atmosphere nithin t h e cell. Oxidize this electrolyte solution a t +0.660 volt us. S.C.E. until a background current of 50 ha. is attained. Stop the electrolysis and zero the integrator. If 1M HC10, is used as the supporting electrolyte, pretitrate at +0.900 volt vs. S.C.E. Titration of Sample Aliquot. Into t h e pretitrated electrolyte solution in the cell, pipet 1.00 ml. of the plutonium(J-I) solution prepared above. Reduce the solution at f0.270 volt 2’s. S.C.E. (+0.290 volt if 1M HClOd is used) until a 10- to 20-peq. excess of iron(I1) has been generated. Stop the electrolysis; read and record the readout voltage, Q R . Zero the integrator. (With the present instrument, the reduction is allowed to proceed until the readout voltage in volts equals 0.2 times the milligrams of plutonium expected in the aliquot.) Now make an oxidation at $0.660 volt us. S.C.E. (+0.900 volt if HC104 is used) until the current again falls to 50 pa. Stop the electrolysis; read and record the readout voltage, Qo. Calculations. With t h e present instrument, t h e relationship betn-een readout voltage and current consumed has been established b y electrical calibration t o be 8.1875 coulombs per volt or 10.14 mg. of plutonium per volt for this 2-electron
change reaction. Consequently, t h e weight in milligrams of plutonium titrated is obtained from the relationship 10.14 (QR-Qo), and this number is multiplied by 10 to obtain the plutonium concentration in the original sample solution. Instruments of this type are often calibrated, and calculations are often made, in this fashion (4). The relationship between readout voltage and coulombs consumed obviously will vary from one instrument to another. ACKNOWLEDGMENT
Appreciation is expressed to J. H. Cooper and his staff for their assistance and for making their laboratory facilities freely available during the course of this work. LITERATURE CITED
(1) Booman, G. L., AKAL.CHEJI.29, 213 (1957). (2) Carson, W. X., Jr., Vanderwater, J. W.,Gile, H. S., Ibid., 29, 1417 (1957). (3) Cooper, J. H., “Plutonium, Potentio-
metric Ceric Sulfate Method,” Oak Ridge Natl. Lab., Method 9 0432620 (8-7-53), ORNL Master Analytical Manual; TID-7015, Sec. 9. (4) Jones, H. C., “Automatic Coulo-
metric Titrator, ORNL Model Q-2005, Electronic, Controlled-Potential,” Methods 1 003029 and 9 003029 (8-17-59); TID-7015, Sec. 1. (5) Kelley, M. T., Jones, H. C., Fisher, D. J., ANAL. CHEM.31, 488, 956 (1959). (6) Kelley, M. T., Jones, H. C., Fisher, D. J., “Electronic Controlled-Potential Coulometric Titrator for Plutonium Analysis,” Third Conference on Analytical Chemistry in Nuclear Reactor Technology, Gatlinburg, Tenn., Oct. 26-29, 1959. (7) Scott, F. A., Peekema, R. M., “Analyeis for Plutonium by Controlled-
Potential Coulometry,” Proc. 2nd, Intern. Conf. on Peaceful Uses of Atomic Energy, Geneva, United Nations, New York, 1958, Vol. 28, 573, 1958. (8) Scott, F. A., Peekema, R. M., “Determination of Plutonium in Irradiated Uranium Fuel Solutions bv Controlled Potential Coulometry,” U. S. At. Energy Comm., HW-58491 (Dec. 10 1958r(9) Shults, W.D., Anal. Chem. Semiann. Progr. Rept., April 20, 1954, ORNL1717. 4 (Classified). 0) Sl&&, W. D., ’“Controlled Potential Coulometric Titration of Plutonium. Application to PRFR Samples,” ORNL2921 (March 1960). 1) Shults. W. D.. Thomason. P. F.,
Anal. Chem. Semiann. Progr. Rept., Oct. 20, 1954, ORNL-1788, 1 (Classified). (12) Waterbury, G. R., Metz, C. F., ANAL.CHEW31, 1144 (1959). RECEIVEDfor review April 15, 1960 Accepted August 22, 1960.
Adsorption Phenomena and Their Effects on Analytical Accuracy in Gas Chromatography ALLAN WEINSTEIN’ Department o f Fuel Technology, The Pennsylvania State University, University Park, Pa.
b When calibration is made with pure substances, the adsorption effect is an important systematic source of error in gas chromatographic analyses. Theoretical examination of this effect, together with the known surge and possible viscosity effects, indicates that the peaks of shortest retention time are most affected analytically. With adsorbed carriers such interference can affect a large number of peaks. Practical procedures are given for avoiding or minimizing such errors.
A
in gas chromatography depends on sample composition (3, 8 ) . An attempt has been made to explain this fact mainly in terms of viscosity and surge effects ( 4 ) , which relate to flow changes occurring during and after passage of a sample through a column. NALYTICAL ACCURACY
Present address, Products Research Division, Esso Research and Engineering Co., Linden, N. J. 1
18
ANALYTICAL CHEMISTRY
I n a previous communication ( I S ) , the idea was proposed that adsorption effects, rather than differences in carrier and sample viscosities, were primarily responsible for flow rate changes. Experimental justification for this view was obtained with the argon Molecular Sieve system, by observing the direction and magnitudes of pressure changes resulting from sample introduction. These different views lead to different interpretations of how such analytical interferences take place, and to different conclusions regarding corrective design. One purpose of this paper is to explore these differences more fully. The effect of an adsorbed carrier on analytical accuracy has received no attention, although such carriers are in common use. It will be shown that adsorption of the carrier plays an important part, and that surge effect corrections ( 4 ) cannot be used successfully for systems employing these carriers. Finally, an attempt will be made to
correlate the more common quantitative procedures and to show how errors due to adsorption effects arise. Such consideration will lead to practical procedures for avoiding or recognizing this important source of error. PROCEDURE
The apparatus has been described previously ( I S ) . The procedure consisted briefly of filling the sample tube with sample gas to the desired pressure, and then bringing the tube up to column pressure with carrier by repeated momentary cracking of the appropriate stopcock. Sample introduction then proceeded in the normal fashion. I n addition to samples of helium, hydrogen, oxygen. nitrogen, methane, and carbon monoxide, a 700-mm. sample of a 60- to 40-volume % mixture of carbon monoxide and helium Ivas run. RESULTS
Since the thermal conductivity cell employed was pressure sensitive, it was
1
---T
I
I
i
+3 1
Thus AP for a dynamic system is relative rather than absolute. I n passing into a column, the concentration of a sample does not remain uniform throughout the sampling zone (9). If the distribution coefficients are constant, Equation 1 is still valid for dynamic systems regardless of the form of this concentration profile, as shown below. Assume t h a t the gas phase conccntration of a sample after introduction into the column is any arbitrary function of distance into the column. Calculating C, and E,, the average concentrations in the gas and adsorbed phases from the necessary integrals,
Calculating the amount of sample adsorbed, A , from Equation 2 by a material balance, -3-
(3) -4 -
I -
100
0
I 200
j
. - l - - - L
300
400
---
SAMPLE GAS PRESSURE, m m Hg at
Figure 1 . pressure
._LI 600
500
!
70 0
25°C.
Variation of adsorption peak height with sample
Pressure chonges a r e proportional to recorder response, but ore of opposite sign; approximate uncorrected retention times of normal peaks of He, Hz, 0 2 , N1, CHI, and C O ore 1 l / ~ ,2, 4,8, 12, and 3 2 minutes, respectively
convenient to follow forecolumn pressure changes by means of the recorded adsorption peaks. The height of these peaks was proportional to the maximum pressure change. Results for the individual gases have already been reported ( I S ) , and are summarized in Figure 1. Flow rate increased n i t h increase in forecolumn pressure, and decreased with decrease in pressure. The flon- rate changes for the pure samples were detected 5 to 10 seconds after the initial pressure changes. For the mixture, a 0.15-mv. positive adsorption peak JTas recorded, indicating a forecolumn pressure decrease of about 0.06 p.s.i.g. Honever, a flow rate increase from 70 to 80 ml. per minute began about 30 seconds after the initial pressure change. This flow rate increase appeared to last until after passage of the helium off the column, and it was followed by a decrease both in flow rate and forecolumn pressure. DISCUSSION
The following treatment pertains to gaseous samples introduced in the manner described. Similar developnient can be made for any method of sample introduction. Adsorption Effect. When a sample gas is i n t r o d u c d onto a column
containing a n adsorbed carrier, some of the sample is adsorbed and some of the carrier is desorbed (eluted). The relative quantities involved depend on the distribution coefficients K, and K , of the sample and carrier, respectively. The simplest method for quantitatively evaluating this effect is to consider a section of column containing carrier in static equilibrium. The carrier in the gas phase only is removed and simultaneously replaced with the same quantity of a mixture of carrier and sample. Performance of a material balance after equilibration of the mixture yields the expression
Necessary assumptions made in deriving Equation 1 are ideal gas behavior, no interference between adsorbate molecules, constant distribution coefficients, and constant temperature. For such a static section, AP is in absolute pressure units. I n order to apply Equation 1 to the dynamic conditions obtaining in chromatography, i t must further be assumed that equilibrium is rirtually instantaneous during sample introduction. The volume in which the mass change takes place is unknown, but is approximately the same for all samples.
The amount of sample adsorbed is therefore independent of the concentration function assumed. The same can be shown for desorption of the carrier, and the use of average or uniform concentrations to develop Equation l is therefore justifiable. The results reported are in good qualitative agreement mith Equation 1. This can be seen most clearly with the aid of Figure 2 , in which pressure changes are plotted as a function of sample distribution coefficient. Assume that argon has a K, of I. For oxygen, 1%-hichhas a distribution coefficient only slightly higher ( I @ , there is predicted and found a very small pressure decrease. For gases of larger K,. progressively decreasing pressures are found which approach an asymptotic value. For gases of K , less than 1, the prpssures increase sharply with small change in K,. Unfortunately, the dead volumes in the apparatus are not knon-n, and the retention times of the samples vary n ith pressure in a complex fashion, so that no quantitative comparison is possible. Equation 1also predicts that pressure changes will be directly proportional to sample concentration, as is found (Figure I ) . Several facets of the above require further discussion. It has been mentioned that argon and oxygen have approximately the same distribution coefficients, since their retention times on KO.5A Molecular Sieve are almost identical ( 2 8 ) . This was measured with hydrogen carrier. On switching t o argon carrier, the retention time (and distribution coefficient) of oxygen suffers little change (6). The difference in the distribution coefficients of argon in both systems is doubtless also small. VOL. 3 3 , NO. 1, JANUARY 1961
19
An important point for the understanding of the following section is that for an adsorbed carrier, V , is greater than Vgas. The exact relationship can be shown to be t0.6 + O ' i
which is obtained from the equation
i by substituting the conditions V , equals Vgaawhen K , equals 0. Equation 5 is similar to an expression already derived (2). It may seem paradoxical, since a sample of K , less than K , must travel faster than the carrier. That this is indeed the case can be understood in terms of the concept of equivalent empty columns ( 5 ) . Phenomenologically, in the argon Molecular Sieve system, the average argon molecule is repeatedly adsorbed in traveling through the column, and is thus delayed. The average helium molecule is adsorbed much less frequently or not a t all, and thus travels faster. Surge Effect. The surge and adsorption effects are related phenomena. According t o mass conservation, any decrease in the amount of gas in the gas phase due t o adsorption a t the entrance of the column must later be followed by a n identical increase in amount a t the exit of the column, or And = - - n o
(6)
-I 01
0
I
5
I
IO SAMPLE DISTRIBUTION COEFFICIENT,
I
15
KS
Figure 2. Plot of Equation 1 for carriers of differing degrees of adsorption For convenience, Q has been set equal to 1 ml./gram in calculating the points;
AP i s in units of c,RT
I t can be shown by means similar to those used in deriving Equation 1that
When the carrier is unadsorbed, Vgas equals V,, and Equation 7 reduces to
Equation 8 is similar to an expression given by van de Craats for the surge effect (4). With an adsorbed carrier, Equation 7 would have to be used to obtain surge correction factors. The factors are negative for samples of V , less than V,, indicating flow rate decreases through the detector. For these factors to be useful, it would have to be assumed that the flow rate decreases occurred only when the samples were present in the detector. Empirically, the flow rate decreases lasted for much greater periods than this ( I S ) . Therefore, the use of Equation 7 to obtainsurge factors is not justifiable. This conclusion can be arrived a t more fundamentally, since the ad-
20
ANALYTICAL CHEMISTRY
sorption effect must also influence the flow rate when such a sample leaves the column. This point will be discussed in a later section. It will also be shown that, even with unadsorbed carriers, surge effect corrections are of little help in improving analytical accuracy. Viscosity Effect. T h a t differences in viscosity between carrier and sample have some effect on column conditions seems undeniable. There is some question, however, as t o the form which a viscosity effect will take, and t o its relative importance. Assuming that a viscosity effect manifests itself as a pressure and flow rate disturbance ( d ) , the magnitude of this disturbance will decrease with increase of retention time of the sample. For example, it can be calculated that the average pressure of a 700-mm. carbon monoxide sample immediately after introduction into the column described is of the order of tens of millimeters. However, the pressure of argon is of the order of thousands of millimeters, and any viscosity effect can be neglected. Substances of relatively long retention time therefore cannot significantly affect other substances by
nieans of a viscosity effect. In contrast, the adsorption effect under these circumstances can be marked ( I S ) . The results given do not permit any quantitative measure of a viscosity effect which produces flow and pressure changes. The pattern of results, homever, indicates that adsorption effects predominate ( I S ) . The extent to which viscosity differences cause pressure and flow changes is open to question. Under the usual conditions found in gas chromatography, it is possible that these differences mill rather result in negligible heating or cooling of the column, due to the differences in frictional forces. Theoretical Analytical Considerations. Van de Craats (4) postulated t h a t the viscosity effect caused pressure and flow disturbances to take place continuously as a sample gas was flowing down the column. Consequently, two separate sample components exerted a continuous influence on one another. When the first component left the column, i t passed through the detector at an altered flow rate, because of the presence of the second component. Since the
output of thermal conductivity cells is flow sensitive, an altered peak was recorded. With the argon Molecular Sieve system, the flow rate did not follow this pattern for gases of retention time longer than that of oxygen. After an initial change due to sample introduction, the carrier flow rate re-equilibrated, and the approximate equilibrium flow rate was then maintained until the sample started to pass off the column. It was possible for nitrogen and methane to have given a van de Craats type of flow change. This is based on the approximate pressures of both of the gases after introduction, and on the appreciable differences betnecn their viscosities and that of argon (4). The absence of such a change can be explained in a t least two ways. First, as has been mentioned, viscosity differences may not cause appreciable pressure or flow changes. Second, van de Craats has asserted that the viscosity effect is suppressed in a system like the one used here, in which constant mass flow of carrier is obtained by means of a sufficiently large pressure drop across a needle valve. However, in the absence of a needle valve, a critical pressure drop exists inside the tank reducing valve. Thus, mass flow should be constant regardless of the presence of the needle valve. A continuous type of flow change did take place with helium and hydrogen samples. However, this change can be explained in terms of the adsorption effect. For samples of K , less than K,, more carrier is eluted than sample adsorbed. This requires that the pressure in the advancing sample zone always be higher than that existing normally. As a consequence, the carrier gas ahead of the sample zone is forced from the column a t a faster rate. This faster flow should persist so long as any of the sample remains on the column, and possibly somewhat afterwards. As mentioned, this is a more fundamental objection to the use of Equation 7 for surge corrections. The results with the carbon monoxide-helium mixture are in accord Kith this explanation. For a mixture composed of several different gases, the pressure change during sample introduction can be shown to be .iP
=
RTQ [ c ,
- Ki ((K,Kc+ QXKi + Q)
> +
where c1, c2 . . . cn are the concentrations of the individual gases in the mixture
and K 1 ,Rz . , , K, are the corresponding distribution coefficients. By judicious choice of concentrations and gases, a zero pressure change can be obtained during sample introduction, as is approximately true for the 60 to 40 carbon monoxide-helium mixture. For this mixture, the combined amount of carbon monoxide and helium adsorbed is the same as the amount of argon desorbed, so that there is no net pressure change or mass transfer. Almost all of the carbon monoxide is adsorbed during sample introduction, since its distribution coefficient is large. I n contrast, little or no helium is adsorbed. Thus there remains in the gas phase of this section of column, after sample introduction, a mixture consisting chiefly of helium and argon. When this new mixture is transported further down the column it elutes more argon: and a flow rate increase takes place. This means that there has been a localized pressure increase viithin the column. In effect, the sampling zone has been shifted further down the column by the initial presence of carbon monoxide. The pressure and flow rate decreases following passage of helium (or hydrogen) off the column can be explained from a mass conservation viewpoint. With a constant mass flow of carrier into the column, there must be a decrease in flow rate folloaing any increase. The corresponding explanation from a hydrodynamic standpoint, involving the propagation of pressure disturbances d o m the column, is complex and has not been developed. With gases having distribution coefficients less than that of the carrier, a continuous flow change takes place. With gases having greater distribution coefficients,re-equilibration of the carrier flow can and does begin after sample introduction. There is a small pressure disturbance set up upon passage of such a sample through the column, but it is negligible until the surge effect takes place. These flow disturbances can affect a large number of peaks, depending on the degree of adsorption of the carrier, In Figure 2, for example, with a carrier of K O equal to 5, continuous flow disturbances occur for all those substances having a smaller distribution coefficient. The flow rate through the detector during passage of each of these substances is dependent on the presence and amounts of the others. In addition, the flow rate changes will last an appreciable length of time after passage of these components off the column, so that peaks appearing later will also be affected. This is not the case, however, in gas-liquid chromatography, where the carrier can usually be considered as unadsorbed. As Figure 2 shows ( K ,
equal to O), only pressure^ and flow rate decreases are possible with gaseous samples. The only flow disturbances of analytical significance occur during sample introduction and during the subsequent re-equilibration of the carrier flow. The duration of flow changes is smaller than those obtaining mith an adsorbed carrier. It is northwhile to examine some of the reasons why detector output is dependent on flow rate. Peak areas are affected by changes in flow rate regardless of the differential detector used (8). This occurs because chart speed remains the same while the substance in question passes through the detector in different time intervals. With thermal conductivity detectors the area can be affected by other factors as well (I, IO). If peak area is used for quantitative analysis, the peaks of shortest retention time will be affected most, since flow changes of the greatest magnitude occur a t the beginning of the determination. The magnitude of the initial flow changes, due to the adsorption effect, depends on the size and composition of the mixture ( I S ) and on other factors. A similar situation pertains if peak heights are used quantitatively. The retention times of the first-appearing peaks will be most affected by changes in carrier flow rate, since the corresponding substances are adsorbed very little. Diffusion will thus change the heights of these peaks most markedly. Such early-appearing substances also possess the highest gas phase concentrations on a molar basis, and hence the largest concentration gradients. These considerations provide a reasonable explanation for the earlier work of van de Craats (S), who found that the peaks of substances of short retention time were greatly affected by composition, while those of long retention time were affected little or not a t all. It is assumed that other sources of error are either negligible or random. As has been noted, a possible viscosity effect cannot explain why a substance of long retention time affects an earlyappearing peak. The futility of applying surge effect corrections, even in gas-liquid chromatography, is also apparent from the above. The peaks of shortest retention time are subject to the greatest error. However, as Equation 8 shows, the correction factors for these peaks are the smallest of all. The surge effect presents another mechanism by which one substance can affect the peak of another, even if V , is greater than V,. When a substance leaves the column, a pressure disturbance propagates back up the column as well as through the detector. The result of this is that a flow change continues for some time after elution VOL. 33, NO. 1, JANUARY 1961
21
of the substance off the column and the forecolumn pressure may change (as was especially noticed with carbon monoxide) However, the magnitude of a delayed flow change is usually small in comparison with the other changes ( 4 ) , and can be ignored if peak separation is adequate. Practical Analytical Considerations. Ideally, a chromatogram should be run with a very small sample, so t h a t flow changes are negligible and resolution is a t a maximum. I n practice this is often impossible for a n y of a variety of reasons. If moderate accuracy is sought, or if samples of widely varying composition are routinely analyzed, calibration becomes necessary. This is commonly done by running each pure component through the column, so that the surge effect is included in the calibration constant. The method proposed by van de Craats (4,in IThich surge corrections are made separately, has been shown to have no advantage over the more direct method. From both a theoretical and empirical standpoint, errors caused by the adsorption effect will primarily alter the first few peaks. As can be observed from the magnitude and duration of the accompanying flow changes ( I S ) , these errors can be quite high, even for analyses a t room temperature. The result is that the sum of the amounts of the components, as read from the chromatogram, is different from the amount of sample introduced. Such data can be normalized to 10070. This results in an improvement in the accuracy of the first appearing peaks at the expense of the later ones. The practical choice of m-hether to normalize the results therefore depends on which peaks are of primary interest. These problems can be circumvented by several means. If there are only two or three components in a mixture, empirical correction factors can be obtained (11). By far the best solution lies in the selection of column packing so as to avoid peaks of short retention time, when possible. Under these circumstances, the use of peak areas for quantitative evaluation is both feasible and preferable. Lastly, the use of adsorbed carriers should be avoided, as these cause prolonged flow rate changes. There are, however. problems to which the above positive measures cannot be applied at present. One such is the analysis of the common permanent gases containing hydrogen or helium, for which the argon Molecular Sieve system is practically the only choice. When strictest accuracy is necessary, resort must be made to the bracketing technique ( 7 ) . Contrary to the opinion of van de Craats (4), gaseous mixtures of the required accuracy can be preI
22
ANALYTICAL CHEMISTRY
pared. The chief problem is the time required for their preparation and analysis. Regarding apparatus design, i t may be possible to suppress any viscosity effect by adjusting column resistance (4). However, there seems to be no means by which the flow changes accompanying the adsorption effect can be eliminated. The use of a buffer volume ( I S ) or constant pressure regulator a t the entrance of the column n ill minimize pressure variations caused by adsorption effects and by differing sample pressures. Beyond this, the exact placement of needle valves, reference cells, or reference columns is irrelevant as regards analytical accuracy. S o internal marker or standard can accurately reflect the f l o ~rate history of all peaks. If one is used, it should possess a fairly long retention time, so that the effects of transient flow changes are minimized. As with the calibration method, the best accuracy can be realized if there are no peaks of short retention time.
NOMENCLATURE
(Units are given where necessary) amount of pure sample adsorbed during sample introduction, mmole C, = average concentration of pure sample in adsorbed phase after sample introduction, mniole/ gram cQ = average concentration of pure sample in gas phase after sample introduction, mmole/ml. cs = concentration of pure sample gas prior to sample introduction, mmole/ml. c,, c2, cn = concentrations of components 1, 2, n in a sample mixture prior to sample introduction, mmole/ ml. K , = distribution coefficient of carrier. mmole/gram adsorbent = ml./ mmole/ml. gas gram; for gas-liquid chromatography, the appropriate dimensionless units may be used K , = distribution coefficient of pure sample gas, ml./gram K1, K1, K , = distribution coefficients of components 1, 2, n in a sample mixture, ml./gram Ann = change in mmoles of gas in gas phase after introduction of pure sample And = change in mmoles of gas in gas phase when pure sample leaves column-i.e., after surge effect AP = absolute pressure change in static system, atm.; relative change in forecolumn pressure in dynamic system Q = ratio of interstitial volume in column t o wt. of adsorbent, nil./gram R = gas constant, liter atm./degree mole S = volume of pure sample, ml. t, = transit time of average carrier molecule, corrected for dead
A
=
ts
=
T = V, = T,i V,
=
=
volume of apparatus and pressure drop = fully corrected retention time transit time of pure sample gas, corrected for dead volume and pressure drop; for small sample = fully corrected retention time absolute temperature, ’ K. fully corrected retention volume of carrier = t, x flow rate, ml. interstitial volume in column fully corrected retention volume of pure sample = t, x flov rate, ml
.
LITERATURE CITED
(1) Bohenien, J., Purnell, J. H., J . A p p l . Chem. 8, 433 (1958). ( 2 ) Bosanquet, C. H., Morgan, G. O.,
“F’apour Phase Chromatography,” D. H. Desty, ed., p. 35, Academic Press, Sew York, 1957. (3) Craats, F. van de, Anal. C h m . Acta 14, 136 (1956). (4) Craats, F. van de, “Gas Chromatography 1958,” D. H. Desty, ed., p. 248, hcademic Press. New York. 1958. ( 5 ) Hanlan, J. F., Freeman. 11. P., Can. J . Chem. 37, 1575 (1959). ( 6 ) Janak, J., Kreici, AI., Dubskv, H. E., Collecfion Czechoslov. Chem. Communs. 24, 1080 (1959). ( 7 ) Keulemans. A. I. 11.. “Gas Chromatography,” 2nd ed., p. 35, Reinhold, S e a York, 1959. (8) Keulemans, A. I. lI., Kwantes, -1, Rijnderq, G. IT, A , , .4nul. C‘h?m. --letu 16, 29 (1957). 19) Said. S..A.I.Ch.E. Journal 2 . 477 (10) Schmauch, L. J., AY.\L. CHEM.31, 225 (1959). (11) Smith. R.S . , Sninehart. J , Lesnini, D. G.. Ibzd., 30, 1217 (1958). (12) Vizard, G S , Kynne, h.,Chem. & Ind. 1959,196. (13) Keinstein, A,, ASAL. CHEK 32, 388
(1960).
RECEIVEDfor review April G , 1960. Accepted October 5, 1960.
Correction Determination of Very Small Quantities of Lead I n this article by R. R. AIarshall and D. C. Hess [AXAL.CHEM.32,960 (1960)], on page 961, Figure 1, the dimension for the inner diameter of the reaction jacket should read 1 ’/9 inches. On page 962, Figures 2 and 3, both figures should have the same scale. One inch is the outer diameter of the graphite crucible or the total width of Figure 2. On page 966, the last author reference in (29) should be Larsen, E., Jr.
