tion of the metal ions is increased. According t o the data shown in this Table V, the conditions for optimum separation of thorium are given in the presence of 5z 12Mnitric acid. I n this optimum mixture-i.e., 0.1M TOPO-methanol-5z 1 2 M nitric acid, the distribution coefficient of thorium does not change when increasing the thorium concentration from trace amounts to 100 mg ThjlO ml mixture. I n this range of thorium concentrations, the coefficient has the value of 0.4. This means that thorium can be readily eluted from a column of the resin irrespective if tracer or macro amounts of this element are involved. However, at still higher thorium concentrations, both the distribution coefficient of thorium and the viscosity of the mixture increase so that such solutions are no longer suitable media for column separations. I n Table VI are shown the distribution coefficients of 20 metal ions on Dowex 50 as determined in O.1MTOPO-methanol-5$’, 12Mnitric acid. These data indicate that thorium can be readily separated from 15 elements while n o separation is obtained from uranium, plutonium, hafnium, and zirconium which, similar t o thorium, have distribution coefficients of less than one. Other elements that are also strongly retained on Dowex 50 from this medium include magnesi um, aluminum, chromium(III), nickel, copper, and lead. Consequently, these metal ions also can be separated from thorium. The applicability of the working procedure described in the experimental part using this optimum mixture (eluent solution) has been tested by numerous separation experiments involving tracer and macro amounts of thorium and microgram
quantities of the other elements listed in Table VI. In all cases, except scandium (see above), more than 99.9% of each adsorbable element was separated from the thorium. Also more than 98z of the thorium was recovered in the combined feed and eluent fractions. Experiments with thorium matrices containing milligram amounts of ytterbium revealed early breakthrough of this heavy rare earth on small (1 gram) columns. However, lowering the nitric acid concentration in the eluent solution from of 1 2 M t o of 8M(see Table V) overcame this difficulty without affecting the elution of the thorium as described in the working procedure. An interesting aspect of the working procedure, not fully investigated in this paper, is its reversibility. Thorium once adsorbed on the cation exchanger in the absence of TOPO is readily eluted with the eluent solution containing TOPO. It is expected that this separation technique might be especially useful for the separation of rare earths and other adsorbable elements from thorium matrices prior to their determination by spectrographic, spectrophotometric, or other means. Furthermore, the method can also be employed for the purification of thorium samples. Since uranium, plutonium, zirconium, and hafnium show a behavior similar t o thorium, it is possible to use the method also for their purification and separation from accompanying metal ions.
5z
5z
RECEIVED for review June 20,1968. Accepted August 21,1968. Based on work performed under the auspices of the U. S . Atomic Energy Commission.
Reaction Rate Measurements with the Fluoride Ion Selective Membrane Electrode. Mechanistic ,Study of the Iron(lll)-Iodide Reaction in Fluoride Media K . Srinivasan and G. A. Rechnitz’ Department of Chemistry, State University of New York, Buffalo, N . Y . 14214 The fluoride ion selective electrode is used in a kinetic study of the iron(ll1)-iodide reaction in fluoride media. The results are explained on the basis of the oxidative inactivity of FeF*+ toward iodide ions; use of the electrode permits an unambiguous distinction to be made between possible reaction mechanisms. THEFLUORIDE ion-selective electrode is useful for investigating the kinetics of reactions involving changes in free fluoride ion concentration such as the formation of FeF2+ and A1F2+ (7). I n these cases, however, the fluoride ion is involved directly in the reaction as one of the reactants; we now report on an example where the fluoride ion is not directly involved as a reactant, but is released as a result of the reaction. A measurement of the rate of increase of free fluoride ion concentration here leads to a decisive conclusion regarding the mechanism of the reduction of Fe3+ by iodide ions in the presence of fluoride.
To whom requests for reprints should be addressed; Alfred P. Sloan Fellow. 1
(1) K. Srinivasan and G. A. Rechnitz, ANAL. CHEM., 40, 1818 ( 196 8).
Although fluoride ions inhibit the reaction between Fe3& and I- via complexing of Fe3+(2), the extent of this inhibition when FeFZ+is the only complex formed and whether or not FeF2+ is completely inactive toward iodide ions are not known. Sykes (3) concluded that the reaction between FeCI2+and iodide cannot be neglected, particularly at lower ionic strengths, in the iron(II1)-iodide reaction in chloride media. A similar conclusion was also drawn in regard t o the reaction between FeBrZ+ and iodide. In the present investigation, the free fluoride ion concentration increases as the reaction between ferric and iodide ions progresses since Fez+ forms a very weak fluoride complex (4). The rate of increase of free fluoride concentration, as monitored by the fluoride ion-selective electrode, should thus demonstrate whether or not FeFZfreacts directly with the iodide ion. ( 2 ) Kolthoff and Sandell, “Textbook of Quantitative Inorganic Analysis,” Third Ed., Macmillan, New York, 1952, p 601. (3) K. W. Sykes, J . Clzem. SOC.,1952, 124. (4) H. W. Dodgen and G. K. Rollefson, J. Amer. Chem. SOC.,71, 2600 (1949); C. Brosset and B. Gustaver, Soetisk Kern. Tidskr, 54, 185 (1942). VOL. 40, NO. 13, NOVEMBER 1968
1955
3
16 -
-
14 -
' 0
x
21
2
4
6 time,
8
IO
12
minutes
Figure 1. Increase of free [F-] during iron(II1)-iodide reaction, in presence of fluoride (25 "Cand p = 1 M ) (1) [H+] = 0.03465M, [Fe3']r = 0.001475M, [F-]T 0.0006896M, [I-] = 0.01385M (2) [H+] = 0.03350, [Fe3-IT = 0.001426A4, [F-Ir 0.0006666M, [I-] = 0.02008M (3) [H+] = 0.03242M, [Fe3+]r = 0.001380, [F-]T 0.0006451M,[I-] = 0.02591M
= = =
EXPERIMENTAL
Stock solutions of sodium fluoride were prepared by weight from the reagent grade salt after drying at 100 "C for 24 hours. Stock solutions of sodium perchlorate containing free perchloric acid were prepared by weighing anhydrous sodium perchlorate (supplied by the G. Frederick Smith Chemical Co.) and adding calculated amounts of perchloric acid to the solutions before final preparation. The concentration of the free perchloric acid in the sodium perchlorate solutions was determined by titration against standard sodium hydroxide. Stock solutions of ferric perchlorate were prepared from ferric perchlorate, Fe(ClO&. 6H20, (supplied by The G. Frederick Smith Chemical Co.) and calculated amounts of sodium perchlorate and perchloric acid were added to the solutions to obtain the desired composition. The concentration of the ferric iron was estimated by titration with a standard solution of the sodium salt of EDTA employing sulfosalicylic acid as the indicator. A stock solution of sodium iodide, prepared by weight from the reagent grade salt, was used as the source of iodide ions. The fluoride solution required for each kinetic run was prepared by mixing the appropriate volumes of the stock solutions of fluoride and sodium perchlorate containing free perchloric acid, so as to obtain a n ionic strength of 1.OM: 25 ml of the final solution was transferred to a dry polyethylene beaker thermostated at 25 "C & 0.1. The stock solution of ferric perchlorate containing sufficient sodium perchlorate and perchloric acid to attain an ionic strength of 1.OM as well as the stock solution of sodium iodide were 0.1. also thermostated at 25 "C
*
1956
ANALYTICAL CHEMISTRY
Figure 2. Test of rate Equation 13
A Beckman Expandomatic p H meter was used to measure the potential of the fluoride ion-selective electrode (from Orion Research, Inc.). The potential was measured against a saturated calomel electrode connected to the experimental solution in the polyethylene beaker by means of an agar bridge containing 1.OM sodium nitrate in polyethylene tubing. The pH meter was connected to a Beckman 10-inch potentiometric recorder equipped with a voltage reference source (Heath Co.) to provide appropriate bucking voltages to the measured cell EMF'S; in this manner, the E M F change could be monitored on a sensitive recorder scale. Each kinetic run is conducted as follows. The fluoride solution in the polyethylene beaker is kept stirred by means of a Teflon-coated magnetic stirring bar, with the fluoride ion-selective electrode in the solution and the agar bridge connected to the calomel electrode. The solution of ferric perchlorate is withdrawn from the thermostated bottle by means of a syringe, and 1 or 2 ml of the solution is injected to the fluoride solution. After the potential of the fluoride ion-selective electrode has attained the equilibrium value, the iodide solution is withdrawn from the thermostated bottle by means of a syringe, and 1 ml, 2 ml, 3 ml or 4 ml, as required, of the solution is injected quickly into the stirred solution in the polyethylene beaker. The recorder is switched on before the injection of the iodide solution. All kinetic data are calculated from the resulting EMF GS. time curves and the known analytical compositions of the initial and final solutions. RESULTS AND DISCUSSION
Potential us. time curves recorded during the reaction of iodide ions with ferric ions in the presence of known concentrations of fluoride constitute the primary data in the present study. By converting chart divisions to appropriate
Table I. Rate Data for Fe(II1)-Iodide Reaction in F- Media (25 "C and p
= 1M)
[Fe3+][I-]2
X (MOW
[H+l ( M ) 0.03235 0.03119 0.02911 0.03589 0.03465 0.03242 0.03235 0.03119 0.02911 0.03589 0.03465 0.03242 0.03119 0.03011 0.02911 0.03465 0.03350 0.03242 0.03465 0.03350 0.03242 0.06400 0.06171 0.05760 0.06640 0.0641 2 0.0600 0,06400 0.06171 0.05760 0.06640 0.06412 0.0600 0.06400 0,06171 0.05760 0.06640 0.06412 0.06OO 0.06640 0.06412 0.06OO 0.1225 0.1184 0.1146 0.1269 0.1184 0.1146
0.7918 0.7636 0,7127 1.527 1.475 1.380 0.7918 0.7636 0.7127 1.527 1.475 1.380 0.7636 0.7372 0.7127 1.475 1.426 1.380 1.475 1.426 1,380 0.7918 0.7636 0.7127 1.527 1.475 1.380 0.7918 0.7636 0.7127 1.527 1.475 1.380 0.7918 0.7636 0.7127 1.527 1.475 1.380 1.527 1.475 1.380 1,475 1.426 1.380 1,527 1.426 1.380
0.1852 0.1786 0.1667 0.1786 0.1724 0.1613 0.3703 0.3571 0.3333 0.3571 0,3448 0.3226 0.7143 0.6896 0.6666 0.6896 0.6666 0.6451 0.8620 0.8333 0.8064 0.1852 0.1786 0.1667 0.1786 0.1724 0.1613 0.3703 0.3571 0.3333 0.3571 0.3448 0.3226 0.7407 0.7143 0.6666 0.7143 0.6896 0.6451 0.8928 0.8620 0.8064 0.1724 0.1667 0.1613 0.7142 0.6666 0.6451
[I-]initial ( M I x 103 7.437 14.34 26.77 7.171 13.85 25.91 7.437 14.34 26.77 7.171 13.85 25.91 14.34 20.77 26.77 13.85 20.08 25.91 13.85 20.08 25.91 7.437 14.34 26.77 7.171 13.85 25.91 7.437 14.34 26.77 7.171 13.85 25.91 7.437 14.34 26.77 7.171 13.85 25.91 7.171 13.85 25.91 13.85 20.08 25.91 7.171 20.08 25.91
units and taking advantage of the Nernstian response (5,6) of the electrode to the free fluoride ions in acid media, the concentration of the free fluoride ions at any instant can be calculated from the relation log
[F-linitis~
- log [F-lt
=
Increase of potential in millivolts 59.16
(1)
where [F-]iDitial = [ F - ] T ~in~the ~ ~solution before addition of Ferric salt (2) 1 KHF[H+]
+
(5) M. S. Frant and J. W. Ross, Jr., Science, 154, 1553 (1966). (6) K. Srinivasan and G . A. Rechnitz, ANAL.CHEM., 40, 509 (1968).
[F-]free.
(M)
initial
x 106
2.07 2.10 2.16 1.13 1.14 1.13 4.57 4.50 4.53 2.37 2.42 2.45 11.2 11.3 11.5 5.60 5.65 5.52 7.52 7.38 7.62 1.43 1.42 1.45 0.890 0.890 0.850 3.15 3.16 3.10 1.88 1.83 1.85 7.11 7.25 7.42 4.07 4.18 4.17 5.53 5.62 5.48 0.669 0.669 0.654 3.02 3.00 2.97
0.584 0.554 0.510 1.21 1.16 1.09 0.490 0.479 0.444 1.11 1.06 0.980 0.332 0.316 0.299 0.852 0.818 0.806 0.764 0.751 0.706 0.672 0.653 0.598 1.32 1.28 1.23 0.574 0.552 0.524 1.21 1.20 1.11 0.445 0.419 0.379 1.05 0.986 0.923 0.934 0.888 0.850 1.37 1.33 1.31 1.15 1.08 1.06
0.138 0.711 1.56 0.090 0.304 0.928 0.257 0.881 2.677 0.193 0.663 2.07 1.41 2.84 4.60 1.21 2.51 4.47 1.60 3.15 5.17 0.082 0.353 0.920 0.068 0.215 0.730 0.154 0.613 1.77 0.114 0.446 1.35 0.308 0.842 2.677 0.246 0.820 2.560 0.293 1.08 3.43 0.147 0.260 0.422 0.149 1.01 1.60
liter-3 x 1010) (ref. Eq. 13) 0.729 2.74 9.65 0.45 1.68 5.82 1.40 5.16 18.0 0.90 3.41 12.0 8.71 18.2 30.2 6.96 14.7 24.1 8.64 17.9 30.3 0.43 1.60 5.62 0.32 1.19 4.03 0.82 3.05 10.5 0.64 2.35 8.27 1.36 5.03 17.4 1.23 4.67 16.3 1.53 5.73 19.8 0.76 1.59 2.60 0.75 5.88 9.75
and
(3) At the acid and fluoride concentrations employed in this study, the species HF2- does not make any significant contribution t o the evaluation of the free fluoride ion concentration. The potential of the fluoride ion-selective electrode L'S. the saturated calomel electrode in a fluoride solution becomes more positive o n addition of ferric ions, owing t o the decrease in free fluoride concentration as a result of the formation of FeF2+. Addition of iodide ions t o the resulting solution shifts the potential t o less positive values, owing to the increase in the free fluoride concentration upon reduction of Fe(II1) t o Fe(I1) by iodide ions. Equation 1 can be employed at any stage to calculate the free fluoride ion concentration, VOL. 40, NO. 13, NOVEMBER 1968
1957
provided the ionic strength is maintained constant, as has been done in this study. Figure 1 represents typical curves showing the increase of free fluoride ion concentration with time on addition of iodide t o solutions containing ferric and fluoride ions. Since the change of free fluoride concentration is quite slow, the kinetic data have been analyzed using the initial rates method. The initial rates of increase of free fluoride ion concentration are obtained by drawing tangents to the free fluoride ion concentration cs. time curves at t = 0. Table I gives the initial rates of increase of free fluoride concentration for different initial concentrations of ferric iron, fluoride, and iodide, To obtain the relationship between the rate of increase of free fluoride ions and the rate of production of ferrous ions, we use [F-]T
=
[F']
Rate
+ KHFIH+l)+ [FeFz+l
=
kl[Fe3+][I-]2
(12)
kl [Fe 3+] [I-]
(4)
In writing Equation 4, the concentration of ferrous fluoride complex has been neglected since it is known t o have a very low formation constant (4). Also, by keeping the total fluoride concentration less than the total ferric concentration, higher fluoride complexes of Fe(II1) are avoided. By differentiating Equation 4, we get
I+---
Ke[F-]
(1
+ KHF[H+])+ =
ki
[Fe
[I-] X
(13)
To test Equation 13, the values of Kh, Ke and KRFat 25 "C and at an ionic strength of 1.OM are taken as 1.66 X lod3, 1.14 X lo5, and 7.94 X lo2, respectively (I, 6, 9). [Fe3+1i,iti,land [FeF2+1initial are evaluated by two methods and averaged. In the first method, use is made of Equation 6, neglecting [Fez+],
Also [Fez+] = [Fe3+IT - [Fe3+] - [FeOH2+] - [FeF2+] =
r
=
Combining equations 7 and 12, we obtain d[F-I dt
+ [HF] + [FeF2+] = [FW
Also, Hershey and Bray (8) previously concluded that the rate of the reaction, Equation 10, is proportional t o [Fe3+][I-Iz when the concentration of ferrous iron is small and that of I- is not less than about 0.003 molal. These conditions are satisfied in the present study since we are considering the initial rates in the absence of any added Fez+ and the concentration of I- used is higher than 0.003 molal. To elucidate the influence of the fluoride ions on Reaction 10, the hypothesis that FeF*+ is not attacked by I- was tested. Since the initial rates of Reaction 10, under the conditions of the present study, should be given by
ll-~i
i.e.,
which yields and
In the second method, use is made of Equation 4, i.e.,
5
dt
1
(7)
[FeF2+liDitiai = [F-IT
- (1 f K~~[H+])[F-]initia~ (16)
and
where Kh
[FeOH 2+][H+] [Fe 3+]
=
and [FeF
K e
- [Fe3+][F-]
(9)
From the work of Fudge and Sykes (7), it has been established that the rate of the reaction Fe3+
+ I-
=
Fez+
+ '/z IZ
can be represented by the relation Rate
=
kl[Fe3++l[I-]
1
(10)
The average deviation of the average values of [Fe3+]initia1 and [FeFz+]initialfrom the individual values calculated by the two different methods is 2 . 5 z . In using Equations 14, 15, 16, and 17, it is assumed that equilibria involving FeFz+, FeOH2+ and H F are rapidly established in comparison with the rate of the reaction between Fe3+ and I-, which is a reasonable supposition. It is also supposed that FeOH2+ does not react with I-, a conclusion drawn by Sykes ( 3 ) in his study. The values of [Fe3+]i.itialand of the function on the right hand side of Equation 13 are also given in Table I. The
+ kz[FeZ+]/[Fe3+] (8) A. V. Hershey and W. C . Bray, J . Amer. Chem. SOC.,58, 1760
(7) A. J. Fudge and K. W. Sykes, J . Chem. SOC.,1952, 119. 1958
0
ANALYTICAL CHEMISTRY
(1936). (9) R. M. Milburn, ibid.,79, 537 (1957).
plot of d[F-]jdt os. the function on the right hand side of Equation 13 is given in Figure 2 and is seen t o be a straight line passing through the origin. Considering the wide range of fluoride concentrations employed, the straight line plot obtained can be taken as proof of the hypothesis that FeF2+ is inactive toward I- and that the fluoride complex inhibits the reaction by reducing the concentration of the free ferric ion, which is the active reactant. This is in striking contrast t o the behavior of FeC12+ and FeBr2+ as reported by Sykes (3). The slope of the plot in Figure 2 is found t o be 17.1 M-l. sec-l which can be taken as the value of kl in Equation 12 a t 25 “C and an ionic strength of 1.OM. This is consistent with the values of 86.6 and 808 at 25 “C and ionic strength of 0.09 and 0.0, respectively, obtained by Hershey and Bray (8), in that the rate constant diminishes with an increase in ionic strength, which is the expected primary salt effect for a reaction between oppositely charged ions.
Thus, the kinetic data obtained with the fluoride ionselective electrode for the reaction between Fe3+and iodide ions in the presence of fluoride ions when FeFZ+is the major complex can be reasonably interpreted on the basis that FeF2+ is not attacked by iodide ions and that the concentration of the free ferric ions reacting with the iodide ions is governed by the equilibrium existing between the free ferric ions and the fluoride complex, i.e.,
Fe3+ f I-
+
Fe2+
+
’/?
I?
(19)
RECEIVED for review June 11, 1968. Accepted August 16, 1968. Work supported by Office of Saline Water, U.S. Department of the Interior.
Alternating Current Polarography: An Extension of the General Theory for Systems with Coupled First-Order Homogeneous Chemical Reactions Thomas G. M c C o r d ’ and Donald E. Smith2 Departinent of Chemistry, Northwestern Unioersity, Ecanston, Ill. 60201
A more exact and complete treatment than previously accorded the general theory of the fundamental harmonic ac polarographic response of systems involving first-order homogeneous chemical reactions coupled to a single charge transfer step is presented. The theory is extended to include an explicit solution for the current amplitude within the framework of the expanding plane electrode model. Rate control by diffusion, a single heterogeneous charge transfer step and any number or type of coupled first-order chemical reactions is considered. The solution presented represents a rigorous treatment of the expanding plane boundary value problem by the Matsuda method which involves just two minor limitations on the magnitudes of the relevant rate parameters. It permits one to write the theoretical expression for the fundamental harmonic ac polarographic response associated with a particular mechanistic scheme in this class simply by inspection of appropriate surface concentration expressions which a r e readily available.
theoretical ac polarographic relationships for a particular mechanism can be ascertained by noting coefficients of convolution integrals in readily obtained surface concentration expressions ( I , 3). To date, this work has been based o n the stationary plane electrode model and current amplitude expressions have been formulated only for special circumstances ( I , 3). Only the phase angle expression (I-3), which is not influenced by electrode growth and geometry with the mechanistic class in question (3-9, is of adequate rigor and scope for general application to data obtained with the dropping mercury electrode (DME). Because of the importance and ubiquitous nature of electrode reactions characterized by coupled first-order chemical reactions, we have endeavored to alleviate these shortcomings in the general theory. The results of this effort are presented here.
IT has been pointed out that the theory of the fundamental harmonic ac polarographic wave for systems characterized by homogeneous, first-order chemical reactions coupled to a single charge transfer step can be generalized to include any number arid type of first-order chemical steps (1-3). The general solution has been formulated in such a manner that the
The general theory of the ac polarographic wave for the case in question can be approached on two levels. The first involves a derivation beginning with a general formulation of the boundary value problem as described by Ashley and Reilley (2). The second uses general surface concentration expressions formulated in terms of convolution integrals as a point of departure ( I , 3). The latter method presupposes the availability of the necessary surface concentration expressions. The greater elegance of the first approach is unquestionable. Nevertheless, we have selected the second because the interpretation of the resulting “general” equation is less involved
NIH Graduate Fellow; present address, General Electric Corp., Materials and Processes Laboratory, Schenectady, N. Y . , 12305. * To whom correspondence should be addressed. (1) H.L.Hung, J. R. Delmastro, and D. E. Smith, J. Electroanal. Chem., 7, 1 (1964). (2) J. W. Ashley, Jr. and C . N. Reilley, ibid., 7,253 (1964). (3) D. E. Smith in “Electroanalytical Chemistry,” A. J. Bard, Ed., Vol. 1, Marcel Dekker, New York, N. Y.,1966, Chapter 1.
THEORETICAL
(4) J. R. Delmastro and D. E. Smith, J . Electround. Chem., 9,
192 (1965). (5) J. R. Delmastro and D. E. Smith, ANAL.CHEM., 38, 169 (1966). VOL. 40, NO. 13, NOVEMBER 1968
1959
