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
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 Materials.
.OB
.06
.04
.02
.02
.04
.06
.08
.IO
Ac
Figure 1. Plot of sedimentation equilibrium data for chymotrypsinogen A
set of conditions were superimposed on the same plate. To avoid a loss in contrast in the fringe region, a mask 1.5 mm. in width was placed over the schlieren light source so that it blocked off the light to the portion of the plate normally occupied by the interference fringes. After the schlieren photograph was exposed, the light source slit was moved into the interference position and the fringe photograph exposed, without shifting the position of the plate. For plots of l / r dc/dr us. Ac, the interference fringe count was used to determine Ac, while dr/dr was read directly from the schlieren photograph as the vertical difference in centimeters between patterns of the solvent and solution sectors. Fringe counts were converted into units of schlieren concentration, square centimeters, by the use of a conversion factor determined from the following relationship: conversion factor = tan 0 x area under peak in sq. cm. fringe count across boundary
(5)
where e is the diaphragm angle. The other quantities required were obtained from a synthetic boundary run in which patterns were recorded by both optical systems. For the machine used in these studies, the conversion factor had the value of 0.01139. Values of partial specific volumes of the proteins were taken from the literature: 0.695 ml./gram for ribonuclease (t?), 0.721 ml. gram for chymotrypsinogen ( 8 ) , and 0.734 ml./gram for bovine serum albumin (1).
from the same experimental data (with the addition of synthetic boundary runs as required), and to values from amino acid analysis. Bovine serum albumin in an initial concentration of 0.40 gram/100 ml. was run a t 6800 r.p.m. and 11.2' for 43 hours. As expected, the resulting l/r dc/dr plot was not a straight line. The slope through the ends of the plot (10) indicated an apparent z average molecular weight of 1.01 X lo5. A separate calculation of the apparent weight average molecular weight by Method 2 of Table I gave a value of 8.5 X lo4. Method 3 of Table I takes fullest advantage of the high inherent accuracy of the interference optical system, but it is strongly dependent upon the results of an auxiliary determination of initial concentration, usually by a synthetic boundary run. While the synthetic boundary method is potentially capable of highly accurate results, in actual practice relatively large errors can result-for example, from the loss of solute out of the plateau region of the cell during the run by sedimentation of aggregated material or by adsorption on the walls of the cell (12). Method 2, which also uses the interference optics, has advantages in that computations are easy and that weight average molecular weights are obtained directly, but again the synthetic boundary determination is required. Method 1, as described here, depends upon measurements from the less accurate schlieren
optical system, but it avoids all potential hazards of the synthetic boundary run. Thus, while the inherent accuracy may be less, a gain in reliability may be expected. Elimination of the synthetic boundary determination has the additional advantage that the total amount of sample required is much less, A minor disadvantage of Method 1 is that the range of macromolecular solute concentrations which can be used must satisfy the requirements of both optical systems. Thus, the interference optics are useful with solute concentrations up to about 1%, so that the upper limit of the initial concentration is about 0.7% or less. The lower limit is determined by the schlieren optics and is about O.l%, although this value will vary considerably depending upon other operating conditions. The conversion factor used in the work reported here is important and must be known accurately. However, conditions for the determination of this factor can be selected for highest accuracy, and the results of several measurements can be averaged. Thus, because the factor is independent of the nature and concentration of the solute and is not influenced by radial dilution, any suitable sample can be used in a convenient concentration and the centrifuge can be run a t the most convenient speed. The conversion factor is a sensitive function of the angle of the schlieren diaphragm, however, so that this quantity must be known accurately, or a calibration run must be made a t the same diaphragm angle setting used in the analytical run. Combined schlieren and interference optics may be used for types of determinations other than sedimentation equilibrium to eliminate the need for routine integration of schlieren patterns. For example, for a mixture of macromolecules yielding a schlieren pattern of two or more peaks in a sedimentation velocity run, the approximate percentage composition can be determined quickly from the fringe shift for each portion of the interference pattern corresponding to a boundary. The schlieren pattern is used to determine the regions of the interference pattern corresponding to separate components, Solute concentrations can be used which
RESULTS AND DISCUSSION
The modified method described has been applied to three test solutes: chymotrypsinogen A, ribonuclease A, and bovine serum albumin. The first two of these were homogeneous preparations, and straight-line plots were obtained for l / r dc/dr us. Ac; a typical plot for chymotrypsinogen is shown in Figure 1. In Table I, typical results for apparent molecular weights are shown to compare favorably to values obtained by other well known methods
Table 1.
Results of Molecular Weight Determinations
Chymotrypsinogen A,a Ribonuclease A,* Method Ma,, X lo-' Ma,, X 10-4 1. This method 2.54 1.37 2. Fringe shift across cell (6) 2.56 1.42 3. Integration of fringes (7) 2.60 1.42 4. Integration of schlieren (10) 2.54 1.41 5. Logarithm of schlieren (6) 2.58 1.42 6. Amino acid analysis 2.51 (11) 1.368 ( 4 ) Concn. 0.25 gram/100 ml.; 14.7' C.; run at 14,000 r.p.m. for 40 hours. b Concn. 0.15 gram/100 ml.; 19.1' C.; run at 20,000 r.p.m. for 30 hours. 5
VOL. 38, NO. 2, FEBRUARY 1966
357
are lower than practical with schlieren optics alone and, thus, errors due to the Johnston-Ogston effect can be reduced.
(3) Hexner, p. E., Radford, L. E., Beams, Natl* Acad* Sei* u* s. 47,
LITERATURE CITED
(5) Lamm, O., 2.physik. Chem. (Leipzig.) A143, 177 (1929). (6) Lansing, W. D., Kraemer, E. O., J . Am. Chem. SOC.57, 1369 (1935). (7) Richards, E. G., Schachman, H. K., J . Phys. Chem. 63, 1578 (1959). (8) Schwert, G. W., J . Bid. Chem. 190, 799 (1951).
(1) Dayhoff, M. O., Perlman, G. E., MacInnes, D. A,, J. Am. Chem. SOC.74,2515 (1952). (2) Harrington, W. F., Schellman, J. A., Compt. Rend. Trav. Lab. Carlsberg, Ser. Chim. 30, 21 (1956).
~ ~ ~ y l ~ ~ $
c. H, w.,M ~ s., ~Stein,~ w.H., J . BWZ. Chem. 219, 623 (1956).
(4) Hirs,
(9) Svensson, H., Acta Chem. Scand. 4,399 (1950). (10) Van Holde, K. E., Baldwin, R. L., ~ J . Phys. , Chem. 62, 734 (1958). (11) Wilcox, P. E., Cohen, E., Tan, W., J . Biol. Chem. 228, 999 (1957). (12) Yphantis, D. A., Ann. N . Y . Acad. Sci. 88, 586 (1960).
C. H. CHERVENKA Spinco Division Beckman Instruments, Inc. Palo Alto, Calif.
Determination of Trace Amounts of Lead in Steels, Brass, and Bronze Alloys by Atomic Absorption Spectrometry SIR: Since the introduction of atomic absorption spectrometry (10, 13) as an analytical tool, many advances have been made, several of which have been discussed in recent reviews by Elwell and Gidley (6), Gilbert (8),and Scribner and Margoshes (11). Applications of this technique to the analysis of trace amounts of lead have been reported for petroleum spirit (a, 9) and urine (16, 16). The determination of larger amounts (0.08-3.2%) of lead in copper base alloys and steels has been described by Elwell and Gidley (5). Other applications to metallurgical analysis have been described by Gidley (7) and Stumpf (18).
The direct spraying of aqueous acid solutions of metal alloys frequently leads to difficulties such as corrosive attack upon the burner head and consequent introduction of metal ions into the flame. Neutralization of the acid, on the other hand, may lead to clogging of the burner head, because of the resulting high electrolyte concentration, and can also reduce the efficiency of spraying by increase of viscosity. As a result it appeared to us that it would be better to extract and concentrate the traces of lead into an organic solvent and spray it directly into the flame. This would have the added advantage resulting from a higher input ratio through the aspiration-type of spray used in this work. This factor has been discussed recently by Dagnall and West (1) in relation to the determination of silver following its extraction from aqueous solutions. EXPERIMENTAL
Apparatus. Absorbance measurements were made with an SP 909A atomic absorption-flame emission spectrophotometer fitted with a lead hollow cathode lamp, Unicam Catalog No. 103898 (Unicam Instruments Ltd., Cambridge, England), equipped with a 0-10-mv. Honeywell-Brown recorder. The absorbance flame-path in this instrument is ca. 7 cm. Air was supplied from a rotary compressor via a regulator, and acetylene gas from a cylinder. 358
ANALYTICAL CHEMISTRY
Procedure. REMOVALOF MAJOR COMPONENT.Determination of Lead in Sleek. Dissolve a suitable weight of sample (containing 0 to 300 pg. of Pb) in 10 ml. of concentrated hydrochloric acid (AR) in a 100-ml. beaker, warming to assist solution. Oxidize the iron present to Fe(II1) by the dropwise addition of concentrated nitric acid (AR). After cooling, transfer the solution to a 250-ml. separating funnel with the aid of a further 15 ml. of concentrated hydrochloric acid. Add 25 ml. of iso-amyl acetate and extract the bulk of the ferric ion (14) by shaking the funnel for 30 seconds. Allow the phases to separate and run the lower aqueous layer into a second separating funnel. Repeat the extraction with a further 25 ml. of iso-amyl acetate. Run the aqueous solution back into the 100-ml. beaker and evaporate to dryness. Baking to hard dryness should be avoided as this will cause low recoveries. The purpose of this separation is merely to remove excess acid and, hence, to facilitate the control of acidity subsequently for the H2Pb14 extraction. Determination of Lead in Brass/ Bronze Alloys. Dissolve a suitable weight of sample (containing 0-300 pg. of Pb) in a small volume of concentrated nitric acid (AR) in a 100-ml. beaker, warming to assist solution. Add 10 ml. of 5% calcium chloride solution, make ammoniacal, and add 10 ml. of 10% sodium carbonate solution; stir well to obtain intimate mixing. Allow the solution to stand for 5 minutes and then centrifuge to collect the precipitate. Wash the precipitate thoroughly with water and redissolve it in a small quantity of nitric acid, transferring the solution back to the original beaker. Evaporate the solution to dryness observing the precaution mentioned above. The presence of small amounts of copper ion in the calcium carbonate does not interfere with the method. EXTRACTION AND DETERMINATION. After evaporating the solution to dryness, redissolve the residue in 10 ml. of 5% (v./v.) hydrochloric acid. Samples containing appreciable amounts of titanium or tungsten cannot be redissolved, but these precipitates do not affect recoveries, Transfer the solution with the aid of a further 15 ml. of 5% hydrochloric acid tlo a 250-ml. separating funnel and add 2.5 ml. of freshly pre-
pared saturated potassium iodide solution. Pipet 20 ml. of methyl iso-butyl ketone into the funnel and shake for 30 seconds to extract the lead. Discard the lower aqueous phase. The organic extract may now be passed directly into the atomic absorption spectrophotometer using the instrumental settings and flame conditions summarized below. The amount of lead present is determined by comparison with a calibration curve prepared by taking synthetic standard iron-lead (0 to 1.6 ml. lO-3M Pb) or copper-lead mixtures through the procedure. The appropriate standard solution should be taken through the procedure with each series of determinations to correct for any slight variation in instrumental response. The following flame conditions and instrument settings were used on the SP 900A spectrophotometer. Slit width, 0.20 mm; wavelength, 2833 A.; lamp current, 6 ma.; and air pressure, 15 p s i . The acetylene pressure was just insufficient to give a luminous flame when the organic extract was being sprayed (manometer reading ca. 3 to 4 cm. of ethylene glycol). The measurements of absorbance were made low down in the flame just above the blue luminous cones of the burner head. RESULTS AND DISCUSSION
The line a t 2833 A. was found to be most suitable for measurements of atomic absorption due to lead. The optimum sensitivity was obtained with a lamp current of 6 ma. and the best flame conditions were found when there was just insufficient acetylene to cause a luminous flame (Figure 1). A slit width of 0.20 mm. was used although this factor xas not critical. The maximum response occurred with extracted lead iodide solutions when absorbance measurements were made just above the base of the flame (Figure 2) * It was found that, relative to aqueous solutions, a five- to six-fold increase in sensitivity was obtained with the ketone extract. This difference, which may be accounted for by a higher throughput ratio of the ketone extract, was investigated a,s follows.
