Anal. Chem. 1993, 65, 2145-2149
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Quantitative Determination of Volatile Products Formed in Electrolyses of Organic Compounds Wayne A. Pritts, Kenneth L. VieiraJ and Dennis G. Peters* Department of Chemistry, Indiana University, Bloomington, Indiana 47405
A straightforward and accurate procedure has been developed for the quantitation of volatile products that are formed from electrolyses of organic compounds. This methodology, which eliminatesthe need for external cold traps, utilizes an internal standard that is present in both the solution and gas phases of a gas-tight electrochemical cell. By sampling the gas and solution phases of the cell at the end of an electrolysis and by using gas chromatography to determine the quantities of the various volatile products in each phase with respect to the internal standard, one can ascertain the absolute yield of each product derived from the electrolysis of the starting material. In this paper, we present the theoretical background for this technique, including the formulation and use of experimentally measured gas chromatographic response factors, and we demonstratethe applicability of the approach for the quantitation of seven volatile products that are formed by the electrolytic reduction of 1,4dibromobutane at a reticulated vitreous carbon cathode in dimethylformamide containing tetramethylammonium perchlorate. This method can be readily adapted to any compound whose electrolysis gives rise to volatile products. In recent years our laboratory has been involved in studies of the electrochemical behavior of a variety of halogenated organic compounds. One of the most challenging aspects of this work has been the quantitation of small amounts of highly volatile hydrocarbons, both alkanes and alkenes, that are derived from the electrolytic reduction of these starting materials. In seeking solutions to these analytical problems, we have developed a relatively simple and highly accurate procedure based on the sampling and measurement of the hydrocarbon products in the solution and gas phases of a sealed electrochemical cell. In the present paper we outline the theoretical and experimental background for this method and we offer some exemplary results obtained for the electrochemical reduction of 1,4-dibromobutane at a reticulated vitreous carbon cathode in dimethylformamide containing tetramethylammonium perchlorate. Initially, in exploring possible ways to capture, identify, and determine the volatile compounds formed as products in an electrolysis, we considered employing an external trap connected to the electrochemical cell. Traps with widely differing designs have been used for many years for the analysis of volatile species.l-1° Conventional methods include t Present address: The CloroxTechnical Center, 7200 Johnson Drive, Pleasanton, CA 94588. (1) Altieri, V. J. Gas Analysis and Testing of Gaseous Materials; American Gas Assoc., Inc.: New York, 1945. (2) Jeffery,P. G.;Kipping,P. J. Gas Analysis by Gas Chromatography; The Macmillan Co.: New York, 1964.
0003-2700/93/0365-2145$04.00/0
the use of coated or uncoated U-shaped columns immersed in a cold bath (liquid nitrogen, dry ice-acetone, or dry icemethanol) to collect gases from some mobile phase. Subsequently, one can attach such a trap to the injection port of a gas chromatograph, whereupon the trap is heated to introduce the sample into the chromatograph; alternatively, samples to be analyzed can be taken directly from the trap. A key assumption is that a trap immersed in a coolant can capture any volatile organiccompound from a stream of cmier gas. In analyzing a mixture of volatile hydrocarbons, Rijks and co-workers6foundthat the efficiency of a coated-capillary cold trap is a function of the length and temperature of the trap as well as the thickness of the coating; these workers encountered problems with the quantitation of hydrocarbons lighter than n-heptane when the trap was not long enough, not cold enough, or not coated. Although other investigators have not seen such effects, one can explain the contradiction by noting that, if components of a mixture of volatile compounds are present at well above trace levels, a slight loss of gas would not be detectable. Research reported by Graydon and Grob7 helps to emphasize the latter misconception. In the realm of electrochemistry, Dougherty and DiefenderferQ captured and identified volatile products of the reduction of several dibromoalkanes by trapping them in an evacuated system connected to the electrolysis cell, whereas Brown and Gonzalez'o used nitrogen to purge gaseous products from an electrolysis cell into a trap immersed in a dry ice-acetone bath. An unfortunate feature of much of the published work dealing with the analysis of volatile compounds is the absence of experimental detail; too often, the authors mention only that a cold trap was used to collect volatile species. To us, these references painted a clear picture of the need for an efficient, simple, and well-documented way to separate, identify, and quantitate volatile products obtained from electrolyses of organic compounds that does not require the use of an external trap. In previous work" the reduction of tert-butyl bromide at mercury cathodes has been examined, and we have identified and quantitated the volatile electrolysis products (isobutane and isobutylene) by direct sampling and gas chromatographic analysis of both the solution and gas phases of a sealed electrochemical cell. In choosing this analytical approach, we eliminated the need for a cold trap, and no buildup of pressure occurs within a sealed cell because we ordinarily deal with low concentrations of starting materials and products-although this would not be the case for large-scale (3) Pankow, J. F.J. HighResolut. Chromatogr. Chromatogr.Commun. 1983, 6,292-299. (4) Willis, D. E.Anal. Chem. 1968,40, 1597-1600. ( 5 )Westberg, H.H.;Rasmussen, R. A.; Holdren, M. Anal. Chem. 1974, 46, 1852-1854. (6) Rijks, J.A.; Drozd, J.;Novak, J. J.Chromatogr. 1979,186,167-181. (7) Graydon, J. W.; Grob, K. J. Chromatogr. 1983, 254, 265-269. (8)Cason, J.; Way, R. L. J. Org. Chem. 1949,14, 31-36. (9) Dougherty, J. A.; Diefenderfer, A. J. J. Electroanal. Chem. Interfacial Electrochem. 1969,21, 531-534. (10) Brown, 0.R.; Gonzalez, E. R. J. Electroanal. Chem. Interfacial Electrochem. 1973,43, 215-224. (11) Vieira, K. L.;Peters, D. G. J. Org. Chem. 1986,51, 1231-1239. 0 1993 American Chemlcal Society
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industrial processes. To quantitate the volatile components in samples of the solution and gas phases of a sealed electrochemical cell, we decided to employ a method based on the use of an internal standard, a well-established practice in our laboratory. An appropriate internal standard must not be electroactive, must be commercially available, must have properties similar to those of the products, and must reside in both the gas and liquid phases of the electrolysis cell. Whereas the reasons for the first two characteristics of the internal standard are obvious, the last two characteristics deserve a brief explanation. Because gas chromatography is our method of choice for the separation, identification, and quantitation of electrolysis products, the internal standard should possess properties (molecular mass and boiling point) comparablewith those of the products; for example,one would select a hydrocarbon species from either the propane or pentane family to serve as internal standard for the quantitation of products obtained from the electrochemical reduction of a l,4-dihalobutane. If one selects an internal standard that exists only in the liquid phase or only in the gas phase, it is then necessary to know the distribution coefficient between the two phases for each desired volatile product; however, since the distribution coefficient depends on parameters such as temperature and pressure, which are troublesome to control, this kind of internal standard is not a good choice.
THEORETICAL SECTION In performing electrolyses of organic compounds, we typically begin by identifying the products qualitatively with the aid of gas chromatography, gas chromatography-mass spectrometry, or another spectroscopic technique; of course, we are guided by our perceived understanding of the anticipated electrochemicalbehavior of the starting material. Once the products have been identified, we select an electrochemically inactive internal standard that can be introduced into the electrolysis cell and that, by virtue of its distinct retention time, can be used to quantitate each of the products by means of gas chromatography. Because we are addressing in this paper the problem of quantitating volatile products that can reside in the gas phase as well as in the solution phase of a sealed electrolysis cell, our goal is to determine the number of moles of each product in each phase. After this information is available, it is a simple matter to obtain the total number of moles of each volatile product contained in the cell and then to calculate the percentage yield of each product in terms of the number of moles of starting material electrolyzed. Definition and Measurement of a Response Factor. To set the stage for the eventual gas chromatographic determination of each volatile electrolysis product, we introduce the concept of an experimentally measured response factor, which allows us to determine the quantity of each product with respect to the chosen internal standard by means of gas chromatography. We must determine a response factor for the quantitation of each volatile product by performing experiments in which known numbers of moles of each product and the internal standard are introduced together into the assembled and sealed electrolysis cell. For simplicity in the present treatment, let us consider a situation in which we use an internal standard for the quantitation of just one volatile electrolysisproduct. Into an assembledand sealed electrolysis cell, we inject a known number of moles of the internal standard, neatand a known number of moles of the volatile product, nprd. When a sample of the gas phase is removed from the cell with a syringe and is injected into a gas chromatograph, two peaks will be observed, one for the internal standard and one for the product, having peak areas
of (Ass), and (Aprd)g, respectively. We can now define a response factor (RF), for the gas chromatographic analysis of the gas phase, (RF), = [ ( A p r ~ ) , / ( A , a [) ,(1~ , ~ ) . J ( n p r ~ ) , l(1) and we can write an analogousrelation for the response factor (RF), for analysis of the solution phase by replacing the subscript g in eq 1 with the subscript 8:
To arrive at a numerical value for a response factor, we must next consider how to introduce known numbers of moles of the internal standard and the volatile product into a sealed electrolysis cell and then how to determine the number of moles of each species that resides in the gas and solution phases of the cell at equilibrium. Calculation of the Number of Moles of Species Injected into the Cell. To compute the number of moles of internal standard or product injected into the sealed cell, one can employ the van der Waals equation,
[ P + ( n 2 a / p ) 1 ( V -nb) = nRT
(3) where n is the number of moles of the species of interest, P and V are the pressure and volume of the species injected into the cell, Tis the absolute temperature, R is the universal gas constant (0.082 06 L atm/K-mol), a is a measure of the attractive forces between molecules, and b is the effective volume of molecules in 1 mol of gaseous species. Values of a and b can be calculated from the relationships a = 27R2T,2/ 64P, and b = RTc/8P,, because the critical temperature (T,) and critical pressure (P,)are available in compilations of such data.12 In the above expression, P is the prevailing atmospheric pressure, because we sample the speciesto be injected into the cell by bleeding that species from a gas cylinder through a short length of plastic tubing, connected to a syringe needle (to prevent mixing with atmospheric gases) into the atmosphere, and V is the volume of species that we transfer from the short length of plastic tubing into the sealed electrolysis cell with the aid of a gas-tight syringe. Parenthetically, we should mention here that for systems where the quantities of materials injected are small-as is true for the experiments to be described later-it is sufficient to use the ideal gas equation instead of the van der Waals equation. Calculation of the Number of Moles of Species in the Solution and Gas Phases of the Cell. Let us begin by defining the ratio, R, of the number of moles of a species in the solution phase (n,)to the number of moles of that species in the gas phase (n,)of the electrolysis celk
R = n,/ng (4) Alternatively, R is the product of the ratio of the volumes of the solution phase (V,) and gas phase (V,) and of the ratio of the molar concentrations of the species in the solution phase (M,) and in the gas phase (M,):
To obtain an experimental value for R , one must know V,and V ,within the electrolysis cell as well as Maand M,. If identical volumes of the solution and gas phases are withdrawn from the cell with a syringe and are injected into a gas chromatograph for analysis, the ratio MJM, is simply equal to the ratio of the gas chromatographic peak areas, AJA,, where A, and A, are the peak areas for the species from the solution and gas phases, respectively. It is a simple matter to correct for the scenario in which dissimilar volumes of the two phases (12) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of New York, 1987; pp 656-732.
Gases and Liquids, 4th ed.; McGraw-Hill:
ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993
are withdrawn for gas chromatographic analysis. To determine V, one can fill the assembled and sealed electrolysis cell (which does not contain the solution to be electrolyzed) with some liquid (water or an organic solvent); afterward, one measures the volume of that liquid to ascertain the total internal volume of the cell (V,3, and in an actual experiment in which a specified volume of solution (V,) is introduced into the cell, V , is simply the difference between Vht and V,, i.e., V, = Vht - V,. Thus, eq 5 is transformed into the operationally more useful relation R = WJV,)(AJA,) (6) which provides a way to obtain R experimentally. Now we must find the number of moles of the desired species that resides in each phase. Rearrangement of eq 4 gives n, = Rn,
(7)
and we can write the following expression for the number of moles (n) of the desired species originally injected into the cek
+
n = n, n, (8) Substitution of eq 7 into eq 8 yields an expression that relates the total number of moles in the electrolysis cell to both R and the number of moles in the gas phase: n = Rn,
+ n, = (R + l)n,
(9)
Solving eq 9 for the number of moles of the desired species residing in the gas phase yields n, = n/(R + 1)
(10)
from which it follows that n, = n - n,
(11)
Thus far, eqs 3-11 apply to an individual compound (internal standard or an electrolysis product). However, it is possible to recast eqs 10 and 11to refer first to the internal standard (n,& = nSa/(Rstd+ 1) (n,& = natd- (nS& and then to the volatile electrolysis product: (nprc-4, = nprd @prod + 1)
(12) (13) (14)
(15) (nprds nprd - @prod), By substituting information provided in eqs 12 and 14 into eq 1, and that provided in eqs 13 and 15 into eq 2, one can calculate numerical values for the desired response factors, (RF), and (RF),, respectively. An unexpected outcome of the preceding treatment is that the response factors for the gas and solution phases for any given product are numerically identical; that is (RF), = (RF),. To demonstrate this fact mathematically, we can combine eqs 4 and 6 for both the product and internal standard to obtain (npId)J(npd),
k[(Aprd)$(Aprd)gl
(16)
and (n,&/(n,& = k[(Astd)b/(Antd),1 (17) where k = VJVr If eqs 16 and 17 are solved for (nPd), and (n&, respectively, and the results are substituted into eq 1, which is then simplified, it becomes apparent that the new version of eq 1is identical to eq 2 and that (RF), = (RF), = RF. Calculation of t h e Product Yield i n a n Actual Electrolysis. When a response factor has been established
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experimentally with known quantities of the internal standard and a pure sample of the electrolysis product, one is ready to perform an actual electrolysis and to determine the (unknown) percentage yield of the electrolysis product in the presence of a known quantity of the internal standard. After the completion of an electrolysis, known volumes of the solution and gas phases are withdrawn from the cell with a syringe and are injected into a gas chromatograph. To calculate the number of moles of internal standard residing in each phase, one uses eqs 3, 6, 10, and 11. Then eq 1 is rearranged to calculate the number of moles of the electrolysis product in the gas phase of the cell, (nPd), = [(Aprd~,(n,~),l/[RF(A,M)el (18) and eq 2 is rearranged to compute the number of moles of the electrolysis product in the solution phase: (npd), = [(Aprd),(n8~),1/ [RF(A,~,I (19) From the preceding two relations, one gets the total number of moles of the electrolysis product, q,d = (npr+ + (npd),, and then the percentage yield of that product is
5% yield = [nprd(lOO)l/n,hu
(20) where nstmeudenotes the number of moles of starting material electrolyzed. EXPERIMENTAL SECTION Reagents. Tetramethylammonium perchlorate (TMAP), from the G. Frederick Smith Chemical Co., was used as received as supporting electrolyte and was stored in a vacuum desiccator over Drierite. Dimethylformamide (DMF), employed as the solventthroughoutthis work, was American Burdick and Jackson "distilled in glass" material. All deaeration and drying procedures were performed with Air Products UHP-gradeargon. All of the following reagents were used as received: 1,4-dibromobutane (Aldrich, 99%), n-butane (Air Products, instrument grade), 1-butene(Matheson,instrumentgrade),trans-2-butene(Aldrich, 99%), cis-2-butene (Aldrich, 95%1, ethylene (Matheson, instrumentgrade),1,3-butadiene(Aldrich,99+%), propane (Matheson, instrument grade), and n-tetradecane (Aldrich). Electrodes, Cells, and Instrumentation. For cyclic voltammetry a glassy carbon rod (Tokai Electrode Manufacturing Co., Tokyo, Japan, grade GC-20) was press fitted into a shroud of Kel-F to provide a disk-shapedworking electrode with an area of 0.077 cm2. For controlled-potential electrolyses, reticulated vitreous carbon disks (EnergyResearch & Generation, RVC 2x145s) were used; the dimensions of these electrodes as well as the procedures for their cleaning have been described previously.ls Detailed descriptions of electrochemical cells for both cyclic voltammetry and controlled-potential electrolysis appear in earlier publications.11JSJ' All potentials in this paper are quoted with respect to a reference electrode consisting of a saturated cadmium amalgam in contact with DMF saturated with both cadmium chloride and sodium chloride;lSJethis electrode has a potential of 4.76 V vs the aqueous saturated calomel electrode at 25 "C. Cyclic voltammograms were obtained through the use of a Princeton Applied Research Corp. (PARC)Model 175Universal Programmer coupled to a PARC Model 173 potentiostatgalvanostatand were recorded with a Houston InstrumentsModel 2000-5-5 X-Y plotter. Controlled-potentialelectrolyses were performed with the aid of the potentiostat-galvanostat that was equipped with a PARC Model 176 current-to-voltageconverter to provide iR compensation. Electrolyseswere programmed and (13) Vieira, K. L.; Peters, D. G. J. Electroanal. Chem. Interfacial Electrochem. 1985,196,93-104. (14) Cleary, J. A.; Mubarak, M. S.; Vieira, K. L.; Andereon, M. R.; Peters, D. G. J. Electroanal. Chem. Interfacial Electrochem. 1986,198, 107-124. (15) Marple, L. W. Anal. Chem. 1967, 39, 844-846. (16) Manning, C. W.; Purdy, W. C. Anal. Chim. Acta 1970,51,124126.
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Table I. Data for Gas Chromatographic Determination of Volatile Products Derived from Electrolysis of 1,4-Dibromobutanea n , X ngX nX compound RF A, A, 105 los lo6 yield, % cyclobutane trans-2-butene cis-2-butene n-butane 1-butene ethylene 1,3-butadiene propane’
1.37 1.07 1.20 1.37 1.48 0.67 1.25
21025 14074 10151 1723 7595 329 762 8041
58091 49322 32911 66965 37916 15864 2495 178476
5.53 4.74 3.05 2.03 1.85 0.18 0.22 2.90
3.11 3.38 2.01 3.59
5.84 5.08 3.25 2.39 1.88 2.04 1.74 0.35 0.15 0.24 13.1 4.21
30 26 17 12 11
I* 1
RF, response factor; A,, peak area for species in solution phase; A,, peak area for species in gas phase;n., moles of species in solution
phase; n,, moles of species in gas phase; n, total moles of species in electrolysis cell; yield (7%) calculated in terms of moles of starting material (1.93X le).In calculatingthe yield of ethylene,one must take into considerationthat 1 mol of starting material gives 2 mol of ethylene. Propane was used as the internal standard.
current-time curves were acquired, stored, and integrated by means of locally written software, which controlled a Tecmar data acquisition board installed in an IBM-PC computer. Procedure for Controlled-Potential Electrolyses and Quantitation of Products. To begin an experiment, a reticulated vitreous carbon disk, a magnetic stir bar, and 50 mL of solvent-supporting electrolyte were placed into the cathode compartment of the cell, and the anode compartment was fitted onto the cathode compartment. Deaeration of the solventsupporting electrolyte was done by passage of argon through a stainless-steel syringe needle inserted through a septum-covered port on the cathode compartment. After being deaerated for 15 min, the solvent-supporting electrolyte was preelectrolyzed at the potential to be employed for an actual electrolysis until the current attained a steady-state background level, during which period the flow of argon was continued. Then the needle was withdrawn to stop the argon flow, and the Teflon valve at the top of the cell was closed to create a ‘gas-tight” configuration. Known quantities of the starting material (1,4-dibromobutane) and an electroinactive internal standard (propane for volatile products or n-tetradecane for nonvolatileproducts) were injected into the cathode compartment of the cell. Immediately, the electrolysis was begun; typically, 50-70 min was required for the current to decay to its previous background level. Upon completion of the electrolysis,samples were taken from each phase of the sealed cell and were injected directly into a Varian Model 3700 gas chromatograph equipped with dual flame ionization detectors. For analysis of the solution phase, a Hamilton 10-pL syringe was used to inject a 5-wL sample; after two or three replicate injections, the chromatographic column was heated at 210 OC for 10-15 min to remove the residue of solvent. For analysis of the gas phase, a Hamilton 1250-pL,gastight syringe was used to inject a 500-pL sample; again, after a set of replicate injections,the column was heated to expel solvent. Gas chromatographic peak areas were measured with the aid of a Spectra Physics Model SP 4400 integrator. Volatile electrolysis products were separated on a 30 m X 0.53 mm wide-borecapillary column (J&W Scientific) that utilizes GS-Alumina as the stationary phase, whereas nonvolatile products, if any, were separated on a 8 m X 0.53 mm capillary column (RSL-300,Alltech Associates) with poly(phenylmethylsi1oxane) as the stationary phase. A computer program written in BASIC, utilizing the equations presented in the preceding theoretical section, was used to compute the product yields; all yields reported in this paper are absolute and reflect the percentage of starting material incorporated into a particular product. If one is seeking to quantitate products that are not volatile or to verify that such species are not formed in the electrolysis, the solution from the cathode compartment that contains the products,solvent,supporting electrolyte,and nonvolatileinternal standard (n-tetradecane) is partitioned between diethyl ether and brine. After the ether phase is washed several times with
brine and then twice with deionized water, it is dried over anhydrous magnesium sulfate and is concentrated by rotatory evaporation to a volume of 1-2 mL. A 1-pL sample of this concentrated ether extract is then analyzed by means of gas chromatography. Product Identification. Among the products derived from the electrochemicalreduction of 1,4-dibromobutane,we identified n-butane, cis-2-butene, trans-%butene, 1-butene,1,3-butadiene, and ethylene by comparing the gas chromatographic retention times for the suspected compounds with those of authentic samples. To confirm the identity of cyclobutane, we employed a Hewlett-Packard 5890 Series I1 gas chromatograph coupled to a Hewlett-Packard Model 5971 mass-selective detector. Mass spectral data (70 eV) for cyclobutane are as follows: m/z (re1 intensity) 56, M+ (54);55, M+- H (25);41, C3H5+(99);39, C3H3+ (24); 28, CzH4+ (100); 27, CzH3+ (37); 26, CzHz+ (19).
RESULTS AND DISCUSSION A cyclicvoltammogram for reduction of 1,4dibromobutane at a glassy carbon electrode in DMF containing 0.050 M TMAP exhibits a single irreversible cathodic wave with a peak potential of -2.00 V at a scan rate of 100 mV s-l. When a set of three controlled-potential electrolyses of 1,4-dibromobutane was conducted with a reticulated vitreous carbon electrode held a t -2.05 V, the products (with their average percentage yields) were as follows: cyclobutane (29%), n-butane (18%),cis-2-butene(15%), 1-butene (ll%), trans2-butene (18%),l,&butadiene (l%), and ethylene (1%). In the remaining portion of this paper, we will illustrate the procedure for the quantitation of these volatile compounds for just one of the electrolyses. As discussed earlier, once the roster of products has been identified, the first step is to determine response factors for the gas chromatographic measurement of these products with respect to an appropriate internal standard; we selected propane as the internal standard for all experiments. Pure samples of all of the products except cyclobutane were commercially available, so that their response factors could be determined directly; however, since authentically pure cyclobutane proved to be elusive, we had to estimate its response factor. Because the gas chromatographic retention times for cyclobutane and n-butane are nearly the same, we assumed that the response factors for these two compounds are identical. Justification for this assumption is seen in our independent observations that response factors obtained experimentally for two pairs of straight-chain and cyclic hydrocarbons (namely, for propane and cyclopropane and for n-pentane and cyclopentane) are similar; for example, we found that the response factorsfor propane and cyclopropane with respect to butane were 0.750 and 0.717, respectively, and that the response factors for n-pentane and cyclopentane with respect to n-hexane were 0.912 and 0.817, respectively. Table I lists the response factors for the products derived from the electrochemical reduction of 1,4-dibromobutane with respect to propane. It is noteworthy that the experimentally measured response factors are in reasonable agreement with a theoretical value of 1.33,which is predicted if the response of a flame ionization detector to compounds possessing four and three carbon atoms is ideal. Now let us consider the treatment of experimental data obtained from the electrolysis of a solution initially containing 4.0 mM 1,4-dibromobutane (26 pL or 1.93 X 10-4 mol) in the presence of propane (1025pL) as internal standard in a sealed cell with a solution-phase volume (V,) of 50.0 mL and a gasphase volume (V,) of 101.3 mL. Table I shows the gas chromatographic peak areas obtained a t the conclusion of the electrolysis for the separate injection of a 5-pL sample of the solution phase and a 500-wL sample of the gas phase. From eq 3, with P = 0.987 atm, V = 1.025 X 10-3 L, T = 296 K, T, = 369.8 K,12and P, = 42.0 atm,12the total number
ANALYTICAL CHEMISTRY, VOL. 65, NO. 15, AUGUST 1, 1993
of moles of propane (npmpans) injected into the cell was calculated to be 4.21 X 106. Then, using eq 6 and the gas chromatographic peak areas for propane in the solution and gas phases,we can find R for propane; in doing the calculation, we must multiply the peak area for the solution-phasesample by 100 to compare it properly with the peak area for the gas-phasesample, because of the 100-folddifference between the volumes of the two phases injected into the gas chromatograph
Next we employ eq 10 to calculate the number of moles of propane residing in the gas phase,
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the data in Table I, the results were as follows:
When we add the number of moles of cyclobutane in each phase, the result is ncy&$-,utane = 5.84 X lw. Using eq 20, one can calculate the yield of cyclobutane: 7% yield of cyclobutane =
ncyclobuWe(lOO)
nstmatl
and eq 11 to find the number of moles of propane in the solution phase:
Once the number of moles of propane is known in each phase, eqs 18 and 19 are used to calculate the number of moles of each product that resides in the solution and gas phases; for example, when we did the computations for cyclobutaneusing
If the same procedure is followed for the other six volatile products, the results compiled in Table I are attained. Note that, in the example we have chosen, the yields of n-butane and tram-2-butene differ from the average values cited earlier in this paper. In practice, however, we ordinarily repeat an electrolysis three to five times so that a reliable average for the yield of each product can be obtained.
RECEIVED for review February 24, 1993. Accepted May 3, 1993.
