fluorides we encountered very well, and it does not interfere with the measuring method. Since we find it somewhat disagreeable to add a sodium-containing compound to the samples, we use it always now instead of the flux, though we have not encountered any troubles with the latter. We still add orthophosphoric acid, however, because it is liquid and volatile and might reach particles of the sample which are not in sufficiently good contact with tungsten trioxide. We add 5 pl of 10% acid instead of the earlier 2 pl of 25%, because it is easier to wet the samples with the larger volume. T o avoid risks of explosion when large samples are burned which develop organic vapors, such samples are always pyrolized under nitrogen first, and the vapors are burned in the intermediate chamber. The orifice U2 is situated in the hot part of furnace N2, so that it cannot be clogged by carbonaceous foam, which can be formed from some kinds of samples. Such foam is broken down by the heat of the furnace before it reaches the orifice. The method of introducing samples through Q into a completely nitrogen filled combustion-hydrogenation tube makes it possible to analyze rather large samples of even rather low-boiling organic liquids. There is no possibility of any formation of explosive gas mixtures. We do not know whether the rigorous gas purification system used really is necessary in the determination of fluorine. We know that it is necessary in the trace determination of sulfur ( I ) , and we use it because we intend to use the same apparatus for this purpose also. The temperature of furnace N4 was 1050 "C in all analyses. We do not know whether this temperature is necessary or optimal or not. In any case, good results were obtained. The spectrophotometric method is essentially that described by Belcher, Leonard, and West ( 4 ) .When we tried to work with small volumes of absorption solution, it was difficult to add the color reagents with a sufficient preci-
sion. The mixed reagent was therefore prepared. I t is added with a syringe with a precision adapter. I t was necessary to use a somewhat lower concentration of acetone to avoid precipitations in the mixture. Also the concentration of the buffer was increased, which was desirable because of the larger samples used. The mixed reagent is stable for several weeks. We keep it at room temperature in the dark. Evaporation of acetone must, of course, be avoided. T o obtain a good spectrophotometric precision, we keep the water and all spectrophotometric reagents at room temperature. We hold all long and narrow cuvets with wooden clamps and do not touch them with our fingers in order to avoid the formation of schlieren in the solution, which would impair the spectrophotometric accuracy. With cuvets shorter than 4 cm, this is not necessary, nor is it necessary with the common wide commercial 10-cm tube cuvets with a volume of 25 ml. The precision of the spectrophotometric method is remarkable in view of the fact that the fluorine-free reagent solution used in the 10-cm reference cuvet has a light absorbance of 1.46 a t 620 nm. ACKNOWLEDGMENT The author is indebted to Ylva K. S.Bjorkman and Lena M. Eriksson for skilled technical assistance. LITERATURE C I T E D (1) (2) (3) (4)
W. J. Kirsten and 2 . H. Shah, Anal. Chem., 47, 184 (1975). R. Belcher, J. Fildes, and A. J. Nutten, Anal. Chim. Acta, 13, 431 (1955). E. Kissa, Microchem. J., 1, 203 (1957). R. Belcher, "Submicro Methods of Organic Analysis", Elsevier, Amsterdam, 1966, p 62.
RECEIVEDfor review July 11, 1975. Accepted September 23, 1975.
Linear Graphical Kinetic Analysis of Mixtures Kenneth A. Connors School of Pharmacy, University of Wisconsin, Madison, Wis. 53706
A mixture of two reactants A and B, reacting by first-order or pseudo-flrst-order kinetics, can be analyzed for the Initial Cz) exp( kAt) vs. exp(kA concentrations by plotting (CF - k B ) f , where 2 is the common product. The slope of the The method can be exresulting straight line is equal to tended to three-component mixtures by including an extrapolation. It is applied to the analysis of mixtures of esters subjected to alkaline hydrolysis.
-
e.
If two reactants undergo a common reaction with different rate constants, their mixtures may often be quantitatively analyzed by means of measurements of the total extent of reaction as a function of time. For first-order or pseudo-first-order reactions, the most convenient way to do this is with a conventional semilogarithmic first-order plot, which will be curved in the early stages of reaction, since both reactants are contributing to the reaction; after the faster component has essentially completely reacted, however, the plot becomes linear, and its extrapolation to zero
time yields the concentration of the slower reacting component in the mixture. Another way to treat the data is by the "method of proportional equations", in which the extent of reaction is measured a t two times, and, with the aid of prior calibration measurements, two simultaneous equations are solved for the two initial concentrations. Mark and Rechnitz ( I ) have described these and related methods in detail. The advantages of the semilogarithmic extrapolation method include its simplicity and its independence of separate rate parameter determinations; in fact, the rate constants can be extracted from the same data used for the analytical determination (2). The weaknesses of this method are its reliance on an extrapolation, often a long one based on the poorest data in the set, and its inapplicability when the relative rate is low and the ratio of slower to faster component is low. Moreover, it makes no use of the best data in the set, those from the early part of the reaction. The method of proportional equations uses data in this time range, but uses them inefficiently. An automated graphical extrapolation method, interesting in the present context ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
87
t
I
005:
t
G02L
100
PO0
300 f
4CC
500
6CC
J
70C
fsec’
Figure 2. Semilogarithmic plot of the kinetic run described in Figure 1
Apparatus. pH measurements were made with a Sargent Model DR pH meter and Corning combination electrode, No. 476051. Reactions were followed with a Cary 14 spectrophotometer having a thermostated cell compartment. Procedure. First, 0.05 ml of an acetonitrile stock solution 0.0025-0.003 M in total esters was added to 3.0 ml of phosphate reaction medium contained in a 1-cm rectangular spectrophotometer cell. After stirring the solution, its absorbance at 400 nm was recorded continuously as a function of time. All reactions were carried out at 25.0 OC. For conversion of absorbances to concentrations the molar absorptivity €400 = 1.99 X l o 4 was used.
RESULTS AND DISCUSSION The alkaline hydrolysis of the p-nitrophenyl esters of some para substituted benzoic acids was selected as the reaction with which to examine the applicability of this proposed method. At constant pH these esters undergo hydrolysis with pseudo-first-order kinetics, and the appearance of the p-nitrophenolate ion is easily followed spectrophotometrically. The relative rates of alkaline hydrolysis of many of these esters have been reported ( 5 ) . Figure 1 shows the plot according to Equation 3 for a mixture of the benzoate (B) and p-chlorobenzoate (A) esters; the relative rate k A / k B = 2.7 and the initial concentration ratio Ci/C: = 1.07 in this system. The plot is made with absorbances rather than concentrations, so the slope and intercept are in absorbance units. Evidently a very satisfactory linear plot is obtained. The points shown here cover the time range from t = 0 to t = 150 sec. The percent recoveries of A and B were 99.1 and 95.3%, respectively. A semilogarithmic plot of the same kinetic run is given in Figure 2, which shows that the extrapolation method would be extremely unreliable in this system, the percentage error in the difference (A, - AtL being very large in the terminal stages of the reaction where the semilogarithmic plot becomes linear. The line drawn in Figure 2 has been made to pass through the correct intercept, but it could not have served as an effective means to determine the intercept a priori. When k A / k B is still smaller or Ci/C! is larger, the failure of the semilogarithmic extrapolation method is even more obvious. Table I lists some analytical results for two-component mixtures obtained with the linear plotting method based on Equation 3. Note that the concentrations actually determined by this method are C i (from the slope) and C i (from the intercept); hence, C i is a derived quantity, and the errors in C i and Cg are not independent. The fraction of B, calculated as the ratio slope/intercept, receives no error 88
ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
Table I. Results of Mixture Analyses by the Linear Plotting Method xa l o S c l ( ~ w ) 1o5c;(~w) _
A
CN C1 C1
a
B
C1 H
F
_
_
kA/kB Taken Found
8.5 2.7
2.0
3.18 2.12 1.06 3.41 2.28 1.13 2.53 3.32 1.10
2.89 2.04 0.96 3.31 2.26 1.35 2.23 3.34 1.28
~
Fraction B
Taken Found
Taken Found
0.99 1.98 2.98 1.07 2.13 3.18 1.46 0.73 2.18
0.24 0.48 0.74 0.24 0.48 0.74 0.37 0.18 0.67
0.98 2.05 3.06 1.27 2.03 2.76 1.31 0.59 1.86
0.25
0.50 0.76 0.28 0.47 0.67 0.37 0.15 0.59
X in X-C,H,COOC,H,-NO,.
contribution from volumetric factors or concentration conversions. The principal source of error in this graphical method is in the k A and k B values required to make the plot. These must be determined in separate experiments on the individual components, and the assumption is made that the same values apply in the reaction of the mixture. Aside from normal experimental uncertainty, changing reaction conditions may weaken this assumption. It is also possible that the two compounds interact in their mixture, with mutual kinetic effects. Some complication of this kind apparently occurred in these systems, degrading the analytical accuracy. For example, the semilogarithmic extrapolation method applied to a mixture of the cyanobenzoate and the chlorobenzoate yielded k A = 0.0335 sec-I and k B = 0.00324 sec-I, whereas the independently measured values (which were used to make the linear plot) were k A = 0.0310 sec-l and k B = 0.00364 sec-l. Figure 3 shows the analysis of a mixture of the cyanobenzoate ( A ) , chlorobenzoate ( B ) , and benzoate (C) esters. These results are found from the plot: lo5 C i , taken 1.41, found 1.45; lo5 COB, taken 1.51, found 1.31; lo5 C& taken 1.41, found 1.60. These experiments reveal that this new graphical method is capable of application to some mixtures that cannot be treated by the semilogarithmic extrapolation method. When k A / k B is small or when ci/cg is large, the new meth-
O5I
Figure 3. Analysis of a three-component mixture; details as described in the text
od is superior. When k A l k B is large, the semilogarithmic plot will usually be the preferred method. Thus, of the mixtures reported in Table I, the cyanobenzoate-chlorobenzoate system can be handled with semilogarithmic plotting, whereas the other two systems require the new method. Although this graphical technique requires that the rate constants be independently measured prior to its application and that Cg be known, its notable advantage is that it can make use of all of the kinetic data, and it nicely complements the semilogarithmic graphical method.
ACKNOWLEDGMENT The ester samples were kindly furnished by Joseph R. Robinson.
LITERATURE CITED (1) H. B. Mark, Jr., and G. A. Rechnitz, "Kinetics in Analytical Chemistry", Wiley-lnterscience, New York, N.Y., 1968. (2) H. C. Brown and R . S. Fletcher, J. Am. Chem. SOC.,71, 1845 (1949). (3) J. B. Worthington and H. L. Pardue. Anal. Chem., 44, 767 (1972). (4) B. G. Willis, W. H. Woodruff, J. R. Frysinger, D. W. Margerum, and H. L. Pardue, Anal. Chem., 42, 1350 (1970). (5) R. J. Washkuhn, V. K . Patel, and J. R. Robinson, J. Pharm. Sci., 60, 736 (1971).
RECEIVEDfor review July 7, 1975. Accepted October 1, 1975. This work was supported in part by National Science Foundation Grant GP-36567.
Thermoparticulation Analyses of Malonic Acid Compounds J. D. B. Smith, D. C. Phillips,' and T. D. Kaczmarek Westinghouse Research Laboratories, Pittsburgh, Pa. 15235
Decomposition studies of malonic and related carboxylic acid compounds were carried out using the new technique of organopartlculation analyses (OPA). When an ion chamber detector technique Is used, malonic acid and seven of its alkyl and aryl carbon-substituted analogues are strong emitters of particulates at temperatures below 200 'C. Chemically similar carboxylic acids, such as oxalic and maleic, do not show this behavior. This particulatlon was found, in several instances, to be in close proximity to the llterature decomposition temperatures for these compounds. However, in other cases, particulation Is observed well beneath and sometimes well above the literature decomposi-
tion values. Mass spectral studles on the effluent arlslng from the decomposition of these compounds were carried out in an attempt to characterize the exact nature of the particulates. Indications are the particulates may consist of aerosol size particles of volatile carboxylic acid "ollgomers" suspended In an atmosphere of carbon dioxide.
Thermoparticulate analysis, which was used by Doyle ( 1 ) for polymer degradation studies, is a technique based upon the detection of condensation nuclei evolved from polymeric materials undergoing decomposition when s-ubjected to ANALYTICAL CHEMISTRY, VOL. 48, NO. 1, JANUARY 1976
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