integration time. Glass capillary spectrometer cells were loaded inside the gas bag. Raman spectra were taken from 890 to 1095 cm-' to include the 936,990, and 1048 cm-l AI analytical lines of PO4", HPO:-, and NO3- ions, respectively, at 22 "C. The capillary cells were positioned perpendicular to the vertical laser beam and the scattered light was collected at 90". Laser heating of the sample was measured with a thermocouple to be about 3 "C. Up to 110 spectra of each solution were collected and averaged to provide improved signal-to-noise ratios. The number of spectra averaged was increased as phosphate concentration decreased. Examples of spectra showing only the phosphate peaks and the benefit of averaging multiple spectra are shown in Figure 1. Computer control and data acquisition were accomplished with a Data General Nova 840 minicomputer. Computer Techniques. The Data General Nova minicomputer was used to normalize and subtract interfering spectral lines and the solvent background contribution from the spectra. The background subtraction routine subtracts a chosen reference spectrum until zero is obtained as determined from a plot of the net peak. Net peaks were integrated by summing the residual counts in the spectrum segment. Accurate subtractions frequently could not be obtained at the lower concentrations because noise and small differences between reference and sample spectra prevent zeroing of the difference spectrum on both sides of the peak. In these cases, peak areas were adjusted by manually zeroing the peaks in plots of difference spectra followed by cutting and weighing. Computerized plotting permits appropriate magnification of difference spectra. Analysis. Reagent analysis was performed by back-titration with 0.0496 M 0.28% NaOH from a 10-mL microburet to end points between 6 and 8 pH units. Standard 1.002 M HN03 and 19.23 M NaOH were prepared by the chemical standards laboratory of Rockwell Hanford Operations. Characterization of these
solutions was based on National Bureau of Standards tris(hydroxymethy1)aminomethane. Stoichiometry of the NaH2P04.H20 was determined to be 100.0 f 1.8%by analysis of solutions of the salt by magnesium ammonium phosphate precipitation and weighing magnesium pyrophosphate (9). Quantification of HPOZ- and PO4" anions in the test solutions was derived from the Raman intensities using 0.1 M NO3- as an internal standard. The ratio of integrated intensities of phosphate A, analytical lines to that of nitrate is related to concentration through calibration curves. A volumetric method for determining free hydroxide in the presence of varying concentrations of di- and tribasic phosphate was deviyd. The method involves a back-titration in which a sample aliquot is added to excess standard acid so that carbon dioxide absorption does not contribute error during room atmosphere titrations. Aliquots of acidified sample are titrated with 0.0496 M NaOH to end points between 6 and 8 pH units. Phosphate is titrated by precipitation of LaP04 simultaneously with titration of the excess acid and acid released from HP043and H2P04-when LaP04 is precipitated. Residual phosphate concentrations were detected by the size of the pH drop with additions of the stoichiometric volume of 0.1 M Lac&. The concentration of free hydroxide in the original test solution can be calculated from the added amount of standard acid, the titrant volume, aliquot sizes, and the Raman spectrometrically measured concentration of HPO$-. Initial evaluation of the method with standard NaH2P04indicated 100.7 % recovery with lanthanum additions at pH less than 4. Analysis of solutions and further evaluation of the method were performed with lanthanum additions made at pH levels between 4 and 6 for better sensitivity of the phosphate end point. According to the evaluation results shown in Figure 2, a phosphate dependent bias occurs. Test solution results were corrected for this bias.
RESULTS AND DISCUSSION Hydrolysis Equilibria. At pH levels greater than 10, tribasic orthophosphate hydrolyzes according to the following reaction:
HZO + Po43-+ HP042-+ OH-
(1)
Preston and Adams (3)studied the equilibrium by dissolving various concentrations of tribasic sodium or potassium orthophosphate in water and determining the concentration of HP042--fromhydrolysis by Raman spectrometry. The concentrations of HPOt- and hydroxide were assumed equal and the concentration of Po43-was obtained by difference. The resulting values permitted calculation of the concentration hydrolysis quotient, Qh, according to the following equation:
Kh =
~ H P O ~ ~ ~ O YHPO~Z-YOHH [HP03'-3
-
apor3-
YP04"
[OH-] = [P043-I
8,Qh
(2) where al is activity, [i] is concentration in molarity, yi is the activity coefficient of species i, and Kh is the thermodynamic hydrolysis quotient. In our work the orthophosphate hydrolysis equilibrium was studied by an independent analysis method that features several differences from the hydrolysis method in order to achieve an analytically applicable measurement of Qh and
888
ANALYTICAL CHEMISTRY, VOL. 55, NO. 4. APRIL 1983
I
I
0.m
I
tl 1.\
I P II Y-4I \ -.I
0.012Cl
0 015 00141
/
/
/
Flgun 3. Hydrolysis quotient for PO,% vs. concentratbn.
estimation of the thermodynamic hydrolysis constant, Kb. Preston and Adams point out that the reliability of their results is limited to above 0.02 M phosphate because of the lack of 'computer time averaging" and the resulting imprecision a t lower concentrations. Therefore, our experiments to determine Kbinclude computer acquisition and averaging of multiple spectra in order to extend the measurable concentration range and to improve the reliability of results. AU operations which might permit aigniiicant atmrption of carbon dioxide by the alkaline solutions were performed under a nitrogen atmosphere, since absorption of carbon dioxide may significantly lower pH and yield high results for Qb especially at low phoshate concentrations. The hydrolysis method for measuring Qhis insensitive at low concentrations where nearly all phosphate is HPO,*-. The theoretical lower limit is where all phosphate is HPOP, near O.ooO1 M, but the practical limit is much higher because the uncertainty of the HP0,2- determination must be much less than the total PO,' concentration for meaningful results. In this study, all solutions were prepared to pH levels where the H P 0 2 - and PO4* concentrations would be similar. All three constituents of the equilibrium expression, eq 2, have been determined to constitute the aforementioned independent analysis method. The internal standard that was incorporated may be an improvement over the external standard used by Preston and A d a m because it cancels any changes in refractive index over the large concentration range studied. Analyses. Peak area measurements for the A, lines of HPO,2- and PO4%,that were straightforward for the solutions of higher concentration, were difficult at lower concentrations where the match between sample and reference spectra failed. Refinement of computer-determined peak areas by cutting and weighing was only partially effective because the real limitation is low peak-to-background ratio when quantifying peaks zeroed on only one side. Tiny mismatches between sample hackground and reference spectra become large errom in the difference spectrum as the peak-to-background ratio approaches zero. Table I contains the measured concentrations for each test solution. The combined uncertainty of measurements at the lower mncentrations is near 13% relative standard deviation. Accurate measurement hy hydroxide concentrations was expected to be the most difficult aspect of the independent
Table I. Analytical Molar Concentrations of HPO,'--PO:Equilibrium a
total phosphate, 103[HP0.'-l,
M
M
103[PO:-l, M
[OH-I, M by titraby pH tion
0.3959 82 302 0.0126 0.0533 0.1994 49 149 0.0132 0.0216 0.0995 28 61 0.0145 0.0195 27 0.0204 0.0249 0.0402 10.6 0.0199 5.9 12 0,0219 0.0264 6.1 f 1.2 0,0219 0.0216 0.00981 3.2 f 0.6 3.4 f 0.4 0.0311 0.0300 0.00498 1.5 f 0.2 0.60f 0.03 1.2 f 0.2 0.0282 0.0311 0.00197 0.00100 0.2Sf 0.02 0.7 f 0.2 0.0341 0.0323 0.4 t 0.1 0.0302 0.0292 0.000497 Lower phosphate concentrations are the mean of multiple measurements. Uncertainties are the standard deviations of those measurements. analysis method hecause of problems in obtaining accurate pH measurements at low hydrogen ion concentrations and because of phosphate interference in titration methods. Therefore, pH measurements were taken a t completion of solution preparation and a volumetric method for determining hydroxide in phosphate solutions was devised to provide a second determination which was independent of pH measurements. With PO,* removed from solution as LaPO,, a sharp acid-base end point occurs. This precipitation-titrimetric method was evaluated for standard recovery of 0.0025 to 0.1 mmol of phosphate with a precision of 1.6% relative standard deviation. Corrections for greater than 100% recoveries, indicated in F i 2, were applied to the test solution analyses as a function of total phosphate. Since lanthanum additions were made at pH levels greater than 4, it seems likely that a finite amount of lanthanum hydroxide forms to cause the high results. Lanthanum additions at lower pH levels may eliminate this complication. Hydroxide concentrations measured by both pH and titration methods are included in Table I. Agreement between the two methods is reasonable at low phosphate concentrations, but the disparity increases with increasing phosphate. Hydrolysis Quotient. Hydrolysis quotients calculated from the data in Table I are listed in Table I1 and plotted in
ANALYTICAL CHEMISTRY, VOL. 55, NO. 4, APRIL 1983
Table 11. Hydrolysis Quotients Dissociation Equilibrium total phosphate molarity
(Qh) for
the HPOa-
1 0 3 ~ ~ ~ ,
[OH-] by [OH-] by pH titration
uncertainty, %
0.3959 0.1994 0.0995 0.0402 0.0199 0.00987 0.00498 0.00 197 0.00100 0.000497
14.5 3.4 4.3 7.1 8.2 6.1 9.9 8.1 10.5 12.7 11.2 *19 11.4 *12 12.9 13.4 13.1 15.0 lt14 * 21 12.6 13.5 7.6 7.3 * 21 Values calculated from mean of analytical measurements. Uncertainty calculated as standard deviation of multiple measurements. Figure 3. The disparity in Qh, depending on the source of hydroxide concentration values, is larger at the higher phosphate concentrations. Since the disparity is greatest there, a greater phosphate interference than indicated by the Figure 2 corrections is suggested. The Q h values calculated from pH measurements show less scatter in Figure 3 than the Qhvalues calculated from volumetrically measured hydroxide concentrations. Therefore, pH measurements appear to provide more accurate data throughout the concentration range for calculating Qk The extrapolation of Qhto zero concentration provides an estimate of K h , the thermodynamic hydrolysis quotient for the HP042- dissociation, to be 0.0141 f 0.00015 M. The uncertainty estimate was obtained by shifting the curve of the line through the range of values permitted by the error bars in Figure 3. An extrapolation of the Qhvalues obtained from the volumetric titrations also intersects the ordinate new Q h = 0.014 M. The independent analysis method implemented in this work provides independent checks on the accuracy of results. The phosphate material balance can be seen from Table I to be mostly in the 90-100% range. Two methods, independent of each other, for determining hydroxide provide a check on possible errors and biases. For example, the pH results verify a problem with the volumetric method at the higher concentrations. The results of Preston and Adams (3) and their extrapolation to zero concentration at Qh= 0.0084 M are also plotted in Figure 3. They did not claim reliability for their results helow 0.02 M phosphate. If their &h values for less than 0.01 M phosphate concentrations are ignored, their data seem to extrapolate to near Q h = 0.014 M. Figure 3 shows smooth curves drawn through the Preston and Adams data and extrapolated to both Q h = 0.0084 and toward 0.014 M. Preston and Adams also presented results for the hydrolysis of potassium orthophosphate. These results are not included in Figure 3 for reasons of clarity, but they also extrapolate to near Q h = 0.014 M at zero concentration if Qhvalues for less than 0.01 M concentrations are omitted. The greatest difference between the results of Preston and Adams and those presented here is in the values obtained for &h at concentrations above 0.01 M. This disparity, on the order of a factor of 10 for the higher concentrations, is very large, especially when the results extrapolate to the same intercept value. The checks in the independent analysis method discussed above instill confidence in the reliability of the results reported here.
887
The value of Kh = 0.0141 f 0.0015 M leads to the third dissociation constant of phosphoric acid, K3 = 7.1 X M at 25 “C. This is compared to quoted values of 2.2 X (10) and 4.8 X M (11). The former appears to be the smallest in the literature, while 7.9 X M (5) and 5.6 X M ( 4 ) seem to be the two largest values. The Raman value for K3 from this work is toward the small end of the range of literature values. The value for K3 estimated by Preston and Adams is 1.2 X M (3). While Raman spectrometry can only detect phosphates at moderately low concentrations, the data in Figure 3 go to a low enough concentration to show that an intercept of 0.020 or more (& < 5X M) is not probable. Partially neutralized phosphoric acid species may form dimers by means of multiple hydrogen bonds according to the model presented by Preston and Adams ( 3 ) . According to spectra which they report, such dimerization of HPOf increases with concentration and amounts to only a small part of the total phosphate at concentrations near 0.1 M. Since the highest HPO4> concentration in the test solutions is 0.028 M (Table I), any effect due to dimerization is likely negligible. In addition, the HPOt- calibration likely compensates for any dimerization effects on the results reported here. The previously discussed advantages of this method for measuring the hydrolysis quotient of orthophosphate are real, but some disadvantages are significant. Analysis of test solutions for three constituents instead of one means more sources of error. Use of an internal standard means a more complex spectrum. At low concentrations where peak areas must be manually determined, the determination of background is more difficult because of HP02- and Po43lines coexisting with the strong nitrate internal standard A< line. While the utilization of computer-acquired and -averaged spectra was helpful and permitted extension of the study to lower concentrations, it is not a cure-all. The ability to make measurements in low peak-to-background situations is governed by the molar intensities of the species being studied as well as by the number of spectra averaged.
ACKNOWLEDGMENT The work of S . W. Dodd in the characterization of NaH2P04.H20,and the experimental contributions of S . W. Dodd and B. K Miewald in conceptualizing this study are appreciated. Registry No. Po4’-,14265-44-2; Na8P04, 7601-54-9.
LITERATURE CITED (1) Miller, A. G. Anal. Chem. 1977,49, 2044. (2) Adams, W. A.; Preston, C. M.; Chew, H. A. M. J . Chem. Phys. 1979, 70,2074. (3) Preston, C. M.; Adams, W. A. J . W y s . Chem. 1979,83, 814. (4) “Stability Constants”; Chemlcal Soclety: London; Spec. Pub1.-Chem. SOC.No. 17. (5) Ghosh, A. K.; Ghosh, J. C.; Prasad, B. J. Indian Chem. Soc. 1980, 57, 1194. Chem. Abstr. 1981,94, 53800H. (6) Chapman, A. C.; Thlrlwell, L. E. Spectrochim. Acta 1984, 2 0 , 937. (7) Steger, V. E.; Herzog, K. 2.Anorg. A/@. Chim. 1964,337, 169. (8) Preston, C. M.; Adams, W. A. Can. J . Spectrosc. 1977, 22, 125. (9) “Scott’s Standard Methods of Chemical Analysis”, 5th ed.; D. Van Nostrand: New York, 1939;Vol. 1, p 696. (10) “Handbook of Chernlstry and Physics”, 58th ed.; Chemical Rubber Company Press: Cleveland, OH, 1977;p D-151. (11) Van Wazer, J. R. “Phosphorus and Its Compounds”; Interscience: New York, 1958;Vol. 1, p 481.
RECEIVED for review March 2,1982. Resubmitted November 8,1982. Accepted December 9,1982. Prepared for the United States Department of Energy under Contract DE-AGOG77RL01030. Presented to the 36th Northwest Regional Meeting of the American Chemical Society, Bozeman, MT, June 17-19, 1981.
