membrane that between 0.05 and 0.25M it became constant a t 0.87 (9). I n a recent review of membrane transport phenomena ( I ) ,both constant and varying f values were reported for glucose and sucrose in the concentration range of 10-5 to 10-4M, depending on the membrane being utilized. These were obtained, however, with dialysis tubing and gels, where the f values were less than 0.2. When varying, these values did increase with decreasing solute concentration. The practicability of the technique is indicated by the fact that f values greater than 0.5 have been obtained for aqueous solutions of organics such as iso-, sec- and tert-butyl alcohol, isopropyl alcohol, glycerol, and sucrose (9). -41though the flow rates of 0.2 ml./sq. cm./hr. a t a pressure of 600 p.s.i. reported here are relatively low and would necessitate inconveniently long times to concentrate large volumes of solutions (10 to 20 liters) down to a few milliliters, with similar membranes a t 750 p s i . flow rates five times as large have been ob-
tained (9). Recently polyion complex membranes have been prepared with water permeabilities of 14 to 17 ml./sq. cm./hr. a t a pressure of 100 p.s.i. with anfvalue of 0.9 for raffinose (7). I n the same study one type of membrane had f values of 1.0 for sucrose and raffinose and 0.25 for sodium chloride. This low value for salt is particularly advantageous when concentrating organics in a salt solution, in that lower osmotic pressures would have to be overcome as the solution becomes concentrated, as compared to membranes with high f values for inorganic salts. The advantage of reverse osmosis for concentrating dilute solutions of organics is that it avoids phase changes, high temperature, or transfer techniques in the concentration process. Although the interest of the authors lies primarily in the concentration of dilute aqueous solutions of organics in natural and municipal waters so as to facilitate their identification and analysis, there are numerous other potential applications for this technique.
LITERATURE CITED
(1) Cummins, A. B., Hutto, F. B., in “Separation and Purification,” A. Weissberger, ed., 2nd ed., p. 711, Interscience, New York, 1956. (2) Friedlander, H. Z., Rickles, R. N., ANAL.CHEM.37, No. 8, 27A (1965). (3) Jesting, E., J. Lipid Res. 5, 135 (1964). (4) Lakshminarayanaiah, N., Chem. Rev. 65. 491 (1965). (5) Li, N. “:,-Long, R. B., Henley, E. J., Ind. Eng. Chem.. 57, No. 3, 18 (1965). (6) Loeb, S., Sourirajan, S., Aduan. Chem. Ser. 38, 117 (1963). (7) Michaels, A. S., Ind. Eng. Chem. 57,
No. 10, 32 (1965).
(8) Snell, F. D., Snell, C. T., “Colorimetric Methods of Analysis,” Vol. 111,
3rd ed., p. 215, Van Nostrand, New York, 1953. (9) Sourirajan, S., Ind. Eng. Chem. Product Research Develop. 4, 201 (1965).
JULIAN B. ANDELMAN MICHAEL J. SUESS
Graduate School of Public Health University of Pittsburgh Pittsburgh, Pennsylvania 15213
Repeated Gas Chromatographic Sampling Technique in Gas Phase Chemical Kinetics Photolysis of Acetone SIR: Pratt and Purnell (9, 10) recently described a convenient technique for the study of the kinetics of the thermal decomposition of acetaldoxime using a specially designed rotary valve (11) to sample repeatedly from the reaction cell directly into a gas chromatograph. Since then, the method has been successfully employed to study other gas phase reactions (2,4-?‘, 12, IS). With this technique, concentration us. time curves for the various products are quickly and easily obtained without the necessity of tedious and often inadequate preliminary fractionations. However, the finite dead volumes unavoidably present in the valve and connecting lines and the finite sensitivity of the gas chromatograph impose a practical lower limit to the size of the sample volume, and consequently the changes in concentration of products and reactants due to repeated sampling are often quite significant. Thus, in the process of adapting this technique to the study of the reaction of methyl radicals with aromatic molecules (S), it became essential to correct for the changes in concentration due to sampling, since the rates of production of methane and ethane from acetone
photolysis have different functional dependences on concentration. The main purpose of this paper is to outline the procedure used in the mathematical analysis of our data, inasmuch as the effect is quite general and appears not to have been considered before. We also describe in some detail the important aspects of our experimental technique. T o illustrate the application of the method and show its v.L
Figure 1. paratus
Schematic diagram of ap-
V, sampling valve;
A, sampling stopcock; B, metal valve; F, furnace; R.C., reaction cell; L, lamp; V.L., vacuum line; G.C., gas chromatograph; P, vacuum pump. Valve shown in “push” position. Dotted lines indicate the positionsof the O-rings in the “pull” position
reliability, we report the results of our measurements of the rate constant for the hydrogen abstraction reaction of methyl radicals with acetone and compare them with the results of earlier workers using more conventional techniques. These results will be used in a later publication to interpret the data in the aromatic systems. EXPERIMENTAL
A schematic diagram of the apparatus is shown in Figure 1. Instead of a Pratt-Purnell valve ( I I ) , we used a commercially available stainless-steel gas-chromatograph sampling valve of the push-pull type (Loe Engineering, Model L-208-6, with Viton “A” 0rings). Connections to the valve were made with 1/8-inch copper tubing using Swagelock fittings. The sample loop was a piece of 1/8-inch copper tubing about 50 em. long; its internal volume was ca. 1.1 cc. The cylindrical borosilicate glass reaction cell (50-mm. id., 176 mm. long) was provided with a flat borosilicate glass window a t one end and a thermocouple well which extended axially nearly the whole length of the cell. It was placed inside an electrically heated aluminum block furnace, the temperature of which was manually controlled. VOL. 38, NO. 2, FEBRUARY 1966
353
Temperature was measured with five thermocouples located uniformly inside the thermocouple well. The maximum temperature spread along the reaction cell was =t1-2' C. To prevent condensation of vapors, the sampling valve, a McLeod gauge, a mercury manometer, the furnace, and the connecting lines were enclosed in a heated box main0.5' C. tained a t 60' The design of the sampling probe connecting the reaction cell to the sampling valve is shown schematically in Figure 2. The probe consists of 1-mm. capillary tubing ring-sealed to the reaction cell and extending from near the entrance window to the sampling stopcock, A . To ensure uniform sampling, two small 2-mm. capillary sideports were attached to the probe a t the center and near the back end of the reaction cell so that the gas flow through each of the three probes was approximately the same. The volume of the probe was small compared to the total volume removed for each sample. Using this probe the concentration of products extrapolated linearly to zero a t the start of illumination, and also the rate of production dropped to zero immediately after turning off the lamp. By contrast, when 6-mm. tubing was used to connect the back end of the reaction cell to the sampling valve, it took approximately 10 minutes for the rate of production to approach a steady value, and another 10 minutes for the apparent rate to vanish after the light was turned off. The light source was a Hanovia Type A high pressure mercury arc. The effective wave length region was above 3000 A. The light beam, which filled the entire cell, was collimated roughly with a quartz condensing lens. The sampling procedure was as follows: The vapors from the reaction cell were expanded into the previously evacuated sample loop by opening stopcock A for 5-10 seconds, and immediately thereafter they were swept into the gas chromatograph by pushing the plunger. After about 1 minute the plunger was pulled back and the sample loop evacuated in preparation for the next sample. Samples were taken every 6 minutes after the beginning of photolysis, for a total period of 30 minutes. Analyses for methane and ethane were carried out in a PerkinElmer Model 226 gas chromatograph equipped with a hydrogen flame ionization detector and using a 1/8-inch packed silica gel column, 4 meters long, a t 110' C. Total analysis time was 4 minutes from injection. Condensible vapors such as acetone are irreversibly adsorbed in the column, and CO is not detectable with the hydrogen flame detector. The pressure in the reaction cell was read a t the beginning and a t the end of each experiment using a mercury manometer. The sensitivity of the gas chromatograph for CHI and C2H6 was determined prior to each run by repeated sampling from the reaction cell filled with a known mixture of CH4,C2H6, and air, In this procedure the partial presthe total pressures of CH4 and sure, and the temperature were com-
*
354
ANALYTICAL CHEMISTRY
1
V.L.
Figure 2. Schematic diagram of the sample probe and reaction cell S.P., sample probe; T, thermocouple well; V.L., vacuum line
parable to the conditions prevailing a t the end of the run. Pressurization of the reaction cell by the addition of air was essential to minimize errors due to incomplete removal of helium carrier gas from the valve and sampling loop between samplings. Acetone (Matheson-Coleman-Bell Spectro grade) was dried with Drierite and thoroughly degassed in the vacuum line. The impurity content determined by gas chromatography was less than 0.027*. THEORY
In the photolysis of a mixture of acetone A and some other compound B, the rate constants for the hydrogen abstraction reactions by methyl radicals are conventionally determined from measurements of the rate of production of methane and ethane using Equation
If the rate of formation of CHa radicals is proportional to (A), then the steady state equation for (CHa) is given by Equation 4. d[CH31 - - - 0 = I,(A)
at
-
where I , is a proportionality constant related to the absorbed intensity and quantum yield, and y is the ratio RC*H~/RCH,. In this equation we make use of the fact that two methyl radicals are used up for every methane that is formed, since the radicals CH2COCHa and B(-H) eventually disappear by recombination with a methyl radical. Since y is a slow-varying function of concentration, and its magnitude ranges from less than 10 a t low temperatures to about 0.1 a t high temperaures, it is a very good approximation to consider l + y as a constant -Le., independent of the number of samples removed. Solving Equation 4 for (CH,) and substituting into Equations 2 and 3, we obtain
1 (0,
where c is the total concentration of vapors, x is a mole fraction, and k1, kz, and k3 are the rate constants for Reactions a, b, and c. CHa
+ A k1 CH4 + CH2COCH3 -+
CH3
+ CH3 ka CzHs +
(a)
(4
Constant k3 is assumed to be known (14) and independent of temperature. The value of kl is obtained from experiments with acetone alone, and the results are used to compute k2 from the mixture experiments. Normally the rates are obtained simply by dividing the concentration of products a t the end of t,he run by the reaction time. In the repeated gas chromatographic sampling technique, the concentrations of reactants (and products) decrease due to sampling, and thus the rates of production are not constant. To avoid graphical differentiation and to take full advantage of the data, we adopt t.he following procedure. The rates of production of methane and ethane are given by Equations 2 and 3.
To integrate Equations 5 and 6 we note that all quantities on the right hand side are constant between samplings (since the change in (A) due to the chemical reaction is negligible), and that all the concentrations are changed instantaneously by a constant factor (a< 1) a t each sampling. Thus, after n samplings the concentrations of CHa and C Z Hare ~ given by Equations 7 and 8. [CH4] = a n J r 0
I,Oo dt + l+r
[C&] = an J K dt 0
2 - 1
+
lz' +- -+ -
K dt
nr
aJn-l)r
(8)
where (A), is the initial concentration of acetone, t is the time, T is the time interval between samplings, and
The ai factor in front of each integral accounts for the decrease in concentra-
T
7-
6-
-'G
; 5*
CO
0
388
moles/cc. 4.33
407
4.12
A
431
3.93
A
471 507
3.54 3.32
556
3.06
L ,'I
OK.
0
-
E
-
-
3.5
-
3.0
- 1.2
-
K.
p moles/cc.
8
407
4.12
A
431 471
3.93 3.54
507
3.32
a
- 1.0
l.
,
4.0
4-
:o
S '
u
Y
3-
P 2-
- 0.05 - .2
0
5
I
I
I
I
IO
I5
20
25
I 30
1 0 35
a
vs. time in the photol-
+
-
&7)
(10)
The factor QI is computed from the initial and final pressures according to Equation 11. Pfinal = P i n i t i a d
-
atlr)/(l - a)
"The ordinate of this run shifted b y 0.5 units
tion of product after j samplings, while the ak(A)oterms inside the integrals in Equation 7 give the actual concentration of acetone present in the time l)lh interval between the k t h and ( k samples. Carrying out the integrations term by term, collecting terms, and in the case of Equation 8 using the formula for the sum of a geometric series, these equations simplify to
ar - (1 1 - a
I-a),min.
Figure 4. Plot of [C~HC]vs. ar(1 in the photolysis of acetone
t ,inin.
Figure 3. Plot of [CHd]/a'/' ysis of acetone
I I -='''I/(
tained, we show here the results with acetone alone. Equations 1 and 10 are, of course, simplified in that XB = 0 and X A = 1. Figures 3 and 4 show typical data a t various temperatures plotted according to Equations 9 and 10. Table I summarizes the results of the calculation of kl/k31/2 as a function of temperature. An Arrhenius plot of the data is linear, and the equation determined by least squares is given by log k1/k3l/~= 4.885 - 2156/T (units: cc. mole-' second-'). The average deviation of all the points from the line is 1.5y0, while the maximum deviation is 2.6%. The pre-exponential factor A1/is 3.1 X lo4 C C . ~ / sec~ ond-1/2, and the activation energy difference E1-1/2E3is 9.87 kcal./mole. These rate parameters have been determined by several workers in the past (15, 16),
and the agreement is in general excellent. Typical of these results are those of Trotman-Dickenson and Steacie (15) who obtained log kl/k3'I2 = 4.85 2124/ T. DISCUSSION
In this paper we indicated one successful application of the method of repeated gas chromatographic sampling and demonstrated the adequacy of the mathematical treatment. We now list some advantages and limitations of the method over conventional methods. The most obvious advantage is the convenience and quickness of chemical analysis, inasmuch as the separation and analysis is done in one step with a minimum of handling. Furthermore, the high sensitivity of gas chromatography permits measurements a t very
(11)
In our apparatus, a varied from 0.96 to 0.98, depending on the temperature of the cell. Plots of [CH4]/at/+ us. t and [ C 2 H ~ ] us. a7 (1 - & 7 ) / (1 - a) should be linear with zery intercept, and the slopes may be substituted directly for the R's in Equation 1 to evaluate kl/k31/2and k2/k31/2. We should point out here that both Equations 9 and 10 are solutions of zeroth order reactions having different boundary conditions. The extension of the method to first or higher order reactions is straightforward.
Table 1.
Rate of Production X 1012 Tyg"
[C,] x 106 (moles/cc.)
386 387 388 407 ~. 41 1 431 436 47 1 473 507 508 540 556 573
4.19 4.33 4.33 4.12 3.93 3.93 3.74
RESULTS
To demonstrate the application of the method and to indicate the limits of precision and accuracy that can be ob-
Rate Constants in the Photolysis of Acetone
0
b
CH4a Cz&* (mole cc.-1 second-')
4.10 4.63 4.56 7.86 8.57 13.1 16.1 22.2 29.2 31.7 34.0 43:6 3.05 ~ . . 3.06 38.5 2.88 51 .O Slope of linear plot [CHh]/ort/r us. t. Slope of linear plot [CzHs] us. a r ( l ~~
.
27.4 23.8 23.6 23.3 25.7 19.1 27.2 10.3 15.4 4.95
6-75
3.67 1.48 1.60
0.761 0.824 1.95 2.18 4.30 4.17 7.47 10.3 14.0
- a t / r ) / ( I - a). VOL. 38, NO. 2, FEBRUARY 1966
355
low degrees of conversion. Repeated sampling leads to improved precision by averaging over a large number of analyses, and provides the opportunity of detecting secondary processes and products which might affect the apparent rate. In the case of acetone photolysis, the accuracy of the rate results is comparable over a wider range of temperature since the accuracy of the analyses is not limited by the small yield of either methane or ethane a t the extremes of temperature. The main limitation of the repeated sampling niethod is the requirement for homogeneous sampling, and, thus, the method can be used only in the photolysis of compounds having low absorptivity, or in thermal reactions where the reaction occurs homogeneously throughout the
entire cell volume. If the reaction is not homogeneous, adequate stirring must be provided. LITERATURE CITED
(1) Benson, S., “Foundations of Chemical
Kinetics,” p. 377, McGraw-Hill, New York, 1960. (2) Casey, K., Edgecombe, F. H. C., Jardine, D. A., Analyst 87, 835 (1962). (3) Cher, M., Hollingsworth, C. S., Sicilio, F., J . Phys. Chem. 70, in press. (4) Edgecombe, F. H. C., Tetrahedron Letters No. 24, 1161 (1962). (5) Edgecombe, F. H. C., Can. 3. Chem.
41, 1265 (1963). (6) . . Kallend. A. S.. Pitts. J. N.. Jr.. Division of Water and Waste Chemistry, 144th Meeting, ACS, Los Angeles, Calif., March-April, 1963. ( 7 ) Kallend, A. S., Purnell, J. H., Trans. Faraday SOC.60, 93 (1964).
( 8 ) Zbid., p. 103. (9) Pratt, G. L., Purnell, J. H., Proc. Roy. SOC.(London) Ser. A, 260 317 (1961). (10) Pratt, G. Purnell, J. H., Trans. Faraday SOC.58, 692 (1962). (11) Pratt, G. L., Purnell, J. H., ANAL. CHEM.32, 1213 (1960). (12) Purnell, J. H., Quinn, C. P., J . Chem. SOC.(London) 1961, 4128. (13) Purnell, J. H., Quinn, C. P., Nature 189, 656 (1961). (14) Shepp,‘ A., J . Chem. Phys. 24, 939 (1956). (15) Trotman-Dickenson, A. F., Steacie, E. W. R., J . Chem. Phys. 18, 1097 (1950). (16) Trotman-Dickenson, A. F., “Gas Kinetics,” p. 201, Butterworths, London, (1955).
MARKCHER C. S. HOLLINGSWORTH North American Aviation Science Center Thousand Oaks, Calif. 91360
Use of Combined Schlieren and Interference Optics for Determination of Molecular Weights from Sedimentation Equilibrium Data SIR: In an important report on the rapid attainment of sedimentation equilibrium in the ultracentrifuge, Van Holde and Baldwin (IO)described three methods for the analysis of experimental data. Their Method 11, in which molecular weight is determined from the slope of a plot of l l r dn,/dr us. n, is of particular interest and utility for the following reasons : moderately short fluid columns are used in the ultracentrifuge cells so that thermodynamic equilibrium is attained in reasonable periods of time, and yet the resolving power of the centrifuge is not lost; knowledge of the initial concentration of sample is not necessary, so that the usual synthetic boundary cell run is not required; extrapolation of data to the ends of the fluid column is not required for homogeneous solutes; heterogeneity in molecular weight or nonideality of the sample solution can be detected with a fair degree of sensitivity from the same graphical analysis of the data used for the molecular weight determination. In the original method schlieren optics were used, and the changes of solute concentration across the cell required for the graphical analysis were evaluated by integration of schlieren patterns. The purpose of this communication is to describe a modification of the method which avoids the necessity for the integration of schlieren patterns. All of the advantages of the original method are retained, but the computations are simplified considerably. The modification is based upon the fact that the information derived from the integration of a schlieren pattern is avaiiable directly from an interference fringe 356
ANALYTICAL CHEMISTRY
pattern obtained under the same experimental conditions. At sedimentation equilibrium, concentration gradients in the cell are recorded by both schlieren and interference optics (7, 9); changes in solute concentration across the cell are then determined directly from the interference fringe count. For solutions of nearly ideal behavior, Equation 35 of Van Holde and Baldwin (IO) can be written in terms of an apparent molecular weight, 1 dc-- -Mapp(1 - 0 p ) w % _
r dr
RT
(1)
where 0 is the partial specific volume of the solute, c and dc/dr are the concentration and concentration gradient of the solute a t radial distance r, p is the density of the solution, w is the angular velocity of the rotor, R is the gas constant, and T is the absolute temperature. When
c
= Crsf f AC
(2)
where crefis the concentration of solute a t some convenient level in the cell, such as the meniscus, while Ac is the difference in concentration between this level and any other level in the cell, Equation 1 can be rewritten as 1 dc dr
-
T
If the usual assumption is made that solute concentrations are proportional to refractive index changes, values of Ac
are derived from interferograms and values of dc/dr are read directly from schlieren patterns. The slope of a plot l / r dc/dr us. Ac is related to the molecular weight of the solute by
Mapp= slope
RT
(1
- 0 p)w2
(4)
EXPERIMENTAL
Materials. Ribonuclease A and chymotrypsinogen A were purchased from Worthington Biochemical Corp. For use, solutions of ribonuclease in 0.135M NaC1-O.OlM sodium phosphate buffer, pH 6.8, were prepared, while chymotrypsinogen A was dissolved in 0.1M sodium acetate-acetic acid buffer, pH 5.0. Crystallized bovine serum albumin was purchased from Pentex, Inc. This sample, which had been under refrigerated storage for several years, was found by recent sedimentation velocity studies to contain approximately 20% of material of higher molecular weight than the monomer. It was used without further treatment as solutions in the same acetate-acetic acid buffer used above. Methods. All equilibrium runs were made using the Beckman-Spinco Model E analytical ultracentrifuge equipped with electronic speed control. The titanium An-H rotor was used for most runs, although the equilibrium An-J rotor was used for speeds below 12,000 r.p.m. Sample cells were filled to fluid column heights of 3 to 4 mm. A technique of overspeeding similar to that described previously (3) was employed to shorten the time required to attain equilibrium. For convenience and highest accuracy in reading photographic plates, schlieren and interference patterns for any one
