established. Nonetheless these results tend to show that the proposed mechanism is capable of reducing w roughly in the observed way. I t is interesting to note that the nonequilibrium distance, 1, must be assumed to equal at least 2.5 d, before reasonable agreement is obtained. This is perhaps due to the domination of short range nonequilibrium by more heavily weighted, long range effects. I t would also tend to explain why the theoretical W , based on l/d, = 1.25, is apparently too low in normal columns ( 1 ) . The comparison of Figure 2 is greatly oversimplified since a "single" theoretical effect is being compared to a number of experimental contributions. h slightly more realistic approach involves the calculation of absolute w values instead of the relative values w/w,. For this purpose we use the 0.5 w/w, f equation w = 0.11 10-3(d,/d,J2, where the first term accounts for very short range effects and the last term accounts for transcolumn effects. These terms are very approximate, having been obtained from a simple random walk picture, but should nonetheless account for order-ofmagnitude effects. I n figure 3 we have plotted w us. d,/dc and compared the values once again with Sternberg and Poulson's experimental plots. The agreement is still moderately satisfactory in the case of Chromosorb P with l / d , = 2.5. The foregoing results do not account for all the factors which might change
+
--- EXP,
.3
It is not fully understood why the glass bead columns have a smaller w than Chromosorb P. While the former pack somewhat more uniformly than the latter, there are enough observable inhomogeneities in a packing of beads to make this explanation seem incomplete. Since w drops so rapidly in glass bead columns it would appear that long range effects (ltdp-lOj are dominant. However the velocity difference cannot be severe or the absolute value of w would be larger. It is interesting to note that the glass bead results conform fairly well to the w equation if only the last term, accounting for transcolumn effects, is used. The problems discussed here are of enough practical interest in chromatography to justify a good deal more experimental and theoretical effort toward their solution.
.2
LITERATURE CITED
CALC. RESULTS STERNBERG
8 POULSON
1.0
.9
.a .7 CHROMOSORB ' P"
.6
.5 .4
.I 0
'------GLASS BEADS .2
I
.4 .6
,8
I
1.0
44 Figure 3. Comparison of experimental and theoretical values of w
the plate height as column diameter is varied. One can observe, for instance, severe changes in packing structure as the column becomes smaller.
(1) Giddings, J. C., ANAL.CHEM.34, 1186 (1962). (2) Giddings, J. C., Robison, R . A., Ibid., 34, 885 (1962). ( 3 ) Sternberg, J. C., Poulson, R. E., Ibid., 36, 1492 (1964). P. D. SCHETTLER C. P. RUSSELL J. C. GIDDINGS Department of Chemistry University of Utah Salt Lake City, Utah 84112 WORKsupported by the Atomic Energy Commission under contract AT-( 11 1b748.
Potentiometric Determination of Single Halides and Mixtures of Halides by Coulometric Generation of Silver(1) in Fused Sodium Potassium-Nitrate Eutectic at 250" C. SIR: Few analytical techniques applicable to high temperature fused salt systems exist. It has been demonstrated that it is possible to generate silver(1) a t 1 0 0 ~ ocurrent efficiency in sodium-nitrate, potassium-nitrate eutectic melt a t 250" C. (3). Further, silver halide salts are relatively insoluble in the same eutectic melt (1, 6). Halides and mixtures of halides have been previously potentiometrically determined using a glass reference electrode in lithium, potassium-nitrate eutectic a t 165" C. by adding weighed amounts of silver nitrate t o melts containing the halides ( 5 ) . This method of addition of silver(1) is less accurate and more timeconsuming. This work demonstrates that halides and mixtures of halides can be conveniently determined in microequivalent amounts by the in situ coulometric generation of silver(1) in sodium, potassium-nitrate eutectic. 610
ANALYTICAL CHEMISTRY
EXPERIMENTAL
Apparatus and Reagents. The electrolytic cell used in this study consisted of a 200-ml. 3-necked roundbottom flask. Because of the danger involved in using ordinary rubber in conjunction with a highly oxidizing medium, silicone rubber stoppers (No. 5) bored with a variety of holes to admit necessary apparatus were used a t the entry ports. Equipment, preparation of the reference electrode [hg/dg(I) 1, and compartmentalization of the melt have been described elsewhere (3, 4). All chemicals were reagent grade and silver wires served for both generating and indicating electrodes. h Sargent coulometric current source, Model IV, supplied the constant current and a Leeds and Northrup Model K-3 potentiometer was used to measure cell potentials. Procedure. The technique used for preparation and purification of the eutectic melt has been described (4). The method for determination of the
individual halides as well as the mixtures consisted of weighing the samples directly into fritted glass sealing tubes which were then placed in the melt and filled with the fused eutectic mixture by gentle suction. The silver indicating and generating electrodes were then placed in the compartment and the cell potential was measured after generation of various increments of silver(1). Stirring of the solution was accomplished throughout generation by vibrating the generating electrode which had a loop wound a t the lower end. The volume of solution in the fritted compartments containing the dissolved halides was in all cases approximately 21/2 to 3 ml. RESULTS A N D DISCUSSION
Titration curves for the pure individual halides show the expected solubility trend. The solubility products for silver iodide, silver bromide, and silver chloride calculated from these
Table 1.
5, 0 . 6 0 0 N 10
-
Sample
X
u 0
--
0.400
- - -
-0.361 V
5 4
3
Potentiometric Determination of Individual Halides Taken, Found, error, Rel.
0.200
req.
KI (25.2mg.) K I 125.1 mn.1 K I (12 5 m i . j K B r ( l 2 5mg.) K B r ( l 1 6mg.) K B r ( 9 96mg.) KC1 ( 1 1 . 1 m i . ) KC1 ( 1 2 . 5 m g . ) KC1 (18 5 mg.) KC1 ( 2 5 6 mg.)
c/o
req.
152 151 121) 121 75 3 74 8 105 104 97 5 96 4 83 7 82 8 149 143 168 162 248 243 343 337
-0.66
-n
8.1
-0 -0 -1 -1 -4 -3 -2 -1
66 95 13 08 03 57 02 75
. )
5
Table II. Potentiometric Determination of Mixtures of Halides
W
I
0.000
2-00
1.0 0
0.00
Q E N E R A T I O N TIME F O R Ag(I) I N SECONDS
(XI09
Figure 1 , Potentiometric determination of mixtures of halides by coulometric generation of Ag(l) and precipitation of silver halides 1. 2. 3.
KI and KCI [Ag(l) gen. a t 9.65 ma.] KI and KBr [Ag(l) gen. a t 4.83 ma.] KBr and KCI [Ag(l) gen. a t 9.65 ma]
data after the method of Flengas and 3.3 X Rideal (I) are 4.0 X and 5.2 x 10-6, respectively, which are in good agreement with these workers, findings in an equimolar sodium-nitrate, potassium-nitrate melt a t 248" C. Table I represents a compilation of the results of triplicate determinations of the individual halides as the potassium salts. For iodide and bromide in the range 75.3 to 152 keq. per 3 ml. of melt the relative per cent error never exceeds 1.13y0. I n the case of chloride in the range 149 to 343 keq. per 3 ml. of melt, the per cent relative error is never less than l.75y0 and is as large as 4.03y0 a t the lowest concentration of chloride. From the shapes of the titration curves and the magnitudes of the solubility products of the various silver halide precipitates ( I ) , this is to be expected. The titration curves in the cases of both bromide and chloride indicate a good deal of rounding in the vicinity of the end point, chloride being worse than bromide. The consistently negative error in analysis is in all probability caused by removal of small amounts of the halides by reaction with trace oxidants present in the melt (NOn, ?Jon+). Figure 1 presents examples of the types of titration curves obtained for mixtures of halides. The shapes of these curves show that the determination of a mixture of bromide and chloride or a mixture of all three is not possible
Rel. Taken, Found, error, req. req. 70
3.00
in this concentration range. For purposes of reference, the end point potentials for the pure halides are reproduced in Figure 1 with dashed lines. Coprecipitation problems are obvious in the cases of mixtures of both iodide and bromide and bromide and chloride. I n the latter case an analysis for each component of the mixture is impossible; the sum of the two, however, may be determined. Tien has determined mixtures of all three in lithium-nitrate, potassium-nitrate eutectic melt at 165" C. (6). The decrease in solubility as a result of the lower temperature and the changed character of the melt produced by substituting lithium for sodium ion apparently renders the analysis of a three-component mixture possible. This is, however, remarkable in light of the work by Jordan and coworkers who have calculated the solubility of silver chloride to be 1.7 x lo-' molal in the same system at nearly the same temperature ( 2 ) . Table I1 incorporates the data on the analysis of duplicate samples of mixtures of halides. T h a t coprecipitation is a problem is evidenced by the positive error in the analysis for the more insoluble component of the mixture. Again, accuracy of 1 to 2% can be obtained by adjustment of the size of the halide samples which make up the components of the mixture. The silver-wire indicating electrode
Sample K I (18.6mg.) KCl ( 1 3 . 2 m g . ) KI (13.6mg.) KC1 ( 1 8 . 5 mg.) KI (11.3mg.) KBr(7.00mg.) K I (13.3mg.) KBr(15.6mg.) KBr ( 1 1 . 9 mg.)
112 177 81.9 248 68.1 58.8 80.1 131 100 Total 272 KCl ( 1 2 . 8 mg.) 172
113 173 82.8 244 68.9 57.6 81.0 129
+0.89 -2.26 +1.10 -1.61 +1.18
266
-2.21
-2.04
$1.12 -1.53
used in this work has been well characterized in the literature with respect to its function as a specific halide indicating electrode ( I , 6). The reversibility of the Ag/Ag(I) reference electrode in fused alkali metal nitrates has also been well established (I, S , 4 , 6). ACKNOWLEDGMENl
The author thanks .the School of Chemistry, University of Minnesota, Minneapolis, Minn. for its support of this work. LITERATURE CITED
(1) Flengas, S. N., Rideal, E., Proc. Roy. Soc. A233 443 (1956). (2) Jordan, J., Meier, J., Billingham, E. J., Jr., Pendergrast, Jr., ANAL. CHEM. 32, 651 (1960). (3) Swofford, H. S., Jr., Ph.D. thesis, University of Illinois, Urbana, Ill., 1962. (4) Swofford, H. S., Jr., Laitinen, H. A., J. Electrochem. SOC.110, 814 (1963). (5) Tien, H. T., ANAL.CHEM.36, 929 (1964). ( 6 ) Tien, H. T., Harrington, G . W,, Znorg. Chem. 2 , 369 (1963).
HAROLD S.SWOFFORD, JR. School of Chemistry University of Minnesota Minneapolis, Minn. 55455
VOL. 37, NO. 4, APRIL 1965
e
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