ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
is expected to be negligible. Solvent transport can often be controlled to some extent. For example, it is possible to reduce or eliminate the difference in the initial water activity, a,, and, therefore, the transport of water, by the addition of nontransportable solute species such as inorganic salts. The duration of an experiment can be reduced by bringing the initial solute activities close to equilibrium a t the beginning of an experiment on the basis of preliminary runs. In the experiments reported here, a, was above 0.998 in all the limbs with a maximum difference of less than 0.0004. The transport of water was thus estimated to be of negligible consequence on theoretical grounds. Since an order of magnitude for rates of water transport in the isoextraction cell may be of some interest for the general use of the method, an experiment was conducted in which 10 mL each of four concentrated NaCl solutions, 5.79 m, with the initial water activity of 0.7698 (111, were placed in alternate limbs of the isoextraction cell along with four 10-mL samples of water. Other experimental conditions were identical to the ones described earlier. On shaking for 68 h, it was found that the salt solutions were diluted by an average factor of 1.08. The initial difference in a, between the water limbs (a, equaling unity) and the salt solutions in this experiment was 0.230 compared to values less than 0.0004 in the experiments reported earlier and the value of about 0.002 corresponding to an osmolality difference of 0.1. The time of shaking was roughly three times the 24 h found satisfactory for solute equilibration earlier. These data indicate that concentration changes due to water transport can be kept well below 0.1%) in the water-chloroform system for solutes with moderate partition coefficients. On the other hand, if isopiestic measurements are difficult for a solvent because of low vapor pressures, equivalent measurements may be possible using the isoextraction cell, an immiscible solvent providing the pathway for the equilibration of the solvent of interest. A related problem concerns the effect of the continuous solvent on the interactions in the solvent of interest. In the present case, the solubility of chloroform in water is only about 0.570by volume at 25 "C (12). The effective of added organic solvents such as methanol, ethanol, or dioxane on the pK,, values of acids in aqueous solutions (11) suggest that the medium effect due to 0 . 5 7 ~chlororform should be negligible.
1591
The agreement of our pK, data with literature data supports this conclusion.
CONCLUSIONS The isoextraction method has been shown to be useful for the determination of the dissociation constants of organic acids. The primary advantage of the method is that it needs only pH measurements and concentration determinations by direct analysis. In this study, for example, no information was needed regarding the interactions of the extracting species in chloroform such as dimerization or hydration. Since concentrations can be determined a t very low levels, this method should be particularly useful for highly hydrophobic acids and bases which have low solubilities in water or which show effects of aggregation or other competing equilibria in dilute solutions. In parallel work, we have determined the pK, values of some bile acids, which exhibit such characteristics, a t concentrations of the order of M (13). The isoextraction cell should be readily adaptable for studying other types of equilibria such as self-association (3-5), mutual association, or complex formation and for other combinations of solvents.
LITERATURE CITED (1) D. Dyrssen, J. 0. Liljenzln, and J. Rydberg, Ed., "Solvent Extraction Chemistry", John Wiley, New York, N.Y., 1967. (2) Y. Marcus and A. L. Kertes, "Ion Exchange and Solvent Extraction of Metal Complexes", Wiiey-Interscience, New York, N.Y., 1969. (3) P. Mukerjee and A. K. Ghosh, J . Am. Chem. SOC.,92, 6403 (1970). (4) P. Mukerjee and A. K. Ghosh, J . Am. Chem. SOC.,92, 6419 (1970). (5) A. K. Ghosh and P. Mukerjee, J . Am. Chem. SOC.,92, 6413 (1970). (6) P. Mukerjee, J . Phys. Chem.. 69. 2821 (1965). (7) R. G. Bates, "Determination of pH; Theory and Practice", 2nd ed., John Wliey, New York, N.Y., 1973. (8) R. A. Robinson and A. J. Biggs, Trans. Faraday SOC.,51, 901 (1955). (9) F. G. Bordwell and G. D. Copper, J . Am. Chem. SOC.,74, 1058 (1952). (IO) R . G. Bates and G. Schwarzenbach, Helv. Chim. Acta, 37, 1069 (1954). (11) R . A. Robinson and R. H. Stokes, "Electrolyte Solutions", 2nd ed., Butterworth, London, 1959. (12) H. Stephen and T. Stephen, Ed., "Solubilities of Inorganic and Organic Compounds", Vol. 1, R 1, Macmillan, New York, N.Y., 1963. (13) P. Mukerjee and Y. Moroi, unpublished work, University of Wisconsin, 1977.
RECEIVED for review December 5 , 1977. Accepted May 22, 1978. Work supported by Public Health Service Research Grant, AM-17281.
Determination of Terminal Thiol Groups in Sulfur Polymers by Laser Raman Spectrometry Samir K. Mukherjee,"' Gary D. Guenther, and Arun K. Bhattacharya* Hooker Chemicals & Piastics Corp., Research Center, Grand Island, New York 14072
Raman spectrometry is potentially one of the most powerful techniques for polymer characterizations (1,2). Its application as a quantitative tool has been quite restricted. In specific instances, the method is extremely useful as an analytical technique, and is just as accurate as other analytical methods (3). Polythioether sealant materials are room temperature curing rubbers which are formed by combining a basic polythioetherdithiol liquid polymer with an oxidizing agent. The 'Present address, Wilson Greatbatch Ltd.. 10000 Wehrle Drive Clarence, N.Y.14031. *Present address, hlobil Chemical Company, Research & Development, P.O. Box 240. Edison, N.J. 08817. 0003-2700/78/0350-1591$01 .OO/O
performance of cured sealant is believed to be dependent on the terminal thiol groups, and determination of the latter can be used as a method of quality control. It is, therefore, of vital importance to the sealant industry to have a viable method for the assay of thiol group content. Polythioether prepolymers ( 4 ) are highly viscous liquids, partially soluble in selected organic solvents, and contain ca. 1-5 70terminal thiols. Accordingly, the known quantitative methods of determination of mercaptan ( 5 ) have limited usefulness for the assay of sulfur prepolymers. We have developed a laser Raman spectrometric method for quantitative determination of the terminal thiol groups, using ethyl acetate as an internal reference. The method 1978 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
involves comparison of the ratio of thiol S-H stretching (2570 f 10 cm-') peak area of the polymer to ester C=O stretching (1740 f 5 cm-') peak area of the internal reference. Instead of ethyl acetate, any suitable organic compound having negligible solutesolvent reactivity and noninterfering Raman bands can be used as a n internal reference.
EXPERIMENTAL Apparatus. Raman spectra were recorded at room temperature on a Spex Ramalog 1401 spectrometer, equipped with Spectra Physics Model 164 argon ion laser and Model 265 exciter, operated under high resolution and appropriate sensitivity conditions at 514.5 nm. Reagents. Analytical reagent grade anhydrous ethyl acetate was used throughout. Prior to use, n-octyl mercaptan was distilled, bp 198.5-199 "C, and the purity was checked by proton NMR spectrometry and gas chromatography (99t 70).All the other aliphatic mercaptans were similarly purified, and their purity was checked. Procedure. Precisely weighed portions of polythioether prepolymer and ethyl acetate were transferred in a properly stoppered vial, and placed in a mechanical shaker for intimate mixing (2 to 3 h). The mixture was drawn into a conventional capillary tube, and carefully sealed so that loss in weight due to evaporation was negligible. All the spectra were scanned in triplicate under identical spectrometer settings. The peak areas were measured by using a planimeter. n-Octyl mercaptan was chosen as the primary standard. A series of Raman spectral scans of a mixture of 0.8051 g n-octyl mercaptan and 2.6528 g ethyl acetate was used to establish the primary standard peak area ratio (-SH/>C=O) of 0.804 f 0.001.
RESULTS AND DISCUSSION T h e application of laser Raman spectrometry as a tool for quantitative analysis depends on the well-recognized fact that the intensity of a Raman band is linearly dependent on concentration of the functional group producing it. Thus, I , = k,c, and I, = k,c,
All the calculations have been carried out by using Equation 1,and expressing band intensities and concentrations in terms
of peak areas and weights, respectively. In order to arrive a t the 70 -SH group content in polythioether prepolymer, it is necessary to multiply c,(II) by 33.07/146.30 (the weight ratio of -SH in n-octyl mercaptan), and to express the result as a percentage of the sample weight. In a typical experiment, 1.7237 g polythioether prepolymer and 0.3271 g ethyl acetate gave peak area ratio (-SH/>C=O) of 1.205 f 0.003, which corresponds to 1.95 0.01% -SH group. In general, the peak area ratios for a series of prepolymers are reproducible to better than f l % , and the assay data have been found to agree very well with the calculated values, obtained from vaporphase osmometry measurements and functionality plots. We have checked the accuracy and reproducibility of the technique by analyzing typical aliphatic mercaptans. The data have been found to agree within f0.5% of theoretical. It may be, therefore, concluded that the method is suitable for quantitative determination of thiol groups in sulfur liquid polymers, and in any other organosulfur oligomers containing as low as 0.5% SH group, subject to the limitations (6, 7 ) of laser Raman spectrometry in general. Finally, our approach has a general applicability. Polymers or organic compounds, containing high intensity Raman active functional groups, can be analyzed quantitatively by choosing a suitable noninterfering internal standard by this technique.
*
LITERATURE CITED S. K. Freeman, "Applications of Laser Raman Spectroscopy", John Wiiey 8 Sons, New York. N.Y., 1974. W. E. L. Grossman, Anal. Chern., 46, 345R (1974); 48, 261R (1976). D. E. Nicholson, Anal. Chem., 32, 1634 (1960). K. Griesbaum, Angew. Chem., In?. Ed. Engl., 9 , 273 (1970). L. 8.Ryland and M. W. Tamele in "The Analytical Chemistry of Sulfur and its ComDounds", J. H. Karchmer, Ed., Wiley-Interscience, New York, N.Y., Part I; 1970, p 465. P. J. Hendra and C. J. Vear, Analyst(London),95, 321 (1970). M. J. Gail, P. J. kncka, D. S.Watson, and C. J. Peacock, Appl. Spectrwc., 25, 423 (1971)
where i stands for unknown (-SH group) and s stands for internal standard (>C=O group). If (I) stands for reference mixture (n-octyl mercaptan and ethyl acetate) and (11) stands for unknown mixture (polymer and ethyl acetate), then
RECEn'ED
for review February 21,1978. Accepted May 4,1978.
Alternative Method of Analyzing First-Order Kinetic Data Lowell M. Schwartz" and Robert
I. Gelb
Department of Chemistry, University of Massachusetts, Boston, Massachusetts 02 725
T h e well-known method of Guggenheim ( I ) allows the estimation of the rate constant h from measurements 4i vs. ti without the need of making the infinite-time measurement 4- and without utilizing nonlinear regression techniques. We have become aware of an alternative method due to Kezdy e t al. ( 2 ) ,which has not found its way into the literature of analytical chemistry, presumably because of its obscure reference. Since first-order kinetic analysis is so widely practiced and because this method is a t the same time simple and well-adapted to automatic data-recording, we offer this account and include a method of estimating an approximate statistical uncertainty of the rate constant, h. As with the Guggenheim method, measurements of 4, the property linearly related to concentration, are taken in pairs $[' and @,", each pair separated in time by the same fixed interval, 7. Any single measurement, @[, varies with the time, 0003-2700/78/0350- 1592$01 OO/O
t,, from the original t = 0, when 4 was known as $o, according to the familiar
4%- 4- = do - 4-
~
e-kt,
(1)
If Equation 1 is written for measurements 4,'at t , and @["at ( t , T ) and these two equations are divided and rearranged, the following is obtained.
+
4,"= $m(I - e-kr) +
(2)
A plot of 4 , " ~ s $L'will . be linear with slope b = e-kr and with an intercept on the 6'' axis of a = &(l- e-kT).The first-order rate constant from the slope is -In b -2.303 log,&
k = - -
7
0 1978 American Chemical Society
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7
(3)
