tone, and diethylamine in squalane all showed a type of plot in which the surface tension CT of the solution fell extremely rapidly with the first small additions of solute, to a constant value which did not change with further addition of solute. This type of behavior, designated by McBain (9) as Type 111, is characteristic of solutes having a polar oxygen or nitrogen part attached to a hydrocarbon part. For ethanol, a constant surface tension was already attained at a bulk solution mole fraction x of 0.01 to 0.03, depending on temperature. For 2-propanol, Parcher and Hussey ( 3 ) used concentrations corresponding to x = 0.014-0.05, values which are almost certainly very far from infinite dilution for CT-x behavior, and at which -doldx is very much lower than at infinite dilution. The slope duldx is related to K I by the equation (7)
where nL is the number of moles of liquid phase per unit volume and y is the activity coefficient of solute in solution. Since -du/dx falls rapidly with x from a high value a t infinite dilution, it is readily seen why Pecsok and others' (4-6) findings of a large K I term a t infinite dilution are consistent with Parcher and Hussey's ( 3 ) observations of a negligible K I term at finite concentration. T o make the point more quantitative, it is instructive to compare the liquid surface contributions to retention for ethanol in squalane at infinite dilution and at a mole fraction of 0.02, approximating to that investigated by Parcher and Hussey for 2-propanol in n-heptadecane. The ratio of the liquid surface and partition contributions to retention is measured by KIAIIKLVL, which can be estimated from a knowledge of -da/dx and A I . The ethanol and squalane system is chosen for illustration because it is the most fully documented of Pecsok and Gump's systems. At infinite dilution, Pecsok and Gump ( 4 ) determined -du/dx to be 1092 dynelcm a t 50 "C or 1249 dynelcm a t 30 OC. A detailed study of literature evidence suggests that the best value to take for A I for squalane at 20% loading on silanized Chromosorb P is about 0.7 m2/g with an uncertainty of about &loo%. Using these values in conjunction with Equation 2, we find that KIAIIKLVL is about 0.8 at 50 "C for a 20% loaded column. At lower loadings, the ratio would be even larger. While this is only an approximate value, it
indicates that the liquid surface contribution is commensurate with the bulk contribution a t infinite dilution. The relative contributions a t finite concentration can be estimated only very roughly from the CT vs. x plot (Figure 2) of Pecsok and Gump's paper ( 4 ) . The slope -da/dx is about 2 orders of magnitude smaller a t 30 "C, and 3 orders smaller at 50 "C, at x = 0.02 than a t infinite dilution. The other term (1 xd In r l d x ) , however, changes by only 12% from x = 0 to x = 0.02 ( 4 ) . Hence, the retention ratio, KIAIIKLVL, is of the order of 0.01 to 0.001 at x = 0.02. The liquid surface contribution is therefore too small to affect chromatographic measurements at finite concentrations around x = 0.02. It thus appears that the data of Pecsok and Gump and Parcher and Hussey are fully consistent. It is, of course, notable that the systems studied were slightly different, but inspection of Pecsok's data for methanol and ethanol leads one to expect that -dc/dx for 2-propanol in n-heptadecane should not be more than a factor of 2 or 3 smaller than for ethanol in squalane, the illustrative system on which the above estimates are based. It is concluded that low molecular weight solutes of the alcohol, ketone, and amine type are strongly adsorbed on saturated hydrocarbon solvent surfaces at infinite dilution, but not at small finite concentrations.
+
LITERATURE CITED (1) (2) (3) (4) (5) (6)
A. E. Littlewood and F. W. Willmott. Anal. Chern., 38, 1031 (1966). P. Urone and J. F. Parcher, Anal. Chern., 38, 270 (1966). J. F. Parcher and C. L. Hussey, Anal. Chern., 45, 188 (1973). R. L. Pecsok and B. H. Gump, J. Phys. Chern., 71, 2202 (1967). H-L. Liao and D. E. Martire, Anal. Chern., 44, 498 (1972). J. R. Conder, D. C. Locke. and J. H. Purnell, J. Phys. Chern., 73, 700 (1969). (7) D. E. Martire, "Progress in Gas Chromatography", J. H. Purnell, Ed., Wiley-Interscience, New York and London, p 93. (8) J. R. Conder and J. H. Purnell, Trans. Faraday SOC.,65, 824. 839 (1969). (9) J. W. McBain, "Colloid Science", D. C. Heath and Co., Boston, Mass., 1950, p 56.
John R. Conder Department of Chemical Engineering University College of Swansea Swansea SA2 8PP, Great Britain
RECEIVEDfor review January 14,1976. Accepted February 10, 1976.
AIDS Determination of Parts-per-Billion Levels of Hydrogen Sulfide in Air by Potentiometric Titration with a Sulfide Ion-Selective Electrode as an Indicator Dewayne L. Ehman Texas Air Control Board, Austin, Texas 78758
Direct potentiometry using a sulfide ion-selective electrode requires frequent electrode calibration with standard sulfide solutions and suffers from errors due to potential response drift, from errors due to responses to ions other than sulfide, and from the lack of precision involved in the determination of a sulfide ion concentration from a logarithmic response curve ( I , 2 ) . However, by using the sulfide ion-selective electrode as an indicator for the potentiometric titration of sulfide ion, these problems can be ignored, since the potential change rather than its absolute value 918
ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
becomes relevant. This article describes the determination of parts per billion (ppb) levels of H2S in air by trapping out the H2S in an aqueous NaOH, ascorbic acid absorber and titrating the resulting sulfide ion with a standard CdS04 solution, using a sulfide ion-selective electrode as an indicator. (Standard solutions of Pb(OAc)z, Pb(C104)2, Hg(NO& and HgC12 were tried as titrants, but they gave no useful inflection points a t the low concentrations of H2S and titrant used.)
Table I. Linearity and Accuracy Data for the H,S Potentiometric Titration Methoda ppb H,S in
standard 0 0 50 50 100 100 300 300
600 600 1000 a
1000 T = 296 K, F
PPb H,S found
Error, %
0 ... 0 ... 56 +12 56 +12 97 -3 105 +5 288 -4 281 -6 561 -7 580 -3 1011 +1 966 -3 = 200 ml/min, and P = 740 m m Hg.
-500
Bo , 10
ml 6.00 x
20
M
CdSO4
Figure 1. Potentiometric titration curve for 0, 50, and 600 ppb H2S in
air Table 11. Reproducibility Data for the H,S Potentiometric Titration Methoda Sample No.
Time elapsed after absorption, h
0:o 0.5 1.0 1.5 5 2.0 6 2.5 7 3.0 8 3.5 4.0 9 10 4.5 120 nanomoles H,S in each sample. 1 2 3 4
a
ml of 6.00 X M CdSO, at end point
20.0 20.0 20.0 20.0 20.0 20.0 19.7
RESULTS AND DISCUSSION If this analytical method is t o be used for the determination of ppb levels of H2S in air, it must be linear over a wide range of H2S concentrations, be accurate, be reproducible, and have few interferences. The linearity and accuracy of the method were tested by performing duplicate determinations on standard concentrations of HaS in air from 50 to 1000 ppb and using the following equation, which assumes that 1 sulfide ion reacts with 1 cadmium ion, to calculate ppb (v/v) H2S in air from each titration:
18.8
19.4 19.4
EXPERIMENTAL Apparatus. Standard HzS-, HzS-NOz-, and HZS-SOz-air mixtures were prepared from weighed Metronics permeation tubes kept at 30 "C in a thermostated water bath with constant, low flow rates of nitrogen over each tube and secondary dilution flow rates of air from compressed laboratory air purified by passing through a Puregas heatless dryer. H:;S-Oa-air mixtures were prepared from a McMillan 0 3 generator using the purified compressed laboratory air. The HzS from the standard air mixtures was trapped out in a glass midget impinger ( 1-mm bore diameter) containing absorber by drawing air through the impinger, a demister, a rotameter, and a flow controller with a vacuum pump. A Sargent-Welch Model PBX pH meter with an Orion Model 94-16 sulfide ion-selective electrode was used for the titrations. The inner chamber of the reference electrode was filled with Orion's 90-00-02 colored filling solution ( 3 ) ;the outer chamber of the reference electrode was filled with an aqueous solution of 10%KN03, 1.0 M NaOH. Reagents. All solutions were prepared from reagent-grade chemicals and doubly deionized water. Procedure. H2S from the standard air mixtures was trapped out in 10 ml of absorber (1.0 M NaOH, 0.1 M ascorbic acid) in a glass midget impinger at a constant flow rate of 200 ml/min for 20 min. (The absorber contained ascorbic acid to inhibit the air oxidation of sulfide ion and to produce a stable electrode potential.) The used absorber in the impinger was then poured into a 100-ml beaker, and 20 ml of fresh absorber was used to rinse the midget impinger into the beaker and to add volume to the solution to be titrated. While being stirred constantly with a magnetic stirrer, this diluted, used absorber was titrated with standard 6.00 X M CdS04 solution, using the sulfide ion-selective electrode as an indicator. Each mV reading was taken 30 s after each addition of titrant. After each titration, the electrodes were stored in fresh or titrated absorber and were blotted dry with a paper towel before each titration. The equivalence point was taken as the point of greatest inflection, which was at about -560 mV, on the titration curve (see Figure 1).
ppb H2S =
V X C X lo6 X 22.4 X 760 X T F x 10-3 x t x P x 273
(1)
where V is the ml of CdS04 titrant at the end point, C is t h e molarity of the CdS04 titrant, T is the temperature in K of the air mixture, F is the impinger flow rate in ml/min, t is the absorption time in min, and P is the atmospheric pressure (uncorrected for sea level) in m m Hg for the air mixture. For a 6 X M CdS04 titrant and a 20-min absorption time, Equation 1 reduces t o the following: ppb H2S = 1.87 X
VXT lo4 FXP
(2)
T h e results, shown in Table I, indicate that the method's linearity and accuracy are quite good for 50 t o 1000 ppb H2S in air. The reproducibility of the method was tested by trapping out 1500 nmol of HaS in 25 ml of absorber and titrating ten separate 2-ml aliquots. T h e results of this test, shown in Table 11, indicate that the precision is excellent, but that the absorbed H2S should be titrated within 2 h for good results. (A subsequent experiment, in which 480 nmol of H2S were trapped out in 20 ml of absorber and separate 5-ml aliquots were titrated after being stored for 0.0, 19.7, and 92.0 h in the glass midget impinger in the laboratory at 23 "C, showed an average sulfide ion decay rate of 0.6% per hour.) The method was tested for interferences by trapping out and titrating standard air mixtures of 740 ppb H2S, 710 ppb NOa; 1000 ppb HzS, 950 ppb SO,; and 180 ppb H2S, 2800 ppb 0 3 . No interference could be found from NO2,
SOz, or 03. This method, then, seems highly suitable for the determination of ppb levels of H2S in air and can be used for measuring the HPS concentration (averaged over 20 min) in t h e ambient air or for standardizing H2S permeation tube systems. Presumably, this method's lower limit of detectability (50 ppb H2S) may be lowered by increasing the H2S absorption time, by increasing the midget impinger flow rate, or by increasing both. ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, M A Y 1976
919
LITERATURE CITED
(3) Orion Research Inc.. Cambridge, Mass., Instruction Sheet for Double-
(1) A. F. Isbeil, Jr.. R . L. Pecsok, R . H. Davies, and J. H. Purnell, Anal. Chern., 45,2363 (1973). (2) Orion Research Inc.. Cambridge, Mass., Instruction Manual for Sulfide ion-Selective Electrode Model 94-16 (1974).
RECEIVEDfor review October 13, 1975. Accepted December 8,1975.
Junction Reference Electrode Model 90-02 (1974).
Atomic Subshell Cross Sections for Qualitative Analysis of Photoelectron Spectra James M. Delaney’ and J. Wayne Rabalais’ Depatiment of Chemistry, University of Houston, Houston, Texas 77004
T o use electron spectroscopy for qualitative analysis, it is important to consider both the energies and relative intensities of the bands in an electron spectrum. Considerable attention has been paid to photoelectron energies; Siegbahn et al. ( I ) have compiled a very useful table of the binding energies for the various subshells of the elements 1 to 104. As an aid to analytical chemists, we present the photoionization cross sections of the elements in graphic form. This graph serves two purposes. First, it provides a quick determination of which orbital of an element will have the largest photoionization cross section. Second, it can be used along with binding energies in confirming elemental analysis of an unknown. In performing a qualitative analysis of the bands in an electron spectrum, one naturally uses Siegbahn’s table to effect an identification of the various elements present in the sample. Often times, there are peaks which are energetically close together or peaks that could correspond to two or more elements. In these cases, we have found it particularly useful to use the relative cross sections in conjunction with the binding energies to obtain elemental assignments. Assignments must be consistent with regards to relative band intensities as well as binding energies. Our experiences indicate that it is usually sufficient to know only the approximate relative intensities to be expected for the bands in order t o make a qualitative analysis. We have found that a plot of the elemental subshell cross sections vs. atomic number is very useful for quick analysis of spectra. The purpose of this communication is to present this plot for use in analyzing electron spectra. The theoretical photoionization cross sections per electron for each subshell of the elements are presented in Figure 1. The cross sections were obtained from the compilation of Scofield ( 2 ) , who used relativistic Hartree-FockSlater wave functions to calculate the cross section for each atomic subshell a t excitation energies from 1.0 to 1500 keV. The plot in Figure 1 consists of the cross section per electron for the lowest energy (most intense) spin-orbital component a t an excitation energy of 1500 eV (approximating that of A1 K a a t 1486 eV). Actually, interpolation of Scofield’s values shows that the relative subshell cross sections a t 1486 or 1254 eV (Mg KD) are very close to those a t 1500 eV. The cross sections in the figure are in barns and each is divided by the number of electrons in that particular spin orbit component. We propose that the table in Ref. 2 be used as follows. After analyzing the energetic positions of peaks in an electron spectrum, one has a good idea of the elemental composition of the sample. In order to confirm this analysis, the approximate relative intensities of the peaks should be Present address: PPG Industries, Pittsburgh, Pa. 920
ANALYTICAL CHEMISTRY, VOL. 48, NO. 6, MAY 1976
compared to the curves in Figure 1. Agreement between energies and intensities provides a cogent elemental analysis. Many of the cross sections vary by as much as four orders of magnitude, making it extremely difficult to observe photoelectron bands from some particular subshells of an element. The figure is also useful in attempting to detect minute quantities of an element in an unknown sample. For example, if one is looking for trace amounts of Eu in a sample, from Figure 1 it is obvious that the best bands to look for are those from the 3d orbitals. These are the ones of highest intensity. The 3p orbitals provide cross sections which are almost as high as those of the 3d orbitals and would also be useful; however, the 4s, 4p, 4d, 4f, and all other occupied orbitals have cross sections that are lower than those of the 3d orbitals by an order of magnitude; consequently, they would be more difficult to observe. Several notes of caution should be mentioned in using this figure. 1) The cross sections plotted are “per electron” and must be multiplied by the electron occupancies of the orbitals in their respective molecules and ions. The plot was made in this manner in order to allow one to estimate the intensities of valence bands, of elements and ions, which may have varied occupancies. For example, in Mo there are 6 electrons occupying the 4d and 5s valence bands, in Moo2 there are only 2 electrons in these bands, and in Moo3 the valence bands of Mo are completely empty. In using the figure for fully occupied core orbitals, one would simply multiply the intensity from the curve by 2 for s bands, by 4 for p3j2 bands, by 6 for d5j2 bands, and by 8 for f7j2 bands. 2) For any given spectrometer one may have to correct the experimental intensities for systematic errors such as electron kinetic energy dependence of the analyzer, photoelectron angular distributions, escape depths of photoelectrons, etc. Most instruments have transmission functions varying with E-l and the escape depth function is roughly E+0.7.Thus, with these instruments, the observed peak intensity relations do resemble cross sections. In contrast, instruments with transmission functions varying as E+’ exert a strong monotonic bias which distorts the observed peak intensities. In most instruments the angle between the photon source, sample, and electron acceptance slit is go’, while the intensities in the figure represent total cross sections, Le., cross sections for ejection of electrons in all directions. Our studies ( 3 ) have shown that the ratio of differential cross section to total cross section, u/utot, will vary by a t most a factor of 2 for the extreme cases of the angular distribution parameter p (i.e., -1 to +2) a t 90’. Therefore, angular distributions can produce some alteration of intensities, although these will remain constant for a given acceptance angle. 3) Scofield’s cross sections are only order of magnitude
