Table I. Calculated Dissociation Constant for HF From Results of Additions of HCI to l m NaCl Solution(1V)”

IH+1 TF-1

[F-I 5.20 X 9.62 X 5.58 3.8 X IO-’ 1.32 3.29 X 1W6 8.49 X 5.58 2.29 X 1.22 1.46 X 10-6 3.47 X 5.56 4.10 X 1.24 8.05 X IW7 7.36 X 10-3 5.54 4.74 X lWE 1.25 3.90 x 10-7 1.67 x 10-2 5.39 5.09 x 10-6 1.28 1.45 X l e 7 4.80 X 5.31 5.16 X 1.35 8.06 X 1 0 - 8 8.79 x 5.08 5.00 X 1.41

Deviation from Nernst behavior equivalent to 5.58 X 10-6m.

Chloride interference and a fluoride impurity in the purified chloride cannot be distinguished by a single experiment. If the experimental data in Figure 1 are corrected for an assumed fluoride impurity in the chloride (solid circles), then Nernst behavior is obtained down to about 8 X 10-6m fluoride. The corrections which give straight lines with the Nernst slope are 6.5 X 10-5m, 1.5 X 10-5m, and 6.0 X lO-om, respectively, for I, 11, and 111. Because these corrections are different for the three 1.00m chloride solutions this clearly cannot be due to chloride. Chloride interference must depend on the chloride concentration which is constant in these three experiments. However, one must allow the possibility that the lowest ob- served correction, 6 X IO-Bm, represents the chloride inter- ference.

This possibility was eliminated by the following experiment which identified the cause of the deviation as a fluoride im- purity. An HC1 solution was added incrementally to a 1 .OOm chloride solution(1V) for which the Nernst correction was 5.6 X lO-6m. Data for measured fluoride concentrations, [F-1, measured hydrogen ion concentration, [H+], and the total fluoride concentration, [FIT, are listed in Table I. The

[HFI concentration was obtained from the difference in [FIT and [F-1. The concentrations of the fluoride species in the table were calculated on the assumption that the Nernst devia- tion in a plot of the type shown in Figure 1 is due entirely to fluoride impurity. If the deviation were chloride interference, then no dependence on pH would be expected; however, the fluoride concentration will decrease with decreasing pH below pH of 4 where some HF is produced. The dissociation con- stant calculated from these data is in excellent agreement with published values (5) (the range of best values in similar media is 1.5 X indicating that the deviation was indeed the result of a fluoride impurity in the chloride.

From the data of Table I the upper limit for the chloride in- terference was set at 2 X 10-8m in view of the constancy of the equilibrium quotient. Also, this enables us to conclude that Nernst behavior (within 10%) is obtained to <2 X 10-7m in the l m chloride medium. The upper limit placed for LaFa solubility, lO-?m, does not alter this conclusion because the free fluoride concentration is buffered in this experiment at 5 X 10-6m. The presence of a fluoride impurity was also verified by addition of beryllium ion which is known to com- plex fluoride strongly (5). When 0.0053m Be2+ was added at pH 2.75, the free fluoride concentration dropped to 7 X 10-8m. This also sets an upper limit for the chloride interference in 1.00m chloride at <7 x 1O-sm. With such extreme selec- tivity this electrode is useful for measurement of fluoride im- purities in chloride to less than 1 ppm and for complexing studies in chloride media involving metal ions which complex fluoride strongly and give rise to very low levels of fluoride.

to 1 . 1 X

RECEIVED for Review October 6 , 1967. Accepted November 17, 1967. Research sponsored by the U. S . Atomic Energy Commission under contract with the Union Carbide Corp.

(5) L. G. Sillen and A. E. Martell, “Stability Constants of Metal- Ion Complexes,” The Chemical Society, London, 1964, pp 256-7.

Instrument for Reproduction of Curves with Independent Abscissa and Ordinate Expansion Clifford S. Garner, Richard B. Gillespie, and R. Graham Hughes Department of Chemistry, University of California, Los Angeles, Calv. 90024

THE USE OF MECHANICAL and optical pantographs for changing the scale of graphed curves is well known. Such devices alter the abscissa and ordinate scales by the same scaling factor. In connection with extensive spectrophotometric investigations of reaction kinetics and stereochemical changes, our laboratory had need of a quick, accurate means of con- verting experimentally recorded spectral curves to plots of molar absorbance index us. wavelength without laborious point-by-point hand plotting. This conversion usually required leaving the wavelength abscissa scale unchanged and expanding or contracting the absorbance ordinate scale by a calculated factor. When the application to be made of such plots is the accurate locating of theoretical isosbestic points for various possible stereochemical consequences of a reaction- (e.g., does species A aquate concurrently to a fixed ratio of cis and trans isomeric products, B and C, and if so, what is that ratio?)-the plots must be accurate over the entire wave- length region involved (not just at the absorption maxima and

minima) and many combinations of such plots may be needed before one is found in accord with the experimental reaction isosbestic points (1-4). Also we wished to be able to take spectra published in the literature and scale them to a standard size, often with different scaling factors for the abscissa and ordinate scales. To meet these needs we have developed such a device, which we call a curve expander, largely built from commercially available instruments.

DESCRIPTION OF CURVE EXPANDER

The basic concept is to use a master X-Y recorder which has a time-sweep slidewire (Moseley 7000A, factory modified to accept a line follower), hereinafter called A , and which is

(1) D. C. Olson and C. S . Garner, Znorg. Chem., 2,558 (1963). (2) L. P. Quinn and C. S. Garner, Zbid., 3,1348 (1964). (3) J. M. Veigel and C. S. Garner, Zbid., 4,1569 (1965). (4) A. A. El-Awady, E. J. Bounsall and C. S. Garner, Zbid., 6, 79

(1967).

444 ANALYTICAL CHEMISTRY

-OUTPUT TO Y AXIS OF

X A X I S OF W RE C 0 R D E R ” B”

I I - - - - - - - - MOSELEY 7000e POTENTIOMETER X-Y RECORDER A B O X

Figure 1. Potentiometer box circuit and diagram of wiring to master A and slave B X-Y recorders

R1 ZK, 10-turn B1 1.35-volt mercury battery Rz ZK, 10-turn Bz-1.35-volt mercury battery

equipped with a photoelectric line follower (Moseley F3B), hereinafter called LF, to drive a “slave” X-Y recorder (e.g., Moseley 135C), hereinafter called B, the X and Y range con- trols of which can be used to vary the expansion independ- ently.

This is accomplished by the circuit in Figure 1. The Y axis of A , locked to the curve being followed by means of the photoelectric LF head, is coupled to the Y axis of B by means of battery B1 (e.g., Eveready E42N) and potentiometer R, (e.g., Beckman Model A 2K helipot), used for setting the Y zero position. Variable expansion of the Y axis of the curve being followed is then set by the Y range control of B. The curve to be followed is scanned at an appropriate rate by the time-sweep generator along the X axis on A . The time- sweep voltage, picked off at the X slidewire of A , is used to drive the X axis of B in synchronism at a rate set by the X range control of B, thus determining the X expansion. Bat- tery Bz (same kind as B,) and potentiometer RZ (same kind as R,) are used for setting the X zero position on B. The poten- tiometer R1 and Rz control knobs are labeled Y ZERO and X ZERO, respectively.

If an X-Y recorder without a time drive of the Moseley 7000A type is used in place of A , an external ramp generator, such as a motor driven slidewire, would be required to drive the X axes, the X expansion then being set with the X range controls of the two recorders. Moreover, in place of a photoelectric line follower, a shop-built stylus can be substi- tuted for the standard pen on A and the curve traced manually.

Assembly. Remove the standard pen from A and fix the LF head in its place. Plug the cable from the LF head into the LF HEAD socket on the LF control box and the Y OUT- PUT cable from the LF control box into the Y input (+ to +, and - to -) of A . Plug the shielded cable from the poten- tiometer box into the RETRANSMITTING SLIDEWIRE socket on A . On our Moseley 7000A recorder it was nec- essary also to run leads from one end of the X slidewire and from its slidewire contact to pins M and N , respectively, of the RETRANSMITTING SLIDEWIRE socket. Connect the X and Y leads of the potentiometer box to the X and Y inputs on B. On A set X RANGE knob to SWEEP, Y RANGE knob to LF, Y AXIS SLIDEWIRE switch to LF, the two DC-AC switches to DC, and the RECYCLE switch to OFF. On B set the two FIX-VAR switches at VAR.

PROCEDURE

The LF head follows printed curves, Xerox or Offset copies, and pencil tracings. Spectral curves obtained with standard pen inks must be reinforced with a soft pencil (black inks made for use with the LF clog our spectropho-

n r

1 ‘

Figure 2. Esr curve to be reproduced (a); curve reproduced with ordinate expansion and abscissa held constant (b) ; curve reproduced with ordinate expansion and abscissa reduction (c)

tometer recorder pens). Extraneous strong lines or marks within ca. 2 mm of the curve to be followed should be erased to avoid probable jumping of the LF head off the curve during the scanning. Grid lines of Cary No. 1200 chart paper do not interfere.

A horizontal Y = 0 line is ruled with a pencil on the Y = 0 axis of the curve on A , and a second horizontal Y = max line is ruled at an arbitrary Y ordinate. Two V’s (the LF will not lock on vertical lines), X = 0 and X = max, are drawn with pencil with their points at arbitrary X abscissas. With the potentiometer box OFF, the X ZERO and Y ZERO knobs of B are used to set the B pen to the origin of the graph grid of the paper on B, then the potentiometer box is turned ON. The LF head is locked onto the Y = 0 mark, and the potenti- ometer box Y ZERO set to bring the B pen to the Y = 0 axis of the graph paper on B. The LF head is then locked onto the Y = max mark, and the B Y RANGE knob set to bring the B pen to the desired Y magnification. The LF head is next locked consecutively on X = 0 and X = max marks, and the potentiometer box X ZERO and B X RANGE controls used analogously to set the X = 0 and X magnification on B. The LF head is then locked onto the curve at extreme left and the A sweep activated to scan the curve. A detailed operating procedure is available from C.S.G.

INSTRUMENT PERFORMANCE AND DISCUSSION

An experienced operator can prepare and reproduce a curve in 5 minutes or less.

Curves in which Y is not a single-valued and continuous function of X must be broken up into sections for which X is always increasing because the timedrive X slidewire of A operates only in the positive X direction. The LF cannot follow vertical nor near-vertical sections of a curve; in such cases the curve expander can be used for the other sec- tions and the near-vertical sections put in by hand. Curves in books and journals can be Xeroxed for use on A .

The extent of expansion or reduction is limited only by the dimensions of the paper which the two X-Y recorders will accept, because the X and Y range controls operate over that full range.

VOL 40, NO. 2. FEBRUARY 1968 445

Accuracy of reproduction is limited by the accuracy of the X-Y recorder slidewire and the accuracy with which the various controls can be set, and is affected by the sweep speed used. A sweep speed of 50 or 20 inches/sec is about right for typical spectral curves, with lower speeds for sharp fine-struc- ture-type peaks and greater speeds for flattish curves. With the Moseley components described, the accuracy is such that if unit scaling factors are used, the reproduced curve will be in register with the curve being reproduced within ca. 0.5 mm at worst. As a further test of accuracy, experimental visible absorption spectral curves of green-blue Cr(en)(OHz)zBrz+ and magenta Cr(en)(OH&Br*f (5 ) were converted by the curve expander to plots of molar absorbance index a,,, US. wavelength on a common scale and superimposed to locate the isosbestic points to be expected in the conversion of the dibromo to the monobromo complex. These predicted values, namely, 430 (24.5), 492 (24.5), and 580 mp (32.0 M-' cm-l), agreed well with the experimental values found (6) by scanning the changing spectra of a solution of the dibromo complex during its aquation to the monobromo complex,

(5 ) R. G. Hughes and C. S. Garner, Inorg. Chem., 6,1519 (1967).

namely, 432 (25.0), 492 (25.0), and 585 mp (31.5 M-l cm-1). The values in parentheses are the molar absorbance indices, and the average estimated probable errors in predicted and found values are & 2 mp and f 0.5 M-1cm-l.

Figure 2 presents an example of reproduction of an esr curve (a), with ordinate expansion by a factor of 1.75 and abscissa scale unchanged in (b) , reproduced at 20 sec/inch, and with ordinate expansion by a factor of 2.8 and abscissa contraction by a factor of 3.8 (c), reproduced at 50 sec/inch. The original curve has narrow peaks and presents a challenge to the curve expander. The difficulty of obtaining curve (c ) by ordinary hand-plotting methods is evident; the curve expander repro- duces such a curve with ease, with either expansion or con- traction.

RECEIVED for review October 16, 1967. Accepted November 24, 1967. Work partly supported by the U. S. Atomic Energy Commission under Contract AT(11-1)-34, Project 12; this paper is Report No. UCLA-34P12-68 to the AEC.

(6) R. G. Hughes and C. S. Garner, Department of Chemistry, University of California, Los Angeles, Calif., 90024, unpublished research, 1967.

I nd i rect UI traviolet Spectrophotometric Determination of Vanadium Utilizing Molybdovanadophosphoric Acid

Robert Jakubiec and D. F. Boltz Department of Chemistry, Wayne State University, Detroit, Mich.

IN A STUDY of the analytical applications of mixed heteropoly acids the composition and extractability of molybdovanado- phosphoric acid were investigated. As a result of this work it was found feasible to separate the mixed heteropoly complex from excess molybdate and molybdophosphoric acid. On the basis of this quantitative separation a new sensitive in- direct ultraviolet spectrophotometric method for the deter- mination of vanadium was developed.

Vanadium(V) is capable of replacing one of the 12 mo- lybdenum(V1) atoms in 12-molybdophosphoric acid to give a mixed molybdovanadophosphoric acid complex in which the phosphorus to vanadium to molybdenum ratio is 1:l:ll. This composition has been verified experimentally.

Kitson and Mellon (I) have studied the molybdovanado- phosphoric acid method for the determination of phosphorus and measured the absorbance of the yellow complex to minimize the effect of certain interfering ions at 460 mp. They established that a 1 :1 ratio for phosphorus to vanadium existed for the complex but could not delineate the ratio of molybdenum to phosphorus because of the excess molybdate required for formation of complex. Gee and Deitz (2) used differential spectrophotometry with absorbance measurements at 390 mp to increase the sensitivity of the method, confirmed the 1:l ratio for phosphorus to vanadium, and suggested a

(1) R. E. Kitson and M. G. Mellon, IND. ENG. CHEM., ANAL. ED.,

(2) A. Gee and V. R. Dietz, ANAL. CHEM., 25, 1320 (1953). 16, 379 (1944).

molybdenum to phosphorus ratio of about 14:l. Quinlan and DeSesa (3 ) determined by factorial experiment the opti- mum concentrations of vanadate, molybdate, and acid for the formation of molybdovanadophosphoric acid. Michelsen (4) using very dilute solutions recommended measurements at 315 mp for improved sensitivity.

In utilizing the formation of molybdovanadophosphoric acid for the determination of vanadium, a mixed reagent containing phosphate and molybdate is used. After forma- tion of the molybdovanadophosphoric acid, the excess mo- lybdophosphoric acid is extracted with diethyl ether. The molybdovanadophosphoric acid is extracted with a 1 :4 pentanol-diethyl ether extractant and the excess molybdate is removed by washing the extract with an acidic aqueous solu- tion. The purified molybdovanadophosphoric acid is back- extracted with an ammoniacal buffer solution and the absorb- ance due to the molybdate is measured at 228 mp.

EXPERIMENTAL

Apparatus. Absorbance measurements were made in 1 .OO- cm matched cells with a Cary Model 14 spectrophotometer. A reagent blank was used in the reference cell.

Reagents. STANDARD VANADIUM SOLUTION (3.01 pg of vanadium per ml). Dissolve 0.3460 gram of reagent grade ammonium metavanadate in 500 ml of distilled water, add

(3) K. P. Quinlan and A. M. DeSesa, Ibid., 27, 1626 (1955). (4) 0. B. Michelsen, Ibid., 29,60 (1957).

446 ANALYTICAL CHEMISTRY