1304
Anal. Chem. 1980, 52, 1304-1308
the j t h of which being equal to Iiwhen 0.99 + j 0.01 5 d, < 1 + j 0.01; i = 1, 2, . . ., n; j = 1, 2, . . ., 900. Thus, e.g., the diffraction pattern interplanar spacing intensity[l]
[AI
I 2.115 1.972 1.224 I
80
100
60
LITERATURE CITED
corresponds to a string of 900 numbers, the 23rd of which being equal to 60, the 98th of which being equal to 80, the 112th of which being equal to 100 and all others being equal to zero: [0, 0 , 0, . . ., 0, 60, 0 , . . ., 0 , 8 0 , 0 , . . ., 0 , 100, 1. 2. 3.
22. 23. 24.
97. 98. 99.
0,
...)
113.
111.112.
0,
0,
01
898. 899. 900.
In this way, a one-to-one correspondence is defined between the set of all diffraction patterns and the class M of all ntuplets of nonnegative numbers ( n = 900). Define further addition, scalar multiplication, and inner product in the class M as follows:
fi + 5 = (hl, hz, . ', h900) *
+ (g1, gz, . . *, g900) = + g1, h2 + g2, ' * .?h900 + g900) ., hgO0)= ( a h l , a h 2 , . . ., ahgo0); (hl
+
ah = a ( h l , hZ,. .
diffraction phase analysis (Equation l),the overlapping of the diffraction lines of individual components of the mixture analyzed corresponds simply to the summation of the corresponding coordinates of their pattern vectors according to the rule of vector addition.
6,5) = ((h, hz, . . ., h g d , (gl, g2, . . ., g
d ) = hlgl + hzgz + ' * + h900g900
Then M is a euclidean 900-dimensional space. Of course, the choice of the number and distribution of the coordinate hyperplanes of this space ( 3 ) can be suitably adjusted to the individual problem in question. Another, more general model was formulated in (2),where powder diffraction patterns were represented as vectors in a real Hilbert space (infinite-dimensional vector space). It is an important benefit of the vector representation of powder diffraction patterns that it removes problems connected with line overlap. In the vector model of powder
J. Fiala, J . Phys. D, 5 , 1874-76 (1972). J. Fiala, J . Appl. Crysta//ogr.,9, 429-32 (1976). P. C. Jurs and T. L. Isenhour, Chemical Applications of Pattern Recognition", John Wiley & Sons, New York, 1975, Chapter 2. P. C. Jurs, Anal. Chem., 43, 1812-15 (1971). J. Fiala, Hutn. Llsty, 32, 435-37 (1977). E. M. Burova, N. P. Zidkov. A. G. Zilberman, V. V. Zubenko, N. S. Nabutovsklj, M. M. Umanskij, and B. M. Scedrin, Krlstallogr., 2 2 , 1182-90 (1977). G. G.Johnson, "Fortran IV Programs (Version XII) for the Identification of Muhiphase Powder Diffraction Patterns", Joint Committee on Powder Diffraction Standards, Philadelphia, Pa., 1970. R. W. Schliephake, News Jahrb. Mineral., 112, 302-19 (1970). L. K. Frevel, Anal. Chem., 37, 471-82 (1965). G.G. Johnson and V. Vand, Ind. Eng. Chem., 59, 19-31 (1967). L. K. Frevel, C. E. Adams, and L. R. Ruhberg, J . Appl. Ctysta//ogr.,9, 199-204 (1976). E. H. O'Connor and F. Bagliani, J . Appl. Crystalbgr., 9, 419-23 (1976). P. Whittle, "Optimization Under Constraints", J. Wiley, New York. 1971. S. L. S. Jacoby, J. S. Kowalik, and J. T. Pizzo. "Iterative Methods for Nonlinear Optimization Problems", Prentice-Hall, Englewocd Cliffs, N.J., 1972. J. L. Kuester and J. H. Mize, "Optlmization Techniques with Fortran", McGraw-Hill Book Company, New York, 1973. R. C. Tryon, and D. E. Bailey, Cluster Analysis", McGraw-Hill Book Company, New York, 1970. J. A. Hartigan, "Clustering Algorithms", John Wiley & Sons, New York, 1975. G. LT Ritter, S. R. Lowry, T. L. Isenhour, and C. L. Wilkins, Anal. Chem., 48, 591-95 (1976). R. M. Wallace and S. M. Katz, J . Phys. Chem., 66, 3890-92 (1964). H. Margenau and G. M. Murphy, "The Mathematics of Physics and Chemistry", Van Nostrand, Princeton, N.J., 1956. R. W. Rozett and E. M. Petersen, Anal. Chem., 47, 1301-08 (1975). J. J. Kankare, Anal. Chem., 42, 1322-26 (1970). D. L. Duewer, B. R. Kowalski, and J. L. Fasching, Anal. Chem., 48, 2002-20 11976); J. Fiala. Cesk. Cas. Fys. A , 20, 1-4 (1970).
RECEIVED for review April 12, 1979. Resubmitted February 7, 1980. Accepted March 10, 1980.
Flow-Rate Independent Component of the Steady-State Current in Tubular Electrodes P. Lawrence Meschi and Dennis C. Johnson* Department of Chemistty, Iowa State University, Ames,
Iowa 500 1 1
The limiting steady-state response of tubular electrodes is predicted by the equation I , = nFAK, Vl"Cb, where a is Practical electrodes frequently respond according to the equation but with slight deviations of a from I/,. ine ear leastmSquares fits of of vs. v 1 ~ / 3 have a intercept when a # 'I3.The Intercept has been interpreted as resulting from the contribution of "end diffusion" to the total flux in the electrodes even though both positive and negative intercepts have been observed. The use of this evidence for end diffusion is brought into question.
I,, = nFAK,VfaCb
In Equation 1: Cb is the bulk concentration of analyte (mol Cm-3), vf is the fluid flow rate (cm3 S-'), cy is a constant dependent on electrode design and the nature of the fluid dynamics, Kl is the limiting mass transfer coefficient (cm'-& sr') which is a function of electrode design, A is the electrode area (cm2), and and have their usual electrochemical signif.under conditions of fluid cance. For dynamics, (y is predicted to be 1,3 and the product AK, is given by Equation 2 (1-4)
AK1 = 5.43D2/3X213 The limiting steady-state response, I,,, of flow-through electrodes is described by Equation 1. 0003-2700/80/0352-1304$01 .OO/O
(1)
(2)
where X is the length of the tubular electrode (cm) and D is the diffusion coefficient (cm2s-l). The validity of Equations @ 1980 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 52, NO. 8, JULY 1980
1 and 2 for interpretation of data obtained with tubular electrodes has traditionally been based on the observation of a linear plot of I,, vs. cb, at constant V f ,and a linear log-log plot of I , vs. V fwith a slope approximately equal to for constant C b (2-5). Values for CY have generally been reported in the range 0.3440.36; we report here a value of 0.234 for an electrode which had not been cleaned. Important assumptions made in the derivation of Equations 1 and 2 include the following: (i) the parabolic profile for laminar flow in a tube is approximated by a linear equation near the surface of the tubular electrode; (ii) cylindrical diffusion to the electrode surface is approximated by linear diffusion; (iii) mass transport by axial diffusion is negligible in comparison to transport by convection; and (iv) the fraction of analyte consumed by the electrode reaction is negligible so that the boundary condition c = C b applies a t the axis of the tubular electrode. In general, these assumptions are valid when the thickness of the diffusion layer is much smaller than the radius of the electrode (i and ii), the flow rate is moderately fast (iii), and the tubular electrode is not very long (iv). These assumptions were tested by Flanagan and Marcoux using digital simulation (6). They determined the error resulting from the assumptions to be negligible for X D l V f < lo4 with only small error for values to Tubular electrodes which are commonly applied to electroanalysis frequently have values of XDIVfgreater than For example: XD/Vf = 1.2 X lo4 for X = 0.2 cm, D = 1 x cm2 and V f= 1 mL min-’. It is not known if the error affects only the practical value of Kl, or if deviation of a from ‘I3might also result. There are many causes for deviation of the observed response of practical electrodes from the theoretical predictions of Equations 1and 2. The assumption of laminar flow is easily negated by the turbulence produced a t irregularities in the wall of the tubular channel, particularly a t the interface of the inlet channel with the electrode surface. Capillary leakage may also occur at this interface, and analyte diffusing into the interfacial space undoubtedly is electrolyzed with a response different than predicted by Equations 1 and 2. A more serious limitation on the theory, which is well within the control of the analyst, is the result of the selection of an electrode potential which is not within the region for a mass-transport limited reaction. The reversibility of electrode reactions is frequently decreased by adsorption of impurities from solution during the electroanalytical application, and deviation of the actual response from the theoretical is increased as the flux of the electroactive species is made larger, i.e., higher Vf and Cb. It appears that a common practice is developing to assume a = 1 / 3 for tubular electrodes and to then test the compliance of these electrodes with the theoretical predictions by examining the linearity of plots of I,, vs. Vf1/3(7-9).Blaedel and Iverson (7) have reported on the response of one electrode for Vf = 1-10 mL m i d . Plots of I , vs. V>I3appeared to be linear; however, lines generated by linear least-squares calculations did not extrapolate to zero for V f= 0 mL m i d . The electrode response was concluded to be of the form
Y =A
+ BVf1J3
( 3)
where A and B are constants and BVf113corresponds to the mass transport-limited response given by Equations 1 and 2, ISB. T h e intercept, A , was postulated to represent a flow rate-independent current, I h d . I h d was observed to be a h e a r function of Cb for a given set of determinations; however, Iind was also found to vary from day to day and to be dependent on the method of electrode pretreatment. The source of Iind was concluded, on the basis of the dependence on c b , to be the axial diffusion of analyte to the electroactive surface a t the ends of the tubular electrode. The slopes of the straight lines calculated by Blaedel and Iverson by the least-squares
140
120
1305
r - 7 t
/A
500
1
L 2 0
04
1 2 Vt”3
(mL
rnl”.’)’’3
Flgure 1. Recalculated values of steady-state current from data in Reference 7. I,, = ~ I F A K , V , ~ CnFAK,Cb ~. = 60.0 nA minm mL-*
Table I. Values of Slope and Intercept for the Linear Least-Squares Fit of Data Plotted in Figure 1 slope, intercept, nA min”3 mL-1’3 nA
01
0.300 113 0.360
51.7 60.0 67.1
7.5 0.0
-7.5
method ( B in Equation 3) were found to be inversely related to the intercept. Furthermore, all lines calculated by Blaedel and Iverson intersected a t V f = 1 mL min-l when they were extrapolated to V f = 0 mL min-’. For an electrode responding according to Equation 1,the slope of the tangent to a plot of I,, vs. Vf1j3 will be 3anFAK1Vfm-’/3Cb.The plot of I,, vs. Vf113will be a straight line, independent of V fonly for CY = For small deviations of a from ‘I3, the plot will appear to be adequately fitted by a straight line for large V f with a slope which is nearly profrom portional to C Y . The curvature of the plot of I,, vs. Vf1J3 the straight line which fits the data at large Vf will be greatest in the region V , 0 mL min-’, where data are usually not obtained because of the difficulty in controlling the flow rate. Because the slope of the linear fit of the data is proportional to cy for V f >> 0 mL min-’, and since all straight lines must intersect at Vf = 1 mL m i d , the intercept of the calculated line will be positive for CY < and negative for CY > Negative values of intercept were reported by Blaedel and Iverson (Table 11, Ref. 7 ) . Here we give results of a recalculation of the data of Blaedel and Iverson from Ref. 7 , and results of our own experiments, to support our contention that the evidence for a flow rateindependent component of the faradaic current in tubular electrodes is the result of the incorrect statistical treatment of data from practical electrodes whose response deviates from the theoretical.
-
RECALCULATION OF BLAEDEL AND INVERSON’S DATA (7) The data of Ref. 7 are given for Vf with units of mL min-’ and conversion to the cgs system will not be made here. The plots of I,, vs. Vf1J3in Figure 2 of Ref. 7 all intersect at I,, = 60 nA for Vf = 1 mL min-l and C b = 4.0 pM. Hence, the numerical value of nFAKl in Equation 1 is calculated to be 15 nA mine pM-’ m P . A value of 15.0 is calculated for nFAK, at Vf = 1.0 mL min-l from the numerical averages given in Table I of Ref. 7. The values of Vf used by Blaedel and Iverson are concluded to be 1,2,3,4,6,8, and 9 mL min-’ on the basis of Figure 2 in Ref. 7 . Values of I,, were calculated for nFAKICb = 60.0 nA minm mL-“ with a = 0.300, ‘I3,and 0.360; and the plots of I,, vs.
r
66
I
,
l
I
I
l
I
1
I
I
A
-
0
Glass-filled T e f ' o n Epoxy Piat,num
0
11
1
I
I
I
1
1
,
I
I
W\
-
I .
to waste
T
5.4 c m
t
contact to I E
liuid in
Figure 3. Cross-section of tubular electrode
mL min-' and were calibrated by measurement of the volume of solution (20-30 mL) delivered into a 50-mL buret during a specified time period. Chemicals. All chemicals were Baker Analyzed Reagents; sulfuric acid was from freshly opened bottles and potassium iodide was used as received. The solution for all experiments reported here was 0.10 M H2S04containing 5.00 X M KI. All water was distilled and demineralized, and solutions of KI were stored under nitrogen to prevent oxidation by air. Procedures. The electrodes were preconditioned in the conventional voltammetric manner by repeated scans of the applied potential between the limits -0.2 V and 1.0 V vs. SCE until consecutive current-potential curves for solutions containing iodide were reproducible. The limiting-current plateau for the anodic wave for iodide was in the range 0.7-0.9 V vs. SCE and measurement of I , was made at a potential of 0.80 V vs. SCE. The sensitivity of the detector was generally observed to decrease slightly over an extended period of use (several hours) or upon storage over night. The sensitivity was restored by polishing the inner surface of the tubular electrode prior to the voltammetric pretreatment. Polishing was with 1-pm Metadi diamond paste from Buehler Ltd., Evanston, Ill. The paste was applied to a 22-gauge Pt wire which was drawn back and forth in the tubular channel of the detector. The paste was cleaned from the channel with a stream of distilled water flowing at high pressure.
RESULTS AND DISCUSSION Values of I,, are shown in Table 11. This includes data obtained without benefit of the polishing procedure applied just prior to the measurement of I,, (Experiment A) as well as data for the same electrode obtained following the polishing procedure (Experiment B). Plots made of I , vs. Vf1I3,shown in Figure 4, appear to be linear and the slopes and intercepts of the plots are given in Table 11. The values of a are significantly less than lI3for data given in Table 11. The linear least-squares f i t to the plots give intercepts which deviate significantly from zero. The experimental values of a , determined from plots of log I , vs. log V ,are also given in Table I1 as well as the slopes and intercepts for the linear fits to plots of I,, vs. V f ausing the experimental values of a. T h e confidence limits (90%) are indicated as well as the coefficient of correlation ( R ) . For other cases observed in our laboratory but not reported here, the nonzero intercepts of the linear least-squares fits to the plots of I,, vs. Val3 were significant only when the experimental values of a were not equal to 1/3. Furthermore, the intercepts were negative for a > and positive for a < lI3. I-E curves recorded for electrodes yielding a < were slightly less reversible than those recorded following application of the polishing procedure. The increase in sensitivity
ANALYTICAL CHEMISTRY, VOL. 52, NO. 8, JULY 1980
Table 11. Experimental Values of Steady-State Current
I, vs.
Experiment A
Experiment B
1.66 2.51 3.90 5.21 6.07 6.96 7.93 8.93
1.70 2.53 3.89 5.24 6.08 6.93 7.85 8.83
15.96 17.77 19.79 21.28 21.73 22.34 23.18 23.82
16.16 18.13 20.57 22.36 23.21 24.05 24.85 25.60
vf"3:
slope ( p A r n i ~ ~ l ' ~
8.66 f 0.43
10.83 f 0.31
R
5.95 f 0.74 0.9976
3.39 r 0.54 0.9993
0.234 * 0.003 0.9987
0.280 f 0.002 0.9997
mL-.1/3) intercept
log I, vs. slope, cy
vf:
R
I, vs. vf": slope, PA min" mL-'Y 14.20 f 0.57 0.12 i 0.84 intercept, p A
R
0.9987
13.93 f 0.28 0.095 k 0.44 0.9997
I, corrected for background observed in absence of iodide. a
1307
CONCLUSION The validity of the concept of a flow-rate independent component of the steady-state current in tubular electrodes which has been proposed to make a significant contribution to the total current even for moderately large V,, e.g., > 1mL m i d , has been brought into serious question. The concept was originally proposed to explain the nonzero intercept obtained for linear extrapolations of plots of I,, vs. V f awhich were made with the assumption that a was equal to the theoretical value of 1 / 3 . The actual value of a describing the response of practical electrodes may vary significantly from and should be calculated from plots of log I,, vs. log V f . Plots of I,, vs. Vfa which are constructed using the experimental a have an intercept which is virtually zero within the uncertainty of the data. We speculate that these findings for tubular electrodes are also applicable to the interpretation of plots of I,, vs. VflI2for flow-through detectors constructed from planar electrodes ( 1 0 , I I ) . Nonzero intercepts for linear extrapolations of those plots have also been explained as the result of a significant flow rate-independent current. APPENDIX: LEAST-SQUARES CALCULATION Calculations of the slope ( B ) and intercept ( A ) of the straight line which best fits data described by the linear equation Y = A + B X is easily accomplished by least-squares regression analysis as reviewed below where .N is the number of data in the set (12).
ZXY - (ZX)(ZY)M/N
T h e linear least-squares method was applied to the analysis of data from tubular electrodes for which the predicted response is given by Equation A-3.
I,, = nFAK,VfaCb
(-4-3)
The slope and intercept were calculated for the best linear fit to plots of I,, vs. Vf1I3as given by Equation A-4. '10
250
130
150
170
190
I,, = A
210
+ BVf1I3
(-4-4)
The transformation of Equations A-1 and A-2 to the form applicable to this case is reviewed below.
t
zx = zvp3 ZY = XI,, = nFAKICbZVf(l Z X Y = nFAKICbZ Vfa+lI3
zx2 = zvf2/3 (zx)2= (ZVfl/3)2
i
i";"
I 0
150
130
v,"
170
90
210
I r t m1n'IOC
Flgure 4. Plots of experimental values of I,. (A) Unpolished electrode: (0)a = (A)a = 0.234. (B) Polished electrode: (0)a =
(A)a =
0.280
which results from polishing the electrode is probably caused by removal of adsorbed material which blocks the active surface area.
(A-6) LITERATURE CITED (1) Levich, V. G. "Physiochemical Hydrodynamics"; Prentice Hall, Inc.: Englewood Cliffs, N.J., 1962; pp 112-1 16. (2) Blaedel, W. J.; Olson, C. L.; Sharma, L. R. Anal. Cbem. 1963, 35, 2 100-2103.
1308
Anal. Chem. 1980, 52, 1308-1310
(3) Blaedel, W. J.; Klatt, L. N. Anal. Chem. 1966, 38, 879-883. (4) Blaedel, W. J.; Boyer, S. L. Anal. Chem. 1973, 45, 258-263. (5) Sharrna, L. R.; Dun, J. Indian J. Chem. 1968, 6 , 593-600; 1969, 7, 485-489; 1970, 8, 170-173. (6) Flanagan, J. B.; Marcoux, L. J. Phys. Chem. 1974, 78, 718-723. (7) Blaedel, w. J.; Iverson, D. G. Anal. Chem. 1977, 4 9 , 1563-1566. ( 8 ) Aoki, K.; Matsuda, H. J. Nectroanal. Chem. 1978, 9 4 , 157-163. (9) Blaedel, W. J.; Yim, 2 . Ana/. Chem. 1976, 5 0 , 1722-1724. (10) Pungor, E.: Feher, 2s.;Nagy, G. Anal. Chim. Acta 1970, 57,417-424.
(11) Feher, 2s.;Pungor. E. Anal. Chim. Acta 1974, 7 1 , 425-432. (12) Blaedel, W. J.; Iverson, D. G. Anal. Chem. 1976, 48, 2027-2028; 1977, 49, 523.
RECEIVED for review November 28, 1979, Accepted March 20, 1980. The support of the National Science Foundation (CHE-7617826) is gratefully acknowledged.
Titration of Organic Compounds as Very Weak Acids with Lithium [ 1,1,1-Trimethyl-N-(trimethylsilyl)]silanamide Dale D. Clyde Trinity University, 7 75 Stadium Drive, San Antonio, Texas 78284
Numerous organic compounds, such as alcohols, acetophenones, esters, anilides, carbamates, and lactams, can be titrated as very weak acids in tetrahydrofuran. End points were determined by potentiometry and by color change of Nphenyl-p-aminoazobenzene. Relative percent errors for the determination of approximately 1.00mmol amounts of sample generally ranged from 2 to 6 % . Examples of compounds which did not react quantitatively with the lithium silylamide reagent were benzophenone, benzyibenzoate, and Nphenylbenzylamine.
Analytical methods for the determination of nitrogenous organic compounds often require time-consuming processes as in the determination of amines and ureas (1). More convenient procedures are direct titrations of these compounds in nonaqueous solvents by the use of sufficiently soluble titrants such as sodium dimethylsulfoxide (Z), lithium aluminum hydride ( 3 ) , lithium aluminum amides ( 4 ) , tetrabutylammonium hydroxide (5, 6), and sodium amide (7). More recently, lithium diisopropylamide in tetrahydrofuran (THF) was employed for the titration of several carbamates (8). Numerous organic substances exhibit acidic characteristics in nonaqueous solvents. Besides alcohols, phenols, or 1,3dicarbonyl compounds, the N-H functional group exhibits an acidity which is dependent upon the activating effect of a neighboring group, especially a carbonyl function. Examples of such nitrogenous, weakly acidic compounds are lactams, ureas, carbamates, and carboxylic acid amides. The weak acidity of these compounds has been explained by the resonance stabilization of the conjugate base (8),as shown below: 0
Rl-~\N/~il I1
-
-
0 Rl/k+N/~"
R' = R carboxylic acid amide R' = RO carbamate R' = R,N urea
For example, when lithium diisopropylamide quantitatively reacts with the hydrogen of the N-H moiety, the conjugate base formed is stabilized by resonance and makes a good leaving group for the completion of the acid-base reaction. It was found, though, that if a phenoxy ester group were a part of the carbamate, it underwent a fission of the 0-CO bond during titration and thus prevented quantitative results. The
reagent had to be freshly prepared for reproducible results (8).
Methods for the determination of carbamates, lactams, and ureas have become important since these compounds are often the active ingredients in many pesticides and pharmaceutical chemicals. Therefore, the purpose of this paper is to compare the properties of lithium [ l,l,l-trimethyl-N-(trimethylsily1)silanamide], (I), with the characteristics of lithium diisopropylamide in order to determine if the former has advantages in terms of stability and sensitivity. I has been reported stable under dry nitrogen (9). In addition to the evaluation of the reagent for nitrogenous compounds, the data are also reported for the titration of oxygen-containing organic compounds.
EXPERIMENTAL Although the end points for the titrations of this work were determined by the color change of N-phenyl-p-amino-azobenzene, a potentiometric titration was performed as a check to determine if the proper color change of the indicator did occur near the equivalence point. For this purpose, a Leeds and Northrup pH meter (Model 7401) and titration cell (Leeds and Northrup Model 7961) were used. A cell cover was held firmly with a special polyethylene ring which snapped in place around the titration beaker. The cover served as a support for a septum through which samples were introduced by syringe. It also supported a glass tube for the continual admission of dry nitrogen. The standard calomel electrode was enclosed in a tapered glass tube. The tube was filled with agar at the tip and served as a salt bridge in order t o prevent mixing with the titration media. It was inserted through a special opening in the polyethylene cover. The indicator electrode was platinum. The potential change of approximately 800 mV was observed for a titration in tetrahydrofuran (THF). Since the electrodes are probably irreversible, the absolute emf readings are without significance. A representative curve is presented in Figure 1 . Indicated in the figure is the color response of N-phenyl-p-amino-azobenzene.During the titrations, the samples were magnetically stirred. Materials. Solvents, THF and benzene, were stored under dry nitrogen in glass stoppered bottles. The tetrahydrofuran (Mallinckrodt analytical reagent grade) was twice distilled from sodium benzophenone ketyl by a procedure recommended in the literature (IO),and the benzene (Mdinckrodt analytical reagent grade) was twice distilled over sodium before use. Solid and liquid samples were Baker Analyzed reagent grade and were used without further purification except for benzoic acid which was resublimed before it was used as a primary standard. Titrant. Lithium 1,1,l-trimethyl-N-(trimethylsilyl)silanamide, (I),was prepared from butyllithium and hexamethyldisilazane.
0003-2700/80/0352-1308$01 .OO/O 'G 1980 American Chemical Society
