certain aromatic hydrocarbons in y-irradiated low-temperature glasses (57,SS). Additionally it has recently been shown that the cation radical of magnesium octaethylporphyrin (59) undergoes a low-temperature dimerization in methanol over the temperature range 0 to -60 “C. At present, we have no evidence with which to support or refute any of these product speculations. Suffice it t o say that these studies will continue and that the 9,lO-DMA oxidation system has provided the first clear example of a situation in which low-temperature electrochemical studies have provided a new and highly provocative piece of electrode reaction mechanistic in(57) B. Badger, B. Brocklehurst, and R. D. Russell, Chem. Phys. Lett., 1, 122 (1967). (58) B. Badger and B. Brocklehurst, Trans. Faraday SOC., 65, 2576, 2582, 2588 (1969). (59) J. Fajer, D. C. Borg, A. Forman, D. Dolphin, and R. H. Felton, J . Amer. Chem. Soc., 92, 3451 (1970).
formation that was not readily available from room temperature electrochemical studies alone. ACKNOWLEDGMENT
Dr. Peter Kissinger provided assistance with spectral monitoring of the diphenylanthracene regeneration reaction and many helpful discussions. RECEIVED for review March 29, 1971. Accepted August 2, 1971. One of the authors (R.P.V.D.) wishes to acknowledge support of a National Aeronautics and Space Administration Fellowship (1967-1970). Various aspects of this work was supported by the Advanced Research Projects Agency under Contract SD-100 with the U.N.C. Materials Research Center and by the Air Force Office of Scientific Research (AFSC), USAF, under Grant AF-AFOSR-69-1625.
Stability Constants of Tin-Pyrocatechol Violet Complexes from Computer Analysis of Absorption Spectra William D. Wakleyl and Louis P. Varga2 Department of Chemistry and Reseraoir Research Center, Oklahoma State University, Stillwater, Okla. 74074 By systematic computer analysis of spectral data, the number of absorbing species, the stoichiometry, and the equilibrium constants of the tin(lV)-pyrocatechol violet system were determined in 1M aqueous chloride solution. The acid dissociation constants of pyrocatechol violet determined in this medium were: pK1 = 0.26 f 0.01, pK? = 7.51 f 0.01, pKs = 8.33 0.02, with pK4not determined. In the presence of 1 to 4 X 10-5M tin(lV) chloride at pH = 3.0, absorbance data over the wavelength range 660 to 265 nm were interpreted in terms of the formation, from HsL-, of 1:1,1:2,and 2:l Sn4+:HzL2-complexes with log *pI1 = 7.80 f 0.13, log *plz = 14.90 i 0.30, and log *pzI = 12.92 i. 0.34. Molar absorptivities of all species were determined as a function of wavelength. Both SnH2L2+and Sn(H2L)2 showed maximum absorbance at 555 nm, with molar absorptivities, 33,730 and 79,620 cm-’ mole-’ liter, respectively. Some possible structures of the ligand and of the metal-ligand complexes are discussed. A modification of Sillen’s general least squares “pitmapping” program, in conjunction with absorbance matrix rank, corresponding solution, and mole-ratio methods, was used in the analysis. The calculation methodology embodied in these programs proved to be a powerful tool for the interpretation of solution spectra in equilibrium systems.
*
STUDIES OF THE ABSORPTION of visible and ultraviolet radiation have long been used to obtain information on complex ion equilibria in solution. However, many spectrophotometric methods used in quantitative analysis have been developed without much knowledge of the equilibria involved or of the structure of the absorbing species. Since the absorbance of a solution is governed by a characteristic intensive factor, the absorptivity, as well as by the concentration of each absorbing species, interpretation of measurements of this Present address, Department of Physical Science, Tulsa Junior College, Tulsa, Okla. To whom reprint requests should be made.
type is complicated if several chromophores coexist. Mathematical models used to describe the systems are usually nonlinear in the unknown coefficients so that iterative leastsquares and graphical methods often are used in these studies to interpret the data. If the systems under study are “illconditioned” such that phase space in the area of the leastsquares minimum is flat or if several local minima are present, then the accuracy and precision of the experimental data are not sufficient to produce unambiguous results except in the simplest cases. Under these conditions, careful stepwise interpretive techniques in addition to more powerful mathematical tools are needed. As shown below, progress in this area is encouraging. Reagents for tin listed by Sandell ( I ) have been described as generally unsatisfactory in sensitivity and specificity. Dithiol was considered the most useful followed by phenylfluorone (2-4). The spectrophotometric method for tin suggested by Ross and White (5) using pyrocatechol violet (PCV, pyrocatechol sulfonphthalein, or 3,3’,4’-trihydroxyfuchsone-2”-sulfonic acid) was described as quite sensitive and less subject to errors that previous procedures. PCV appeared to form at least two complexes with tin(1V) at a recommended pH of 3, but no information was given regarding the nature or stabilities of these complexes. Since several metal ions have been reported to form stable chromogenic complexes with PCV at high acidities (6), the nature and stabilities of the tin(1V) complexes were of particular interest in these laboratories in studies on general methods (1) E. B. Sandell, “Colorimetric Determination of Traces of Metals,” Interscience, New York, N. Y . , 1959. (2) R. L. Bennett and H. A. Smith, ANAL.CHEM.,31, 1441 (1959). (3) C. L. Luke, ibid., 28, 1276 (1956). (4) [bid., 31, 1803 (1959). (5) W. J. Ross and J. C. White, ibid., 33, 421 (1961). (6) V. Suk and M. Malat, Chemist-Analyst, 45, 30 (1956).
ANALYTICAL CHEMISTRY, VOL. 44, NO, I , JANUARY 1972
169
of analysis of the class of easily hydrolyzed metal ions of high charge-radius ratio. EXPERIMENTAL
Instruments. Absorbance measurements were made with
a Cary Recording Spectrophotometer, Model 14, using matched I-cm fused silica cells. Absorbance data, 6s. 1M NaCl and estimated t o +0.001 absorbance unit, were tabulated at 5-nm intervals. Glass-calomel electrodes, used for all p H measurements, were calibrated against standard buffer solutions to 0.05 p H unit prior to each use. Measured p H values t o two decimal places were retained in the calculations. Stock Solutions. Samples, 0.1932 gram, of Eastman AR grade PCV were dissolved in 500 ml of deionized water. Fresh solutions were prepared weekly. Stock Sn(1V) solu-
Soln No.
PH
tions were prepared by weighing anhydrous AR grade sodium stannate into 6.13M HC1. Pyrocatechol Violet Solutions. Two sets of PCV solutions were used in this study. The first set, consisting of nine solutions at constant concentration of 8 X 10-5M and various acidities, was used t o determine the acid dissociation constants of PCV. The solutions, adjusted with HC1 and NaOH to the p H range 0.42 to 8.18, were made up to 1M C1- with NaCl. The p H data and the absorbance matrix of this solution set from 700 t o 260 nm is given in Table I. The corresponding spectra given by Suk and Malat (6) were similar to those measured here, but the present spectra covered a wider wavelength range. The second set, used to establish the principal PCV ligand species at the optimum p H for metal-ligand formation, consisted of six solutions at PCV concentrations ranging from 2 t o 7 X 10-5M, all at p H = 3 and (Cl-) = 1M. The
Table I. Absorbance Matrix of 8.0 X 10-5MPCV Solutions as a Function of pH and Wavelength Absorbance 3 5 6 7 8 4 1 2 5.20 3.05 4.09 6.03 7 .-11 1.01 2.02 0.42
9 8.18
A, nm
700 695 690 685 680 675 670 665 660 655 650 645 640 635 630 625 620 615 610 605 600 595 590 585 580 575 570 565 560 555 550
545 540 535 530 525 520 515 510 505
500 495 490 485 480 475 470 465 460 455
170
0.001 0.001 0.001 0.002 0.003 0.005
0.006 0.009 0.010 0.01 1
0.016 0.021 0.028 0.037 0.049 0.068 0.092 0.127 0.174 0.242 0.333 0.452 0.598 0.772 0.972 1.160 1.324 1.455 1.534 1.555 1.527 1.466 I . 382 1.288 1,194 1.109 1.026 0.948 0.876 0.815 0.772 0.741 0.724 0.725 0.734 0.756 0.783 0,808 0.837 0.862
0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.002 0.003
0.001 0.001 0.001 0.001 0.001 0.001 0,001 0.001 0.001 0.001
0.004
0.001 0.002 0.003
0.006 0.008 0.011
0.014 0.018 0.024 0.033 0.042 0.058 0.078 0.102 0.138 0.173 0.211 0.244 0.277 0.298 0.311 0.318 0.324 0.330 0.339 0.352 0.370 0.398 0.430 0.474 0.527 0.589 0.652 0.723 0,808 0.892 0.969 1.048 1.120 1.182 1.229
0.001
0.004 0.004
0.005 0.006 0.007 0.008 0.008 0. oG9 0.011 0.016 0.020 0.029 0.037 0.046 0.056 0.069 0.083 0.101 0.123 0.153 0.187 0.230 0.281 0.339 0.408 0.481 0.566 0.650 0.749 0.840 0.947 1.031 1.121 1 ,207 1.277 1.333
0.001 0.001 0.001 0.001 0.001 0.001 0,001 0.001 0.001 0.001 0.001 0.002 0.003 0.04 0.004
0.005 0.005 0.005 0.005 0.005 0.005
0.005 0.005
0.006 0.009 0.012 0.019 0.028 0.036 0.047 0,062 0.081 0.105 0.136 0.171 0.218 0.267 0.328 0.392 0.470 0.554 0.642 0.739 0.838 0.940 1.025 1.120 1.200 1.273 1.327
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
0.001 0.001 0.001 0.001 0.001 0.002 0.002 0.003 0.003 0.003 0.004
0.005 0.005 0.006 0.006 0.006 0.007 0.007 0.007 0.007 0.007 0.007 0.008 0.010 0.014 0.018 0.026 0.033 0.042 0.052 0.070 0.089 0.113 0.143 0.181 0.227 0.278 0.335 0.402 0.480 0.561 0.652 0.747 0.842 0,946 1.034 1.126 1.212 I .282 1.337
0.001 0.008 0.019 0.029 0.042 0.055
0.068 0.078 0.081 0.083 0.082 0.081 0,080 0.080 0.080 0,080 0.083 0.089 0.092 0.097 0 . 100 0.103 0.107 0.108 0.109 0,108 0.108 0.107 0.108 0.112 0.120 0.132 0.152 0.174 0.208 0.244 0.292 0.348 0.411 0.479 0.559 0.647 0.734 0.824 0.923 1.012 1.096 1.178 1.241 1.292
0.001 0.010 0.025 0.042 0.058 0,076 0.092 0.103 0.108 0.111 0.109 0.108 0.106 0.107 0.112 0.116 0.130 0.144 0.158 0.168 0.170 0.171 0.169 0.164 0.161 0.157 0.152 0.150 0.149 0.151 0.156 0.165 0.181 0.201 0.230 0.264 0.308 0.360 0.420 0.488 0.568 0.647 0.734 0.827 0.914 1 .Ooo 1.082 1.158 1.219 1.266
0.001 0.014 0.030 0.046 0.068 0.089 0.107 0.122 0.136 0.150 0.164 0.183 0.217 0.263 0.330 0.423 0.543 0.677 0.800 0.900 0.954 0.964 0.942 0.903 0.858 0.813 0.776 0.740 0.708 0.674 0.644 0.617 0.592 0.570 0.558 0.552 0.556 0.568 0.586 0.608 0,642 0.674 0.715 0.756 0.804 0.848 0.887 0.928 0.959 0.987
0.001 0.014 0.031 0.050
0.074 0 . 100
0.128 0.153 0.174 0.202 0.234 0.282 0.356 0.454 0.600 0.800 1.040 1.320 1.574 1.780 1.913 1,960 1.931 1.853 1.774 1.680 1.617 1.547 1.478 1.414 1.342 1.267 1.189 1.113 1.046 0.980 0.927 0.874 0.832 0.790 0.750 0.713 0.686 0.657 0.636 0.611 0.596 0.577 0.560 0.548
Continued next page
Soh No. PH A, nm 450 445 440 435 430 425 420 415 410 405 400 395 390 385 380 375 370 365 360 355 350 345 340 335 330 325 320 315 310 305 300 295 290 285 280 27 5 270 265 260
1
9
0.42
1.01
3 2.02
0.875 0.888 0.889 0.884 0.866 0.845 0.811 0.778 0.737 0.698 0.661 0.631 0.609 0.592 0.583 0.577 0.567 0.544 0.520 0.489 0.462 0.425 0.398 0.381 0.374 0.381 0.400 0.418 0.424 0.428 0.439 0.489 0.610 0.744 0.796 0.774 0.702 0.625 0.561
1.262 1.276 1.279 1.261 1.228 1,183 1,121 1.058 0.986 0.916 0.852 0.780 0.722 0.672 0.630 0.596 0.569 0.544 0.528 0.514 0.506 0.496 0.487 0.481 0.480 0.482 0.494 0.507 0.517 0.524 0.539 0.573 0.649 0.768 0.852 0.844 0.759 0.644 0.547
1.373 1,394 1.394 1,376 1.344 1.289 1,224 1.150 1.072 0.996 0.919 0.841 0.772 0.717 0.664 0.627 0.602 0.582 0.568 0.557 0.549 0.539 0.532 0.527 0.519 0.514 0.516 0.521 0.526 0.532 0.549 0.582 0.654 0.769 0.870 0.876 0.791 0.672 0.558
L
Table I. (Continued) Absorbance 4 5 3.05 4.09 1,366 1.386 1.389 1.370 1.331 1.281 1.222 1.149 1.065 0.990 0.912 0.837 0.769 0.709 0.654 0.609 0.577 0.548 0.529 0.519 0.514 0.511 0.508 0.506 0.506 0.512 0.527 0.541 0.551 0.563 0.577 0.602 0.674 0.786 0.875 0.868 0.778 0.661 0.556
compositions and spectra of these solutions are given in Figure 1. Tin(1V)-PCV Solutions. Four series of solutions, designated here Series I, 11, 111, and IV, were prepared from Sn(1V) and PCV stock solutions t o contain, respectively, 1.0, 2.0, 3.0, and 4.0 X 10-5M Sn(1V) at PCV: Sn molar ratios 7 : l t o 1:6. All solutions were adjusted to p H = 3.00 f- 0.05 and 1M C1-. The absorption spectra and composition o f t h e four solution sets are given in Figures 2-5. These absorbance data tabulated at 5-nm intervals were corrected for base-line drift before their use in the analysis of composition and stability constants of the Sn(1V)-PCV system. Computer Programs. Six routines were u:ed in various capacities for the analysis of absorption spectra. The Matrix Rank program of Wallace and Katz (7) as modified by Varga and Veatch (8) was used t o determine the number of absorbing species in solution. The Species Number program of Coleman, Varga, and Mastin ( 9 ) gave information o n changes in the number of absorbing species with solution composition within each solution series. This calculation, while conveniently accom(7) R. M. Wallace and S. M. Katz, J . Phys. Chem., 68, 3890 (1964). 39, 1101 (1967). (8) L. P. Varga and F. C. Veatch, ANAL.CHEM., (9) J. S. Coleman, L. P. Varga, and S. H. Mastin, Znorg. Chem., 9, 1015 (1970).
1,380 1.396 1,405 1.381 1.346 1,292 1,228 1.154 1.077 0.991 0.916 0.840 0.772 0.717 0.668 0.630 0.603 0.585 0.569 0.558 0.552 0.547 0.538 0.529 0.521 0.518 0.518 0.521 0.527 0.531 0.547 0.578 0.651 0.770 0.869 0.871 0.786 0.670 0.560
6 5.20
7 6.03
8 7 .-11
8.18
1.328 1I355 1.360 1.350 1.324 1.286 1 ,227 1.155 1.081 0.996 0.922 0.847 0.773 0,707 0.651 0,608 0.575 0.546 0.524 0.509 0.502 0.495 0.491 0,487 0.481 0.476 0.470 0.471 0,476 0.490 0.514 0.557 0.640 0.763 0.862 0.862 0.773 0.565 0.547
1.303 1.324 1.333 1.319 1 ,297 1,256 1,200 1,128 1.053 0.980 0.900 0.827 0.753 0.702 0.643 0.598 0.566 0.538 0.517 0.505 0.496 0.487 0.480 0.476 0.468 0.463 0.460 0.463 0.472 0.485 0.516 0.556 0.641 0.760 0.850 0.838 0.752 0.638 0.534
0.998 1.008 1,011 1.008 0.998 0.974 0.947 0.902 0.854 0.798 0.752 0.704 0.657 0.618 0.580 0.552 0.527 0.508 0.488 0,475 0.466 0.453 0,446 0.440 0.442 0,452 0.474 0.511 0.557 0.606 0.648 0.678 0.708 0.758 0.788 0.750 0.664 0.556 0.491
0.536 0.531 0.531 0.534 0.546 0.551 0.554 0.554 0.548 0.542 0.536 0.530 0.523 0.516 0.512 0,508 0.502 0.492 0.482 0.472 0,458 0,443 0.431 0.431 0.442 0.468 0.518 0.603 0.701 0.794 0.856 0.864 0.828 0.773 0.710 0.632 0.553 0.496 0.472
9
plished graphically for one and two species cases, was most efficiently done by machine for three species in solutions. Programs 3 and 4 were developed t o systematically plot the corresponding solution function, E, us. total ligand concentration, and evaluate corresponding values of the average ligand number, Z, and free ligand concentration (L) for each solution series. The method is similar to that outlined by Rossotti and Rossotti (IO). The Formation Function program of Varga (11) evaluated the stability constants, given the (Fz, (L))data obtained from the Corresponding Solutions programs. Since the results could be valid for mononuclear complexes only, the anomalous results obtained from some solution sets gave the first indication of polynuclear complexes. The Pit-mapping program of Sillen (12) and Sillen and Warnqvist (13) was used for the final calculation of equilibrium constants, given the absorbance data, the solution compositions, the information o n number and nature of the complexes gained from the programs above, and initial estimates of the constants and molar absorptivities. This is a general least-squares curve fitting program for nonlinear as (10) F. J. C . Rossotti and H. S. Rossotti, “The Determination of Stability Constants,” McGraw-Hill, New York, N . Y . , 1961. (11) L. P. Varga, ANAL.CHEM., 41, 323 (1969). (12) L. G. Sillen, Acta Chem. Scand., 18, 1085 (1964). (13) L. G. Sillen and B. Warnqvist, Ark. Kemi, 31, 315-390 (1969).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
171
-
1.2
y0.9 0
2
m
a
%
2 0.6 -
-
0.3
I
0.0
roo
600
500 WAVELENGTH (nm)
I
I
400
300
Figure 1. Spectra of PCV at pH 3 Solution
Concn, M X 1W
Solution
Concn, M X 10s
1
2.0
4 5 6
5.0 6.0 7.0
2 3
3.0 4.0 1.5-
1.2 -
io0
500 400 WAVELENGTH (m)
600
300
Figure 2. Spectra of 1.0 x 10-5M Sn(1V) in PCV (Series I) Solution CPCV, M x 106 Solution cpcV, M x 105 1
0.5
2 3 4
1.0 2.0
3.0
well as linear functions adapted especially for the analysis of absorption spectra. Assuming that Beer’s law is obeyed by each of the J species in solution, the error-square sum, U,is defined in the program:
u=
c ik
J
(Ail,
-
c
Cj*EJk)2
(1)
j=1
where i is the solution number, k is the wavelength, A is the observed absorbance, C is the species concentration and B is the molar absorptivity. The minimum error-square sum, Urn,,, is obtained when = 0, resulting in J simultaneous equations at each wavelength. It is assumed, for nonlinear systems, that the area surrounding the minimum 172
5 6
7 8
4.0 5.0 6.0 7.0
value of the error-square sum, known as the “pit,” is described by a second degree surface (12). The method of variation and refinement of the constants has been summarized in matrix notation (12), and the code used in these studies was adapted from the Fortran version of the program as compiled by Nagano and Metzler (14) and Thomson (15). (14) K. Nagano and D. E. Metzler, J . Amer. Chem. SOC.,91, 2891
(1969). (15) J. A. Thomson, “Computer-Assisted Studies on Quinizarin-
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
2-Sulfonic Acid and its Complexation with Iron(III),” Ph.D. Thesis, The University of Waterloo, Waterloo, Ontario, 1970.
I.5-
1.2 -
0.9
Y
3a
w
2 0.6
0.3
0.0 100
500 400 WAVE L E NGM (nm)
60 0
300
Figure 3. Spectra of 2.0 X 10-5M Sn(1V) in PCV (Series 11)
cpcv, M x 105
Solution 1 2 3 4
1.0 2.0
7
3.0
8
CPCV,
M
x
106
4.0 5.0 6.0 7.0
300
500 400 WAVELENGTH (nm)
600
100
Solution 5 6
0.5
Figure 4. Spectra of 3.0 X lOV5MSn(1V) in PCV (Series 111) Solution 1 2 3 4
CPCV,
M
x
106
cpcv, M x
Solution
0.6
5
1.0 2.0 3.0
7
105
4.0 5.0 6.0
6
THEORY AND CALCULATION OF RESULTS Acid Dissociation Constants of PCV. Matrix rank calculations on the PCV absorbance data of Table I, assuming an instrumental photometric error, AT, of 0.005 absorbance unit (8), indicated four absorbing species over the given pH range. The red form which absorbed strongly at 550 nm in the highly acid solutions No. 1 and No. 2 of Table I was the neutral molecule, H 4 L (6). Between pH 1 and 2, the color changed sharply because of ionization of the sulfonic acid group (6) forming the yellow
H3L-. This species, with maximum absorbance at 440 nm, was the predominant species from pH 2 to 5. Between pH 5 and 6, the color changed to violet, forming HzL2- which absorbed at 595 nm. No obvious color changes were apparent from pH 6 to 8.18, but the matrix rank calculation detected a 4th species in the solution set, presumably HLa-, Independent rank calculations indicated 2 dominant species in solutions No. 1-5, and 3 species in solutions No. 3-9. The species, H L - , was present in both groups. Loss of
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
173
Figure 5. Spectra of 4.0 X 10-jM Sn(IV) in PCV (Series IV)
cpcv, M x
Solution 1 2 3
4
Solutions: AT
1-8
2-8
1-8
3-8
1-7
1-5
1-7
0.001
4 4 4 4 35 3 3 3 3 3
3 3 3 3 3a 3 3 3 3 3
4 4 4 4 4“ 4 4 4 3 3
3 3 3 3 3a 3 2 2 2 2
4 4 4 ’ 4 3a 3 3 3 3 3
3 3 3 3 3a 3 3 2 2 2
3 3 3 3 3a 3 3 2 2 2
0.007
0.008 0.009 0.010 a
(HL3-) = Cpcv~r (H2LZ-) = C ~ ~ ~ C Y K ~ ’ ( H + ) (H3L-)
=
l/[l
(HL-)(H+)/(H4L)
(2)
Kz
=
(H2L2-)(H+)/(H3L-)
(3)
K3
=
(HL’-)(H+)/(HzL2-)
(4)
+ Ki’(H+) + Ki’K2’(HI-)’ + K I ’ K ~ ’ K ~ ’ ( H + )(5) ~]
Subroutine EQUIL in the Pit-mapping program was coded to calculate the equilibrium concentrations of all species at 174
C~~VCYK~’KZ’(H+)~
(6)
(7) (8) (9)
Six iterations within the Pit-mapping program were required for convergence to a minimum error-square sum of 0.982. The final values of the constants were:
were converted to the corresponding formation constants, Kt’, i = 1, 2, 3, starting from HL3-. The fraction, C Y , of the total ligand concentration as the least dissociated species, HL3-, was then CY
=
(H4L) = C~CVCYKI’K~’K~’(H+)’
the 4th proton cannot be detected in the p H and wavelength ranges studied here (6). The stepwise dissociation constants of PCV, written in the usual way : =
105
3.0 4.0 5.0
the given values of total ligand concentration, CXV, and pH, given an initial guess of 0.26 for pK1 (typical of sulfonic acids) and estimates of pK2 and pK3 (7.2 and 8.0, respectively) from Ryba and coworkers (16):
Accepted value.
KI
cpcv, M x
5 6 7
Table 11. Number of Absorbing Species in Tin(1V)-Pyrocatechol Violet Solutions Rank Series I Series I1 Series 111 Series IV
0.002 0.003 0.004 0.005 0.006
Solution
105
0.66 1.0 2.0 2.5
pKi
=
0.26 zt 0.01
pKz
=
7.51
* 0.01
pK3 = 8.33
+ 0.02
The final values of the molar absorptivities as a function of wavelength calculated by the program for the several PCV species are shown in Figure 6. The concentrations of the PCV species as a function of pH calculated using the constants above are shown in Figure 7. At pH 3, the acidity recommended by Ross and White ( 5 ) for the analysis of tin by PCV, Figure 7 shows that the concentration of the HpL- species is dominant. Matrix rank calculations on the absorbance data of Figure 1 verified the presence of a single observable species. The Species Number program (9) applied to the same data gave a series of straight lines through the origin indicating, also, the presence of’a single absorbing species. (16) 0. Ryba, J. Cifka, M. Malat, and V. Suk, Collecf. Czech. Chem. Commun., 21, 349 (1956).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
*w
12
-
620
h
i
:
560
500
440
380
260
320
WAVELENGTH (nm)
Figure 6. Molar absorptivities or PCV species
The absorbance data at the peak maxima for PCV in Figure 1, 440 and 280 nm, were found to obey Beer's law over the concentration range studied. The molar absorptivities were 17,385 and 10,785 cm-1 mole-' liter at 440 and 280 nm, respectively-in excellent agreement with the corresponding values calculated by the Pit-mapping program (Figure 6). Number and Nature of Sn(1V)-PCV Complexes. Since the Pit-mapping program tested but one model at a time, it was more efficient in both programming time and computation cost t o determine the number and empirical formulas of the Sn-PCV complexes externally rather than by trial and error within the program itself, Matrix rank calculations, made on several combinations of solutions from each series shown in Figures 2-5, are summarized in Table 11. Absorbance readings from 660 to 265 nm at 5-nm intervals were used as input data. The number of absorbing species in each set analyzed of Series I was three using AT = 0.005. However, at AT = 0.004, the rank of solutions 1 through 8 was four. This was due to the presence of the small absorption band at 610 nm in solution 1 shown in Figure 6. This peak at 610 nm occurred only in those solutions where the ratio PCV:Sn was less than one. Since the free ligand, H3L-, absorbed at 440 nm and contributed a rank of one, the number of metal-ligand species in Series I was three. The same reasoning applied to the results obtained for Series 11. The rank of three for solutions 1 through 5 of Series I11 was due to the presence of three metal-ligand species, since the free ligand absorbance at 440 nm was negligible. The observed rank of four for solutions 1 through 7 was due to the three metal-ligand species and the absorbance of the free ligand in solutions 6 and 7. The rank of Series IV was three also since there was no free ligand excess. When solutions having values of the ratio PCV: Sn less than one were omitted from the rank calculations, the rank was diminished by one. The species responsible for this observation absorbed at 610 nm, and the possible presence of a polynuclear complex was indicated. The Species Number program, described previously (9), tested each data set for linearity assuming one, two, and three absorbing species with nonconstant stoichiometry. The best straight-line fits were obtained for the three species case.
24-
E t
E [
6810-
i2-
g 14?
16-
'Et
/ PI -
I
I
I
2
3
4
I
I
I
I
I
3
6
9
8
9
20 0
1
PH
Figure 7. Relative concentrations of PCV species us. pH
cpcv= 8.0 x
10-5~
The calculations were made on solutions 2 through 8 of Series I, 3 through 8 of Series 11, and 1 through 7 of Series 111 and IV. Two graphical procedures were used next to obtain information concerning the composition of the Sn(1V)-PCV complexes. While these methods were not essential for computer analysis of the data, they gave valuable information regarding the models which should be tried in the Pitmapping program. Mole-ratio plots, as described by Yoe and Jones (17), were made at 550 nm and 610 nm for each of the four series of solutions. The results are shown in Figure 8. At 550 nm the break in the mole-ratio plot for Series I occurred at a value of two for the ratio PCV: Sn corresponding to a complex of the composition ML2. The maximum value of PCV:Sn decreased from Series I through Series IV and the breaks in the curves occurred between values of one and two for the ratio. This indicated a mixture of 1 : 1 and 1 :2 Sn(1V)PCV complexes. The slope of the mole-ratio plots at 610 nm showed a break at a PCV:Sn value of one-half indicating the presence of a dinuclear complex, M2L.
(17) J. H. Yoe and A. L. Jones, IND. ENG. CHEM.,ANAL. ED., 16, 111 (1944).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
175
Figure 8. Mole-ratio plots of Sn(1V)-PCV absorbance
log *PI1 log *PI2 log
*PZl
Urnin
Table 111. Formation Constants of Tin(1V)-Pyrocatechol Violet Complexes Series I Series I1 Series 111 Series IV Av 7.649 7,765 7.970 7,823 7.80 14.594 14.758 15.282 14.963 14.90 13.210 12.451 13.136 12.889 12.92 0.132 0.337 0.184 0.193
The Holme-Langmyhr method (18) for determining the values of m and n in the complex M,L, was used t o check the existence of the dinuclear Sn(1V)-PCV complex. The value of the ratio n/m was one-half and n was equal to one verifying the earlier results. The method of corresponding solutions (10) could not be used for a quantitative interpretation of spectrophotometric data in the presence of polynuclear complexes, but the method was used to check for the presence of such species. The Corresponding Solution program was run on the absorbance data of all 4 solution series (Figures 2-5). Corresponding solutions plots were obtained in the wavelength range 515 to 590 nm, but n o well behaved curves were obtained in the region of 610 nm. Corresponding (E, [L]) data points were obtained a t 535, 550, 565, and 580 nm, but different curves were obtained a t each wavelength-the result expected if polynuclear species were present. Stability Constants of the Sn(1V)-PCV System. For the formation reactions Sn4+
+ H3L-
+ 2H3L2Sn4+ + H3L-
Sn4+
-j
-j
-+
+ Sn(H2L)2+ 2H+ Sn2H2L6++ H+ SnH2LZ+ HT
(10)
(1 1) (12)
(18) A. Holme and F. J. Langmyhr, A m i . Chim. A c f a , 36, 383 (1966). 176
Std dev
0.13 0.30 0.34
the overall formation constants are *&, *&, and *PzI’ respectively. Omitting charges, the mass balance equations for ligand and metal are: CpcV= [H,L] C S= ~ [Snl
+ [SnHzL] + 2[Sn(H2L)d + [ S ~ Z H Z L(13) I
+ [SnHLI + [Sn(H2LM + 2[SnzH2Ll
(14)
In terms of the formation constants, Equations 13 and 14 become
*PdSnl2/[H11 - CPCV= 0 (15)
which, when given the * P constants, H+ ion concentrations and the analytical concentrations of ligand and metal, may be solved for the two unknowns [H3L]and [Sn], by Newton’s method. Initial approximations were [H,L] = CPCVand [Sn] = CS,. Using these roots, the concentrations of all Sn(1V)-PCV complexes were calculated from the formation equilibrium expressions of Equations 10-12. By using Cramer’s rule, these concentrations were employed t o obtain a better estimate of the molar absorptivities required by the Pit-mapping program to minimize Equation 1.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
WAVELENGTH (nm)
Figure 9. Molar absorptivities of Sn(1V)-PCV species
Separate calculations were run on the solution compositions and absorbance data of each solution series presented in Figures 2-5. Initial estimates of log *PI‘, log *BIZ, and log *Pz1were 7.8, 14.7, and 13, respectively. A maximum of 5 iterations was required for convergence in each series. The “best” formation constants are given in Table 111. The final set of molar absorptivities 6s. wavelength for the individual Sn(1V)-PCV complexes, as calculated by the program, is shown in Figure 9. By use of the constants of Table 111, the concentrations of all Sn(1V)-PCV complexes were determined as a function of ligand concentration, as shown in Figure 10.
42
2
t
56-
E 88 97-
51011-
I
I
DISCUSSION
1
In conjunction with the programs designed to give the number and compositions of species in solution from spectrophotometric data, the “Pit-mapping” program for the calculation of stability constants proved to be an efficient tool, both from the standpoint of programming and computation time. By comparison of values of Urnin,easy decisions were possible between alternate models and different data sets. Poor models were readily eliminated. The acid dissociation constants of PCV and the stability constants of the Sn(1V)-PCV complexes were obtained with good precision, and the results verified the use of pH 3 for the spectrophotometric analysis of the Sn(1V)-PCV system. At this pH the concentration of the reacting ligand species, H3L-, was dominant. In addition, the molar absorptivities of the MA and MA2 complexes were both at their maximum, 33,730 and 79,620 cm-1 mole-’ liter, respectively, at a single wavelength, 555 nm, as shown in Figure 9. These are large numbers for molar absorptivities, indicating a high degree of conjugation in the chromophore and verifying PCV as a highly sensitive reagent for the analysis of Sn(1V). The relative concentrations of the various tin(1V) species shown in Figure 10 indicate clearly the advantage of maintaining to 10-4M excess PCV in the analytical system to suppress the formation of weakly absorbing M and M2A species.
3
1
2
1
1
1
0
-
I
I
I
I
I
I
9
8
7
6
5
4
LOO (HI L -1
Figure 10. Relative concentrations of Sn(1V)-PCV species US. free ligand concentration
The apparent preference of Sn(1V) to react with the PCV species, H3L-, with subsequent elimination of a proton to form Sn(1V)-PCV chromophores of the composition Sn,(H&), has not been explained. One aspect of the PCV molecule, however, which was not discussed by Suk and Malat (6), is the possible resonance stabilization of the HzL2-form of the molecule: OH
Ho\
/
Ho\
OH
/
&so3Only the HzLZ-form should be so stabilized, and if stabilization is induced by the field of the highly charged Sn4+ ion, this could account for the preferred existence of the HzL2species as ligand. Also, resonance stabilization would help explain the large molar absorptivities of the various
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
177
chromophores, especially MA2 where the metal ion bridged two such resonating ligands. The role of chloride in these complexes could not be studied by the present method, but it is probable that chloride ions occupy vacant coordination positions on Sn(1V). It is suggested, also, that chloride-bridge structures are important in the dinuclear, M2A, complex.
RECEIVED for review August 31, 1970. Accepted August 23, 1971. Abstracted, in part, from the Ph.D. thesis of W. D. Wakley, Oklahoma State University, Stillwater, Okla., July, 1970. This work was supported, in part, by the Research Foundation and Computer Center at Oklahoma State University, and by a training grant from the Federal Water Quality Administration.
Determination of Molar Substitution and Degree of Substitution of Hydroxypropyl Cellulose by Nuclear Magnetic Resonance Spectrometry Floyd F.-L. Ho, Robert R. Kohler, and George A. Ward Research Center, Hercules Incorporated, Wilmington, Del. 19899 Two independent NMR procedures for the determination of the number of moles of alkylene oxide combined per anhydroglucose unit (molar substitution, MS) in propylene oxide derivatives of cellulose are described. One of these also is capable of determining the average chain length of the substituent chains and, therefore, the average number of hydroxyl groups substituted per anhydroglucose unit (degree of substitution, DS).
HYDROXYPROPYL CELLULOSE containing at least two moles of combined propylene oxide per anhydroglucose unit is a water-soluble polymer which exhibits an unusual combination of properties-e.g., polar organic solvent solubility, interfacial activity, and thermoplasticity. This polymer is manufactured by Hercules Incorporated under the trade name Klucel. The way in which these properties contribute to performance in a variety of uses depends on the number of moles of combined propylene oxide per anhydroglucose unit (MS) and on the number of hydroxyl groups substituted per anhydroglucose unit (DS). The MS of hydroxypropyl cellulose can be determined by a classical terminal methyl procedure ( I , 2 ) , in which the C-methyl is oxidized by chromic acid to acetic acid, which is then distilled from the reaction mixture and titrated with standard base. Some chromic acids are also distilled from the mixture and are corrected for by an iodometric procedure. Newer approaches for the analysis of substituted celluloses based on instrumental analysis have recently appeared in the literature. A combination chromic acid oxidation-gas chromatography procedure for ethoxyl content of ethyl cellulose has been reported (3). Mass spectrometry has been used to obtain the degradation profile of water-soluble cellulose ethers ( 4 ) to allow direct comparison of different modified cellulosic products. However, despite considerable research efforts, satisfactory methods for determining the DS (1) K. G. Stone, “The C-Methyl Group” in “Treatise on Analytical Chemistry,” Part 11, Volume 13, I. M. Kolthoff and P. J. Elving, Ed., John Wiley and Sons, New York, N.Y., 1966. (2) K. V. Lemieux and C. B. Purves, Can. J . Res., Sect. B , 25, 485 (1947). (3) H. Jacin and J. M. Stanski, ANAL.CHEM., 42, 801 (1970). (4) H. R. Harless and K. L. Anderson, Text. Res. J., 40, 448 (1970).
178
of hydroxyalkylcellulose have not as yet been developed (5, 6). A method for determining DS by the reaction of hydroxyethyl cellulose with phthalic anhydride in pyridine was reported by Senju (7). Froment (8) used this method on hydroxyethyl and hydroxypropyl cellulose based on the observation that this reaction only occurs on hydroxyalkyl hydroxyl groups. In our laboratory it has been shown that the results obtained using this procedure vary significantly with changes in the reaction conditions. This report describes rapid and specific NMR experiments designed t o measure both DS and MS of hydroxypropyl cellulose. EXPERIMENTAL
All spectra were obtained on a Varian A-60A N M R spectrometer at an ambient probe temperature of 40 “C in standard 5-mm 0.d. glass tubes (Wilmad Glass Co.). Deuterated chloroform (Stohler Isotope Co.) was used as a solvent throughout this work. Tetramethy lsilane (Matheson, Coleman & Bell Co.) was used as an internal standard for chemical shift reference. The trichloroacetylisocyanate used was reagent grade, from Eastman Kodak Co., and was found by proton N M R to contain no detectable impurity other
9 than a trace amount of its proton analog, CHC-N=C=O. Samples of hydroxypropyl cellulose (Klucel E, Hercules Incorporated) were dried at 110 “C for 2 hours before each use. A weight loss of about 4 to 5 % upon drying was noted. Procedure. In the “direct ratio” experiment, samples were dissolved in CDC13 in 5-ml vials to about 5% in concentration. Generally the solution was heated at 50 “C for about 30 minutes t o complete dissolution of the sample. The solution was then cooled to room temperature and filtered through a cotton plug into an N M R sample tube in which the spectra were run. Generally, spectra were obtained with 500 Hz and 1000 H z sweep widths and integrated 10 times with both upfield and downfield sweeps. The precision of the peak area measurement for each individual N M R peak was found t o be better than 3 % at the (5) E. D. Klug, Food Technol., 24, 51 (1970). (6) M. G. Wirick and M. H. Waldman, J . Appl. Polym. Sci.,14, 579 (1970). (7) R.Senju, J . A g r . Chem. Soc. Japan, 22, 58 (1948). (8) G. Froment, Znd. Chim.Belge, 23, 115 (1958).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 1, JANUARY 1972
