continue to increase above this HC1 concentration. The increase in per cent iron removal seems to depend on the concentration of the FeC1-4 species in the aqueous phase which in turn is governed by the chloride ion concentration in this phase (5). The results in Figures 2 and 3 indicate that the removal of tri-n-octylamine hydrochloride ion pair in addition to the simultaneous sublation of Fe(1II)-amine complex is possible. This conclusion supports our previous assumption that the formation of Fe(II1)-amine species may also occur within the organic phase. The solvent extraction-i.e., intimate mixing of the two liquid phases by shaking-of Fe(II1) at 9.6M HC1 concentration in the initial aqueous phase was also investigated and compared to solvent sublation in the equivalent system. A 250-ml separatory funnel was vigorously shaken for an equivalent period of 180 minutes even though equilibrium is known to be established in a matter of a few minutes (5). The values 43 and 96.8 % for the recovery of iron and amine, respec-
tively, in the organic phase were obtained. Because the values agree with the corresponding solvent sublation results, it was concluded that at the state of equilibrium the distribution of the species is the same and independent of the extraction technique employed. This result indicates that over the long run, bulk water dragged up into the anisole layer and reextracted into the aqueous medium can create the liquidliquid equilibrium state under the conditions of these experiments. However, the rate of approach to equilibrium as well as the mechanistic details of the extraction process differ for the two methods. If desired, advantage can be taken of the slow extraction rate for separation purposes (2) in solvent sublation. RECEIVED for review September 9,1968. Accepted January 21, 1969. This work was supported by Grant WP 01129-02 from the Federal Water Pollution Control Administration, U S . Department of Interior.
Derivative Spectroscopy and Its Application to the Analysis of Unresolved Bands I. G . McWilliam1 Central Research Laboratories, Imperial Chemical Industries of Australia and New Zealand Ltd., Newson Street, Ascot Vale, Victoria 3032, Australia
IT IS RECOGNIZED that the first derivative of a spectral or chromatographic band is very sensitive to change in the band shape. This fact can be used both for qualitative (1-3) and quantitative (4) analysis. To date, however, no work has been reported on the application of the derivative technique for quantitative analysis where two components overlap to such an extent that even the derivative curve shows no clear separation of the peaks. The present work reports on the application to this problem of an oscillating plate differentiator used in conjunction with a Grubb-Parsons type S.4 infrared monochromator (5). Production of Derivative Spectra. It has been shown elsewhere (5) that derivative spectra can be produced by interposing an oscillating beam-deflecting plate in the optical path of a monochromator (see Figure 1). Several similar devices have also been reported recently (6, 7). Referring to Figure 1, a relatively simple expression can be derived relating the angle of rotation of the plate, i, the plate thickness, t, the refractive index of the plate, n, and the effective displacement of the slit, As. The displacement from 'Present address, Chemistry Department, Monash University, Wellington Road, Clayton, Victoria 3168, Australia (1) C. S. French and A. B. Church, Carnegie Znst. Wash. Yearbook, 54, 162 (1954-55). (2) A. T. Giese and C. S. French, Appl. Spectrosc., 9, 78 (1955). (3) T. Kambara, K. Saitoh, and K. Ohzeki, ANAL.CHEM.,39, 409 (1967). (4) G. L. Collier and F. Singleton, J. Appl. Chem. (London), 6, 495 (1956). (5) I. G. McWilliam, J. Sci. Instrum., 36, 51 (1959). (6) R. E. Drews, Bull. Amer. Phys. SOC.,12, 384 (1967). (7) A. Gilgore, P. J. Stoller, and A. Fowler, Rev. Sci. Znstrum., 38, 1535 (1967).
674
ANALYTICAL CHEMISTRY
the normal of the emerging ray, and of the extrapolated incident ray, at the rear face of the plate will be t tan r and t tan i, respectively. Hence As = (t tan i - t tan r) cos i cos i = t (sin i - sin r . cos r =
L ( n - C)S n
sin i
cos r
For small values of i, Ai (in radians) t As N - ( n - 1) Ai
n
For most practical purposes, the error introduced by the approximation is very small. Taking n as 1.55, the error in As is less than 0 . 3 x for i = 5 " , 1 . 6 x for i = loo, 6 % for i = 20" and still only 13% (As is underestimated) for i = 30". The corresponding wavelength variation depends on the optical geometry of the instrument. For a prism instrument it is of the form Ai
11 const.
tan i
(%)
xAx
where i is the angle of the incident ray on the prism. Because variation in the term (AnjXAX) is relatively small over a fairly wide wavelength range [0.00066-0,0009 for a sodium chloride prism over the range 2-20 p (S)],the above expression reduces to Ai N const. XAX Application to the Quantitative Analysis of Unresolved Bands. The present application of the derivative technique to the analysis of unresolved bands is based on measurement of the maximum and minimum of the first derivative curve.
I
PLATE1
r
1
1
I
Figure 1. Displacement of slit position by beam-deflecting plate In Figure 2 the first curve represents a symmetrical band or peak due to a minor component. The derivative curve, immediately below, is symmetrical and the ratio of the maximum and minimum of the first derivative is equal to unity. This ratio, which is a measure of the symmetry of the original peak, is termed here the peak ratio. The second curve in Figure 2 represents a compound peak formed by the overlap of the major peak and a second symmetrical peak, displaced slightly from the center of the major peak, due to a minor component (broken curves). As can readily be seen, for a compound peak which is not symmetrical, the peak ratio will differ from unity, and can therefore be used as a measure of the amount of one component in the other. The separation range over which the peak ratio concept in its simple form is viable can be defined with the help of published derivative curves (2). (These curves are, unfortunately, not sufficiently accurate to provide reliable peak ratio cs. concentration plots, although their general trend agrees well with the experimental curves which are discussed below.) As the peak separation increases, the derivative curve becomes more complex, the degree of complexity depending on the relative heights, widths, and separation of the two components. For two Gaussian peaks of equal width, it would appear that the peak ratio (as defined here) can be used unambiguously as a measure of impurity content up to a maximum peak separation of about 2u, where u is the standard deviation, provided that the impurity peak height does not exceed about 25 of the major peak ( 2 ) . With closer peaks, as in the examples below, higher percentages can be tolerated.
I
I 0
20
40
80
LO
PER CENT ACETONE IN CHLOROFORM
Figure 3. Peak ratio YS. concentration curves for acetone in chloroform (8 p bands)
WAVELENGTH
(A)
Figure 2. First derivative curves for a symmetrical peak and for a compound peak containing a displaced impurity band The 8 p bands of acetone and chloroform, whose peak maxima differ by 0.04 p (a separation of about 0.04 u),provide the first example of the use of the technique. In Figure 3 the peak ratio for the 8 p acetone-chloroform peak is shown as a function of concentration at two sample thicknesses. The derivative curves were obtained using a sodium chloride plate 4.5 mm thick and an angular oscillation of 3”. Several points are evident from Figure 3. First it is seen that the peak ratio is markedly dependent on the sample thickness. This results from the fact that the transmission derivative dZ/dX, is used rather than d(1og Z)/dX ( 4 , 8). However, this has the advantage that any ambiguity caused by the double-valued nature of the peak ratio us. concentration curve can be overcome by measuring the ratio at two sample thicknesses. The ratio is independent of incident radiation intensity, and it was found that the ratio for 1.63 acetone in chloroform (1.24) was unaffected by reducing the Nernst current from 0.9 to 0.6 A. (8) W. A. Roth and K. Scheel, Eds., “Landolt-Bornstein Physikalisch-Chemische Tabellen 11,” Vol. 2, Julius Springer, Berlin, 1923, p 913.
0
2
4
6
8
10
12
14
16
18
20
22
PER CENT ADlPONlTRlLE I N BENZONITRILE
Figure 4. Peak ratio vs. concentration curve for adiponitrile in benzonitrile (4 p bands) VOL. 41, NO. 4, APRIL 1969
675
Second, the sensitivity of the method in this particular example is greatest over the range 0-5% acetone, and it is possible to determine 1 acetone in chloroform to + 0.05% with the unresolved 8 p band. Third, whereas the peak ratio for pure chloroform is close to 1.00, the ratio for pure acetone is much lower due to the asymmetrical shape of the acetone peak. It should also be noted that, although a perfectly symmetrical peak will give a peak ratio of 1.00 (assuming negligible distortion due to instrumental factors), the reverse does not necessarily apply. A second example is shown in Figure 4. This is the analysis of adiponitrile in benzonitrile with only the unresolved 4 ji CN . the derivatives are obtained bands (separation 0 . 0 6 ~ ) Because by operating the instrument in the single-beam mode, some interference may occur in this particular case due to overlap of the CN and atmospheric carbon dioxide bands. Provided,
however, that the carbon dioxide concentration remains constant, its only effect will be to modify the shape of the peakratio us. concentration curve. (Alternatively, of course, the instrument could be purged to eliminate this interference.) Conversely, it is possible to modify the shape of these curves, and therefore the sensitivity of the method, by the addition of a known amount of interfering material. ACKNOWLEDGMENT
The author gratefully acknowledges the encouragement and assistance of Dr. J. H. Beynon and Mr. M. St.C. Flett, Research Department, Imperial Chemical Industries Ltd., Manchester, England, where this work was carried out.
RECEIVED for review November 18,1968. Accepted December 23, 1968. ~
Anion Determination with Ion Selective Electrodes Using Gran’s Plots Application to Fluoride Arnaldo Liberti and Marco Mascini Istituto Chimica Analitica, Unicersith di Roma, Rome, Italy WITHTHE RECENT introduction of ion selective electrodes, very sensitive analytical tools have become available for many ions. The construction and the operation of these electrodes is similar to glass pH electrodes and as they are both indicators of single ion activities in aqueous solution should be valuable for a large number of physico-chemical investigations. Since the evaluation of concentration is frequently of more interest than activity, a number of procedures have been suggested to express the millivolts response in terms of concentrations. Though the described procedure can be extended to most electrodes, the present experimental work and discussion refer to a fluoride ion electrode which has been extensively used by various authors for fluorine determinations in bone ( I ) , tungsten ( 2 ) , chromium plating baths (3), urine (4), enamel of teeth (3, saliva ( 6 ) , and others (7-8). The procedures which have been suggested can be grouped as follows: preparation of fluoride solution at an ionic strength close to the samples under investigation to build up a reference calibration curve for the indicator electrodes; dilution of the samples 1 : 1 with a solution of high ionic strength [total ion strength adjustment buffer, TISAB (7)] and use of a reference calibration curve; titration of the fluoride ion with thorium or lanthanum (8-9); the use of linear null-point potentiometry (IO).
The titration procedure has been recommended by Lingane (8) to obtain higher precision but a number of limitations have been noted: the equivalence point is not the point of maximal slope, but has to be determined in careful titrations of precisely known amounts of fluoride in the particular medium used; the titrations are quite time consuming as equilibria are rather slow to be obtained, namely, near the equivalence point; thorium and lanthanum salts are not primary standard and require standardization. The procedure described in this paper makes use of Gran’s plots (11-12) ; this method, permitting the weighing of several data points is more accurate than a single point direct potentiometry measurement and yields satisfactory results for a number of applications.
(1) L. Singer and W. D. Armstrong, ANAL.CHEM.,40, 613 (1968). (2) B. A. Raby and W. E. Sunderland, ibid., 39, 1304 (1967). (3) M. S. Frant, Plating, 54, 702 (1967). (4) L. Singer, W. D. Armstrong, and J. J. Vogel, Abstract, 45th General Meeting of Inter. Assoc. Dental Research, p 77, March 1967. (5) B. Richardson and H. G. McCann, ibid., p 77. (6) P. Gron, F. Brudevold, and H. G. McCann, ibid., p 79. (7) M. S. Frant and J. W. Ross Jr., ANALCHEM.,40, 1169 (1968). (8) J. J. Lingane, ibid., 39, 881 (1967); 40, 935 (1968). (9) T. S . Light, Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1967. (10) R. Durst, ANAL.CHEM.,40, 931 (1968).
where E, E,, and E, are, respectively, the equilibrium potential, the normal potential, and the liquid junction potential. COVo and CV are, respectively, the concentration and volume of the sample solution, and of the standard solution; y i s the activity coefficient of the fluoride ion. From Equation 1 is obtained:
676
ANALYTICAL CHEMISTRY
THEORY
To a sample solution in which a fluoride and a reference electrode are immersed, known amounts of standard fluoride solutions are added and the potential difference is measured. The potential of the indicator electrode according to the Nernst equation is: 2.3RT (COP‘, C V ) 2.3RT E=E,-log Y 4 F log v, F
+ +v
+
(1)
( v O + v ) X 1 O - E & - ? = 1 0 - ( E O + *.3RT E ) L x y x (CJ,
+ cv) (2)
~
~~
(11) G. Gran, Analyst, 77, 661 (1952). (12) F. J. Rossotti and H. Rossotti, J. Chem. Educ., 42, 375 (1965).
