NATUREAND CONCENTRATION OF REDUCTANT. Several mild reducing agents were substituted for chlorostannous acid in the established procedure. (One-amino-2-naphthol4-sulfonic acid-sodium sulfite) and L-ascorbic acid gave pale blue reduction products, and then only very slowly. Iron(I1) acted more rapidly, but the color was only slightly more intense. Hypophosphorus acid behaved similarly to l-amino2-naphthol-4-sulfonic acid and ascorbic acid. Hydroxylamine hydrochloride failed to reduce a hafnium-containing solution at all. Hydrazine hydrochloride and chlorostannous acid gave the best results. However, the blue color in the hydrazine solution became dark green after 8 to 10 minutes, and the corresponding blank changed color from pale blue to orange-yellow in approximately the same length of time. On this basis, chlorostannous acid was chosen as the most satisfactory reductant, and 3.0 ml of a 0.025M solution was selected for final use. ADHERENCE TO BEER’SLAW. The system obeys Beer’s law over the approximate range of 8 to 50 ppm of hafnium. The deviation at concentrations below the lower limit is probably caused by incomplete conversion of metal ion to the absorbing species. The upper limit approached the absorbance limit of our instrument. The molar absorptivity of the complex was calculated to be 6.7 X l o 3 l/mole-cm. EFFECTOF DIVERSE IONS. The results of this study are shown in Table I. Ions investigated were considered tolerable at the stated concentration level if the absorbance of a standard hafnium-containing solution was affected by no more than =t27$ Insoluble precipitates were formed with Ag+, Pb2+, Ba2+,Bi3+, Snzf, and Sb3+under the conditions used. Either by preventing reduction or by forming reducible complexes themselves, HSO4-, Poda-, VOa-, citrate, NOZ-, and tartrate interfere seriously.
DISCUSSION AND CONCLUSIONS
Evidence has been presented for interaction between hafnium(1V) and isopoly molybdate in our system. The resulting species is probably of the normal 12:l type-for example HfO(Mo301&~-, analogous to the normal 12-molybdozirconic acid system. It was also shown, however, that this resulting species was not reducible to a blue hue unless sulfate was present. Sulfate complexes of heteropoly anions have been reported (15, 16), and it is presumed that a sulfatomolybdate is a necessary intermediate. This is concluded from the fact that an increase in temperature was a necessary condition for reducible complex formation, but not a sufficient one. The nonreducible sulfatomolybdate must then react with the hafnium(1V) at a lower temperature to give the reducible ternary species. Actual reduction of the intermediate to measure hafnium(1V) concentration must be preceded by elimination of excess isopoly molybdate which is also reducible to a blue hue. Sulfuric acid, when present in concentrations greater than 2N accomplished this. It was concluded that in this analytical system, the reducible intermediate containing hafnium must constitute a “mixed” heteropoly acid, the exact nature of which reduces to a problem of speculation on structure in the aqueous acidic solution. RECEIVED for review January 22, 1969. Accepted April 1, 1969. (15) G. C . Dehne, Ph.D. Thesis, Purdue University, Lafayette,
Ind., 1963. (16) K. Schriever and R. Toussaint, Chem. Ber., 91, 2639 (1958).
I CORRESPONDENCE
I
Note on the Polarographic Theory for an ECE Mechanism SIR: Chemical reactions following charge transfer and producing a species which enters a second charge transfer reaction are well known in polarography as well as with other electrochemical methods. These chemical reactions may proceed as heterogeneous processes--e.g., proton transfer to anionic species generated by the first reduction process and being adsorbed at the interphase-as well as by a homogeneous mechanism. First or second order kinetics-e.g., dismutation-may apply in this latter case. If the rate of reaction is low, then the kinetics may be followed by controlled potential electrolysis giving rise to an accumulation of the intermediate product (or, if dismutation occurs, to a steady state concentration of the depolarizer) in the bulk of the solution. A direct electrochemical response, however, is only observed, if the electrochemical response time-e.g., the polarographic drop time-is not too small as compared with the time constant of the reaction. Polarographic currents will then exceed those due to the first charge transfer process. If the interposed chemical reaction constitutes an equilibrium, which is in favor of the electroinactive species B,
On the other hand, if kb < k,, the transformation of B to the electroactive C causes the polarographic limiting currents to be intermediate between those corresponding to the transfer of nl and (n, n2)electrons, respectively, but different from both limiting cases sufficiently for the evaluation of k,, only as far as -2 < log ( k f 7 )< +2, where 7 is the polarographic drop time. Taking kb = 0 and (for abbreviation) kf = k , the problem is described by
+
Da =
Db = -kb Dc =
1142
ANALYTICAL CHEMISTRY
(1)
+kb
where a , 6, c denote the concentrations of species A , B, C, and the operator 9 is given by
The initial and boundary conditions are t = 0,x 2 0 t 2 0,x’m
the rates of both forward and backward reactions being very fast, then the well-known treatment developed by Koutecky is applicable.
0
t>O,x=O:
a=aL;b=
a = c =
0;
aa -+ ax
c = O
ab
- =axo
(3)
The extra current, iz, exceeding that of diffusion controlled nl electron reduction, il, is given by
(4) with
d k t ) II
0.5 k t
1
+ 0.5 k t
fits the data from rigorous evaluation within an error not exceeding 0.02 unit only for kt < 1 and for the interval 5 < k t < 10. An approximate solution for large values of k t can be achieved as follows. According to Kouteckf (3), Equation 1 for species B can be replaced by
and the corresponding ratio of polarographic mean currents if k is large enough. Since with ( k t )l i e d k t ) d(kr)
(7)
In a more recent paper published in this journal, Nicholson, Wilson, and Olmstead ( I ) stated, that the theory for this sequence of reactions, which is called an ECE mechanism, though developed for other electrochemical techniques, had not been dealt with before for classical polarography. A complete solution of the problem, as described above, however, was given by the present author some years ago ( 2 ) . The manner in which the function +(kt) is calculated, is very similar in both works; the final expressions, however, are different. Whereas we expressed the solution explicitly by +(kt) =
it follows from boundary condition Equation 3 that
Setting $=b+c
we have from Equations 1-3, and 15
2
;k t X
t =
a$ = 0 0,x 2 0
t>O,x+m
(1 - ~in~’~p)exp[-pkt(l - ~in~’~p)]dp S , 1 r 2
4-
dB (8)
it was given in Reference ( I ) by the integral equation
This problem can easily be solved by making use of a replacement of the variables x and t as in References ( I ) and ( 2 ) and by Laplace transformations. The solution is given by
where y and g&) correspond to Hence, with Equations 5 and 16, we have
4 gc(y> = +(W
(11)
Equations 8 and 9, however, are in full conformity with one another, as can easily be seen from a comparison of the series expansion of the exponential function in Equation 8, which has been used by us ( 2 ) for calculating +(kt) at small values of the argument. The values of +(kr) tabulated in both works agree within 0.01 unit. For practical purpose it would be preferable to have a simple approximate expression replacing the involved Functions 8 or 9, as it is possible for the Kouteckf function. From 0.5 k t at small the series expansion it follows, that +(kr) values of k t . The corresponding approximation taking into consideration that +(kr) + 1 for (kt) -P m , (1) R. S. Nicholson, J. M. Wilson and M. L. Olmstead, ANAL. CHEM., 38, 542 (1966). ( 2 ) B. Kastening and L. Holleck, 2.Elektrochem., 63, 166 (1959).
dkt) = 1
- 0.573 dkt
This approximation holds within an error of 0.02 unit for k t 2 4. A simple expression suitable for a reasonable approximation of +(kt) within the whole range of values of k t cannot be given. Two simple expressions, however, can be derived, which are approximate representations of the function $(kT) as defined by Equation 7 and the ranges of validity of which overlap each other. This seems to be rather important, because polarographic mean currents are more convenient in practical application than the instantaneous currents as used in Ref ( I ) , though instantaneous currents may be more conclusive as to the prevailing mechanism, if complete current-time curves are recorded. (3) J. Koutecky, Collect. Czech. Chem. Commun., 18, 597 (1953). VOL. 41, NO. 8,JULY 1969
1143
Inserting the first approximation for small values of kt 0.5 k t , in Equation 7 gives $(kr) E 0.27 kr, which can, accounting for $(kr) + 1 for kr + QI , be replaced by
4(kt)
$(kr) N
0.27 kr
1
+ 0.27 kr
(20)
represent +(kr) for kr 5 4, and kr 2 4, respectively, within an error of less than 0.01 unit, which, under usual conditions, resembles the limits of polarographic accuracy. Equations 20 and 21 are recommended, therefore, for a convenient evaluation of rate constants from polarographic mean currents, if an irreversible first-order ECE mechanism
Inserting, on the other hand, the approximation, Equation 19 in Equation 7, we obtain (21) As judged from the data of Ref ( 2 ) obtained by rigorous integration of Equations 8 and 7, the approximate functions
BERTEL KASTENING Chemisches Institut der Hochschule 86 Bamberg, Germany RECEIVED for review December 6, 1968. Accepted February 27, 1969.
Some Observations on the Phenylfluorone Method for the Determination of Tantalum SIR: During the course of a program to determine basic solubility data of high purity transition and refractory metals and refractory metal alloys in liquid lithium or potassium (1, 2), difficulty was observed in reproducibly measuring trace quantities of tantalum in the liquid metal solvent. By using Luke’s method (3), analytical results in the 40-100 pg Ta range appeared adequate for the early phase of the solubility program; however, in attempting to extrapolate Luke’s method into the less than 10-pg range (Luke’s calibration curves had been generated using 0,40, 80, and 120 pg Ta), erratic data were obtained such that the validity of our earlier results was seriously questioned. A survey of calibration curve data generated over the previous two years of operation, when plotted as net absorbance per microgram of tantalum (normalized for path length) us. chronological time, showed a number of widely discrepant sets of points, although the standard curve generated by the individual points within a set had been nicely linear with a good correlation coefficient. Additional concern was evidenced when standard curves prepared from two sources of high purity tantalum metal showed slight differences of unknown significance. A study was undertaken to ascertain the true reliability of the phenylfluorone method for the determination of tantalum as a trace constituent (2-10 ppm) in lithium or potassium metal. Hill (4) had reported Luke’s method to be unreliable for less than 40 pg Ta because of tantalum loss during Luke’s evaporation and fuming steps. Hill’s modification to Luke’s method permitted determination of 2-50 pg Ta to about f5% (relative) at 10 pg. In attempting to duplicate Hill’s data with Ta solutions prepared from high purity metal, we were able to demonstrate statistical reproducibility in the 2-10 pg Ta range; however, slight differences existed between the absorbance observed in our laboratory and that reported by Hill. Inasmuch as the conduct of the solubility experiments (I, 2) introduces the possibility of a molybdenum impurity in the solute lithium or potassium, it was felt ad(1) R. L. McKisson, R. L. Eichelberger, R. C. Dahleen, J. M. Scarborough, and G. R. Argue, NASA Report AI-65-210, Canoga Park, Calif., Mar. 1965; also released as NASA-CR-610. (2) R. L. Eichelberger, R. L. McKisson, and B. G. Johnson, NASA Report AI-68-110, Canoga Park, Calif., Feb. 1969. (3) C. L. Luke, ANAL.CHEM.,31,904(1959). (4) J. H. Hill, Analyst (London) 91, 659 (1966). 1144
ANALYTICAL CHEMISTRY
visable not only to investigate this apparent difference in absorbance but also to corroborate Hill’s observation that the presence of 100 pg Mo does not affect the measurement of 10 pg Ta and that the presence of 100 mg KC1 does introduce a negative bias. To this end, a series of standard curves over the range 0-10 pg Ta was prepared from solutions as follows: 1) tantalum only with direct color developmentLe., no extraction, 2) tantalum only using Hill’s method, 3) tantalum 0.5 gram KCI with direct color development, 4) tantalum +0.5 gram KCI using Hill’s method, 5) Ta 0.5 gram LiCl with direct color development, 6) Ta 0.5 gram LiCl using Hill’s method, and 7) Ta 100 pg Mo using Hill’s method. Day-to-day precision of the individual curves appeared satisfactory. When the individual curves were normalized to zero absorbance at zero micrograms Ta, the results shown in Figure 1 were obtained. Curve 8 represents Hill’s data and curve 9 represents Luke’s data corrected to a 25 ml volume (he used 50 ml) and extrapolated into the 0-10 pg Ta range. With the exception of curve 7 (which solutions contained Mo), all of the results using Hill’s method demonstrate excellent agreement in apparent contradiction to Hill’s observation relative to the influence of Mo and K. We agree with Hill that at least one hour is necessary for color development. The differences in the slopes of the curves for unextracted and extracted solutions containing only tantalum (curves I and 2, respectively) suggested the possibility of incomplete extraction (-85%). A tantalum solution was spiked with ls2Ta radioactive tracer and carried through the extraction according to Hill’s method. A single extraction recovered 98% of the initial spike activity attesting to essential completeness of extraction. The apparent enhancement of the phenylfluorone color due to the presence of molybdenum (curve 7, Figure 1) and the extent, if any, to which it biases the tantalum measurements next came under study. Luke (3) had reported a Mophenylfluorone absorption maximum at 565 nm; however, he used EDTA prior to color development to complex the molybdenum to preclude interference up to 1 mg Mo. Neither Luke nor Hill discussed or described the absorption spectrum of the system. This part of the investigation provided the best insight into the apparent source of erratic results. The absorption spectrum of phenylfluorone (2,3,7-trihydroxy-9phenyl-isoxanthene-3-one)exhibits a strong maximum at
+
+
+
+
