ions. Because chromium is the only element listed which is normally found associated with vanadium in analytical samples, such as steels, the problem is not too serious. The interference of iron, due to the color of the ferric ion, can be easily eliminated by the addition of fluoride ion, as shon-n in Table V. Care must be taken t o avoid a large excess of fluoride, as large quantities of this ion interfere. The interference of organic acids, if any are present, can easily be removed by destroying the organic niaterial Kith nitric acid.
acid. I n addition, the results obtained are precise and accurate. Chromium, the most serious interference, must be completely removed. Interference of iron is eliminated by complexation with fluoride. Because of the necessity of removing chromium, if present, the determination of vanadium by this method may be lengthy, but no more so than by other standard colorimetric methods under the same conditions. A minor disadvantage is the rather narrow p H range that must be maintained. As p H meters are now commonplace, this requirement is not a serious defect.
CONCLUSIONS
The proposed 3-tungstovanadic acid method is very sensitive, exceeding the sensitivity of the well-known method based upon tungstovanadophosphoric
(3) Crouthamel, C. E., ri al., ANAL. CHEM.27,507 (1955). (1) Gibbs, W.,Am. Chem. J . 3, 411
(1881). (5) McCabe, C. R., Chen. Eng. 13, 243 (1911). (6) Prandtl, W.,Z . anorg. allgem. Chem. 92. 198 (1915). ( 7 ) Rosenheim,' A, Pieck, SI., Ibid., 98,223 (1916). / \ 8) Souchay, P., Compl. rend. 247, 1619 (1958). (9) Vosburgh, W. C., Cooper, G. R., J . Am. Chem. SOC.73,137 (1941). (10) Willard, H. H., Young, Philena, 1x0. EXG. CHEY.. AXAL.ED. 6. 48 (1934). ( l i ) Wise, IT7., Brandt, JT'. IT., ANAL. CHEM.27, 1392 (1955). (12) Wright, E. R., hlellon, 11. G., IND. EXG.CHEW,AXAL.ED. 9,375 (1937). (13) Yoe. J. H.. Jones. A . L.. Zbid.. 16. . 111 (1944). ' RECEIVEDfor review July 27, 1959. Accepted November 16, 1969. Kork supported by fellowship grants from the United States Rubber Co. and the Union Carbide Chemicals Co. I
LITERATURE CITED
(1) Bach, J. M., Anales asoc. quim. arg. 28, 108 (1940). (2) Boeri, E., J . Exptl. Biol. 27, 253 (1950).
.
Polarography of Thiocyanate Ion Complex Ion Formation with Mercury(l1) Ion C. J. N Y M A N and GENE S. ALBERTS Departmenf of Chemistry, Washington Sfate University, Pullman, Wash.
b The potential concentration data for the anodic polarographic oxidation of mercury in solutions of thiocyanate may b e interpreted on the basis of the formation of complex ions of the type [Hg(SCN)j](2-j) where j has values from 2 to 4. The formation constants of the complex ions were evaluated to b e K? = (1.18 =t0.08) X 10l6;Ka = (8.9 i 0.8) X and Kq = (8.7 =t 0.6) 1020.
x
T
lo'*;
complex ions of mercury(I1) and thiocyanate have been investigated by several groups. The species [Hg(SCS)2] was reported ( I S ) to have a formation constant of 2.95 X 10'7 in chloride media and 1.32 X 10" in bromide media a t 26" C. as determined spectrophotometrically. An equilibrium constant of 4.78 X 10' at 16" C., determined by a magneto-optic method (Faraday effect), was reported (4) for the stepwise formation constant, kd of [Hg(SCK)8]-1 from [Hg(SCN)*]. These same authors presented data from which the stepwise constant, k4, was calculated to be 5.25. The ion [Hg(SCN)4]-2 has been variously reported to have a formation constant of 2.0 x l O l 0 a t 18" C. ( 7 ) ; 2.5 x loz2at 18" C. (6); 9.7 X loz1a t 25" C. HE
(11); 4.68 X loz1 a t 20" C., 1.70 X loz1a t 25" C., and 6.30 X 1020a t 30" C.
in solutions of ionic strength 0.3M ( I , l a ) . All the values of K 4 were obtained by e.m.f. methods using a mercury indicator electrode, except the first mentioned value, which was obtained polarographically. I n view of the small amount of information available on K 2 and Ks and the wide spread of values for R4, the system was investigated further over a wider range of concentrations by the polarographic method. EXPERIMENTAL
Polarograms of all solutions were first determined automatically using the Sargent Model XXI recording Polarograph to observe the general characteristics of the wave, and then, to obtain more precise potential-current data, an essentially manual procedure was employed. The potential was set, and the current was allowed t o come to a steady value, and then the potential was determined with a n external potentiometer. All potentials were corrected for the internal resistance (iR drop) across t h e cell, and were considered to be precise within *0.3 mv. All measurements were made a t 25' C. Solutions were prepared from redistilled water n i t h chemicals of reagent
grade. The sodium thiocyanate stock solutions were standardized volumetrically against silver nitrate, and the solutions used for the measurements were prepared by a n appropriate dilution. Purified nitrogen was bubbled through these solutions prior to obtaining polarograms. The polarographic cell (IO) consisted of separate compartments for the solution under investigation and for the reference electrode, which in this case was a saturated calomel electrode. These two compartments were connected by a large diameter U-tube filled with 37, agar electrolytc gpls. These tubes were prepared mith three different sections of gels in a given tube, the first section containing potassium chloride gel, the second containing sodium chloride gel, and the final containing sodium perchlorate. K i t h this technique, foreign electrolyte was prevented from entering the calomel electrode, and chloride ion was prevented from entering the solutions undrr investigation. The sodium chloride in the center section was necessary to avoid the precipitation of potassium perchlorate that would occur if the two outer sections were in contact. A given U-tube was used only once. RESULTS
A single anodic wave was obtained for thiocyanate ion in the absence of VOL. 32, NO. 2, FEBRUARY 1960
207
Table I. Variation of Half-Wave Potentials for Sodium Thiocyanate Solution as a Function of Thiocyanate Concentration a t the Electrode Surface (SCS),
i\Iole/L. 2.08 x 3.12 x 5.20 x 8.32 x 9.95 x 1.49 x 1.99 x 2.98 x 3.98 x -1.98 x
10-4 10-4 10-4 10-4 10-4 10-3 10-3 10-3 10-3 10-3
(Eli2) c ,
Reciprocal Slopes
i,, pa.
a
Volt. us. S.C.E.
0 : 033 0.036 0.03i 0,037 0.03i 0,037 0.043
0.864 1.344 2.30 3.60 4.35 6.30 8.24 12.60 16.6 20 5
2.08 2.10 2.16 2.22 2.25 2.33 2.39 2.48 2.54 2.58
0.226 0.221 0.216 0.209 0.208 0,199 0.195 0.192 0.186 0.185
0 ;6-13
added mercuric ion in buffer solutions ranging from pH 3 to 8, u-herein the half-wave potentials were unaffected by changes in pH. As the thiocyanate solutions were found t o have a p H between 6 and 7 , no buffering was attempted in the solutions esamined. Kolthoff and Miller (6) have shoir n that this nave is due to the osidation of mercury to [Hg(SCS),] when the thiocyanate concentration is on the order of 10-3Jf. The equation of the polarographic 11-ave can be shon n to be (6. 9)
if only one compleu sprcim esiqts in the solution under consideration. I n the aliove equation, E" is the formal potential of the mercury-niercury(I1) ion half cell a t 1.0111ionic strrngth and taken as 0.589 volt us. S.C.E. at this ionic strength (9).i is the current flon-ing in microaiiiperes a t potential E d e . i d is the diffusion current of thiocyanate ion. K j is the formation constant of the comples species [Hg(SCN),](2-1), k , is the Ilkovi? equation constant for thz comples species. and k t is the Ilkovic equation constant for the thiocyanate ion. A series of polarograms was run a t an ionic strength of 1 . O V in n-hich the concentration of thiocyanate ion n-as varied from 2 X IO-' to 5 X 10-3-lL with sufficient sodium perchlorate added to maintain the ionic strength. The half-wave potentials found are recorded in Table I and are believed to be precise within + 3 mv. This uncertainty is somewhat greater than usual because of the difficulty in obtaining precise values of id due to the oxidation of mercury to mercurous ion a t potential> only slightly more positive than the formation of the thiocyanate complexes. According to Equation 1, a plot of log i ' ( i d - i)' CS. E d e should yield a straight line of reciprocal slope RT/nF for some value of j . By trial and error it ivas found that such plots gave the best straight lines for j = 2. indicating that the major species formed 208
ANALYTICAL CHEMISTRY
(SCS),
Mole/L. 1.04 x 1.48 x 2.31 x 3.68 x 4.26 x 6.4 X 8.4 x 1.16 x 1.53 x 1.90 x
10-4 10-4 10-4 10-4
10-4 lo-' 10-4 10-3 10-3 10-3
in these solutions is [Hg(SCN)*]. The reciprocal slopes of such plots are listed in Table I, and they increase from a value approaching 0.033 to 0.043 as the concentration of thiocyanate increaqes. The reciprocal slopes for the lowest concentrations are in reasonable agreement n ith the theoretical value, 0.0296. The increase of slope could mean either that the reaction becomes more irreversible as the concmtration increases, or that higher comples species begin to appear in the solution. I t is assumed that the latter is the situation here, because the oxidation process in higher concentrations of thiocyanate ion n a s proved to be a reversible one. The finding that a t low concentrations the data can be interpreted on the basis of the species [Hg(SCN)*] is in agreement with the findings of Kolthoff and Miller (6). The general equation relating the potential of the dropping mercury electrode to the current flowing when mercury is oxidized to form complex species is given by E d c = E"
+ RT - In i l k c nF RT In F , ( X ) ( 2 )
z
where (3, 8, 9)
+
+
1 K I (SCN), FdX) K2 (SCS); . . Kj(SCN), (3)
+
+
I n this equation, (SCS), represents the concentration of thiocyanate ion a t the electrode surface. When the current flowing is equal to one half the diffusion current, the potential E d c is equal to )~ the half-wave potential ( E ~ / Zand Equation 2 becomes on rearrangement
$ln F,(X)
=
Eo
-
+
(El,2)c
The equilibrium constants are best evaluated from Equation 3, and the values of F , ( X ) are readily obtained from Equation 4, where the terms on the right side are experimental quantities. The constant k,, which equals i d / C , can be determined by measuring the cathodic diffusion current, i d , flow-
ing due to reduction of a given concentration C of mercury(I1) in a solution of sufficient concentration of thiocyanate ion to convert the mercury to a complex species. k , n a s found to be 6.08 X IO3 l a . 'molelliter for the electrode system employed here. The value of k , is a function of thiocyanate ion concentration. but because it varies only slightly, it nas assumed to be coilstant throughout the series investigated. The concentration of thiocyanate at the elrctrode surface, (SCS), a t ( E ~ / Z ) ~ , is a more difficult quantity to determine, and is given by the equation (bCS),
=
( S C S ) - zj/Lt
(5)
nhere (SCS) is the Concentration of thiocyanate ion in the bulk of the solution. j is the average value of 1 a t the half-wave potential. and k r is the 11kovir: equation constant for thiocyanate ion. K h e n only one complex species is formed, R t = ji, ( S C S ) . and in this report X , iTas evaluatcd from the most dilute solutions where the principal species formed was [Hg(SCS)?] n i t h 1 = 2 . The value found n aq 8.6 X lo2 pa. mole liter anti n as assumed to have reniaincd constant in solutions n here higher complex species are formed. Khcn more than one species exists in solution. j becomes a function of i. and it< value a t ( E 12 ) c cannot be directly determined from the quantity 2kt(SCx)/ id. To calculate (SCS),, it n a s assumed that J had a minimum value of 2 and approached 3 as (SCS) increased, as indicated by the changes in slope of the log plots, and also, that only the t n o species [Hg(SCN)n] and [Hg(SCN)s]were present in the solutions listed in Table I. Furthermore, approximate values of KP and K 3 are needed to determine k3, the constant which relates the concentrations of the t\To species mentioned through the relationship. KX/Kz
k3
[Hg(SCN)a-]o/ [Hg(SCS)*],[(SCY)],
The desired approximate value of
K P was calculated to be 1.2 X 10l6 from the data in Table I, assuming J to have a constant value of 2 nhen estimating the values of (SCN),, and an approximate value of K3 = 9 X 10'8 was calculated from the data in Table I1 assuming the value of ( S C S ) , = (SCS). I n this latter approximation. an approximate value of K 4 mas also estimated to be 9 X 1020. I n practice, the values of j and (SCS), were estimated as in the folloning example for (SCS) = 3.12 X 1O-'JI. -2 preliminary value of j n a s assumed to be 2.06, from R hich a tentative value of (SCS), \\as determined from Equation 5 as 1.62 X 1O-'X. From k3 and this tentative value, the ratio of [Hg(SCS)3-] [Hg(dCS),] n a s dr-
termined as 0.114, from which j was calculated to be 2.10. Then by using Equation 5 again, (SCN). was calculated to be 1.48 X 10-4M, which was the value used in calculating the equilibrium constants. The various solutions were treated in order, and as a first approximation, the value of j for a solution of given bulk concentration of thiocyanate was employed as the preliminary value of j a t the next higher concentration. From the values of (SCN), thus calculated and the data in Table I, a final value of the formation constant, Kz, of the species [Hg(SCN)2] was calculated to be (1.18 i 0.08) X 10'6 by the graphical method. From these plots, an approxiniate value of K3 was found to be (9 f 2) X 1018. This latter constant is, however, more reliably determined from the data for higher concentrations of thiocyanate ion reported in Table 11. I n solutions where the concentration of thiocyanate ion is so great that it is not practical t o obtain the complete wave-Le., above about 5 X 10-3M -the relationship between potential and concentration of complexing agent has been shown to be described by the equation
Table
Variation of Potential at l p a . (E$ as a Function of Thiocyanate Ion Concentration at Electrode Surface
E:, Volts S.C. E.
(SCN), Mole/L. 3.98 x 4.98 x 9.95 x 1.49 x 1.99 x 2.49 x 3.98 x 5.97 x 9.95 x 1.99 x 2.98 x 4.98 x 9.95 x
us.
10-3 10-3 10-3
0.1260 0.1160 0.0870 0.0680 0.0546 0.0436 0.0212 0.0012 -0.0249 -0.0600 -0.0815 -0.1072 -0.1437
10-2 10-2 10-2 10-1 10-l 10-l 10-1
ion in a solution of ionic strength unity. This quantity is given by the expression E: = E"
- RT - In k , nF
where k,, as measured experimentally for the electrode employed here, was found to be 6.29 X lo3 pa./mole/liter. The value 0.477 volt us. S.C.E. was obtained for E: in a solution of unit ionic strength from Equation 8 and the value of E" mentioned earlier. From Equation 7, it is noted that a reversible process requires a plot of Ed.&.us. log i to have a slope of RT Such plots of experimental data indicated a reversible 2-electron oxidation process over the entire range of thiocyanate concentrations where this equation of the current voltage is applicable. An underlying assumption in the derivation of both Equations 1 and 7 is that chemical equilibrium must be established a t the drop surface in times very short compared t o the drop time. The fact that the log plots just mentioned have slopes of RT/nF tends to substantiate this assumption. I n Table I1 are presented the data for solutions of thiocyanate ranging
E: - E: - RT - In k J k , = nF
where E: is the potential of the dropping mercury electrode a t the arbitrary current of 1 pa. The equation for the current voltage curve under these conditions is (7)
for low current values. E: of Equation G is the potential of the dropping mercury electrode a t 1 pa. if mercury were to be oxidized to mercury(I1)
c
II.
c
-
IC I
3 , Av. No. of
(SCN),, Mole/L.
(SCN)/% 3.24 3.33 3.49 3.60 3.66 3.71 3.80 3.86 3.91 3.95 3.97 3.98 3.99
3.61 x 4.60 x 9.55 x 1.45 x 1.95 x 2.45 x 3.94 x 5.93 x 9.90 x 1.98 x 2.97 x 4.97 x 9.94 x
10-3 10-3 10-3 lo-* 10-2 10-2 10-2 10-2 10-1 10-l 10-1 10-1
from 4 X to 1M with sufficient added sodium perchlorate to bring the total ionic strength to 1 . O X . It was proposed that these data should also be interpreted with the aid of Equation 4 by the graphical method. Here, as in the more dilute solutions, a knowledge of the concentration of thiocyanate ion at the electrode surface when a current of 1 pa. TTas flowing mas necessary. Evaluation of this quantity may be approximated closely through Equation 5 in a manner similar to that described above, assuming the ions [Hg(SCN)3]- and [Hg(SCN)4]-2 are the principal species present. Even though the last term of Equation 5 is of little significance except for the lowest concentrations, the correction was included in the calculations. Small errors in j produce insignificant errors in the final constants. Figure 1 is a plot of (RTInF) In F , ( X ) us. log (SCS), for the data in Tables I and 11. The data were finally interpreted as indicating the existence of the following species in the solution: [Hg(SCN)2], [Hg(SCh-)3]-1, and [Hg(SCN)4]-2with formation constants Kz = (1.18 f 0.08) X lo", KB = (8.9 f 0.8) X 10'8, and K4 = (8.7 + 0.6) X lozo, respectively. K2 was evaluated from the data in Table I and then employed in the determination of K 3 and K 4 from the data in Table 11. The solid curve in Figure 1 was calculated using these values for the constants, and it is observed that the interpretation adequately accounts for the data. DISCUSSION
A comparison of the results obtained in this and earlier work is in order. The value of K z found polarographically in this investigation is smaller than the values obtained optically (IS) by a l -factor of roughly 0.1. The optical 3c 40 Rvalues were obtained as a result of F. x studies of solutions containing mixed Figure 1. Variation of RT/nF In F,(X) with log (SCN), halide and thiocyanate-mercury(I1) complexes. The fact that the value of 0 Calculated from Table I K Z resulting from chloride solutions 0 Calculated from Table II Curve calculated using formation constants listed in text differed by a factor of 2 from that ob60
1-
VOL. 32, NO. 2, FEBRUARY 1960
209
the equation Ell2 = -0.152-1.25 log (SCN) for the relationship between E112 (volts US. S.C.E.) of mercuric ion and thiocyanate concentration. The value of Ellz for mercury is a function of total mercury concentration as well as the concentration of thiocyanate, and unfortunately, Korshunov and Shchennikova did not specify the mercury concentration. As a result, exact comparison is difficult. Assuming a reasonable concentration of total mercury on the order of 10-4 to 10-3~v, their potentials are in the range expected on the basis of comparison with those obtained here. The value of the “theoretical half-wave potential” for reduction of mercury(I1) to mercury used by those authors was 0.387 volt us. S.C.E., which corresponds to the value of E: = 0.477 volt us. S.C.E. employed here. Using an equation similar to Equation 6, the value 0.387 was determined by Korshunov and Shchennikova from knowledge of the half-wave potential of mercury in iodide media and the stability constant of [Hg14]-2,taken as 2 X 1030. As the constant for the iodide complex is similar to those most often quoted (W), one can only surmise that some error, experimental or otherwise, was made in their roundabout procedure.
tained in bromide media leads one t o suspect that both may be in error due t o failure to take into account properly all the possible equilibria in these complicated systems. The ratio of K 3 / K zcorresponds to the stepwise formation constant, k3, and the value found here is 7.53 X lo2, a factor of 16 greater than that reported by Gallais and Mounier (4). Furthermore, the ratio of K4/K3 = k4 = 98 is approximately a factor of 20 greater than that reported by these authors. No immediate explanation is apparent. The value of K4 = 8.7 X lo2(’,when compared with those reported earlier, differs least from the value 1.7 X loz1 reported by Toropova ( l a ) , where the differences in ionic strength employed could account for the discrepancy in the two values. Thus the value obtained polarographically in this investigation would lend support to the value reported by Toropova from elwtromotive force measurements. The question arises as t o why the earlier polarographic result (7) for K a is only 1/40 that reported herein. Because of the general agreement of the value of K 4 reported here and the value of Toropova, i t would appear that the earlier polarographic value is in error. The earlier authors presented
ACKNOWLEDGMENT
The authors are grateful to the Office of Ordnance Research, U. S. Army, for financial support under Contract No. D.4-04-200-ORD-567. LITERATURE CITED
(1) Bjerrum,
J., Schwarxenbach, G., Sillen, L. G., “Stability Constants of Metal-Ion Complexes. Part 11. Inorganic Ligands,” Spec. Publ. 7, p. 42, Chemical Society, London, 1958.
(2) Ibid., p. 121. (3) DeFord, D. D., Hume, D. N., J . Am. Chem. SOC.73, 5321 (1951). ( 4 ) Gallais, F., RIounier, J., Compt. rend.
223,790 (1946). 15) Grossmann. H., 2. anora. Chein. 43.
RECEIVEDfor review July 6, 1959. -4ccepted Pl‘ovember 6, 1959.
-
0
r
e
.
Some Factors Affecting Flame Photometric tmission of Rubidium in an Oxygen-Acetylene Flame T. E. SHELLENBERGER, R. E. PYKE,’
D.
B. PARRISH, and W. G. SCHRENK
Kansas Agricultural Experiment Station, Manhattan, Kan.
b The flame photometric characteristics of rubidium were studied in the presence of relatively large quantities of potassium and other cations. Intensity of the rubidium line a t 780 mp was recorded using a Beckman Model DU flame photometer equipped with a photomultiplier and a strip-chart recorder. Excitation source was an oxygen-acetylene burner. When potassium was present in relatively large quantities, the apparent emission of rubidium was increased by overlapping of emission from the 770-mp potassium line and enhancement of rubidium emission in the flame. The overlapping potassium emission was corrected by background subtraction. Effect of potassium emission on rubidium may b e controlled by adding excess potassium to the test solution. Flame variations during excitation may b e minimized by including lithium ( 6 7 1 mp) as an internal control. 210
ANALYTICAL CHEMISTRY
G
Parrish, and Schrenk (1) have discussed difficulties in determining rubidium by chemical and spectrographic methods. These n-orkers reported a flame spectrographic method for rubidium, using a large Littrow spectrograph equipped Kith a natural gas-oxygen flame excitation source and special plate mask. They found that a Beckman flame photometer used without a recorder apparently did not permit sufficient resolution for the determination of rubidium in the presence of relatively large quantities of potassium. Pro, Nelson, and Mathers (S), however, determined rubidium and cesium added to whiskey using a Beckman DU flame photometer with simulated standards to circumvent potassium and sodium interferences. A Beckman DU flame photometer equipped with a multiplier phototube and strip-chart recorder was used in LESDEKIXG,
this study to investigate factors affecting rubidium emission. EXPERIMENTAL PROCEDURE
Reagents and Standards. Stock solutions as chlorides were made t o known concentrations with analytical grade reagents, from which aliquots were taken a n d diluted t o give t h e ion concentrations used in t h e various trials. Analytical solutions were made t o a final concentration of 20y0 isopropyl alcohol by volume ( 2 ) . Apparatus. A Beckman spectrophotometer Model DU, equipped with a flame photometer attachment, Model 9200; oxygen-acetylene burner; photomultiplier unit, Model 92300; spectral energy recording adapter; and Brown Electronik recorder, with 0- t o 10-mv. scale and 1/2-second pen response was used. 1 Present address, Texas Woman’s Univereity, Denton, Tex.
