33 1
ELECTROLYTE CHOICEIN STABILITY CONSTANT STUDIES
Some Considerations of the Electrolyte Used to Maintain Constant Ionic Strength in Studies on Concentration Stability Constants in Aqueous Solutions.
Application to the Polarographic Evaluation of Thallium (I) Complexes by A. M. Bond Department of Inorganic Chemistry, University of Melbourne, Parkville, Victoria 6062 Australia (Received M a y 26, 1969)
In studies of metal ion complexes formed in solution, the magnitudes of equilibrium constants existing between the various species are usually sought. Ideally, these constants are obtained from -slationships between activities of each of the species present under equilibrium conditions. Often, however, the activities are unknown and concentrations instead of activities must be used. These latter concentration equilibrium constants, as distinct from activity equilibriumconstants, are a function of the ionic strength of the medium and consequently must be evaluated from sets of measurements all made at the same ionic strength. Most studies to date on concentration equilibrium constants, such as stability constants of metal ion complexes in aqueous media, have arbitrarily chosen perchlorate or nitrate media to maintain the ionic strength constant, with the assumption that this added perchlorate or nitrate electrolyte is noncomplexing toward the metal ion being studied. Furthermore, as a consequence of this attitude, little quantitative information on the actual stability of perchlorate or nitrate complexes is available, In this work, consideration is given to errors and effects introduced into results obtained for concentration stability constants in making the assumption that the added electrolyte is noncomplexing with special reference toward the commonly used polarographic method for determining stability constants. Results are then given for stability constants of perchlorate, nitrate, and chloride complexes of thallium(I), obtained by the polarographic method, using fluoride solutions as the noncomplexing medium, to show that perchlorate and nitrate may not always be the best choice as an inert electrolyte and that thought at least should always be given to possible alternatives.
Introduction I n solution studies of complex ion species formed between metal ions and ligands, the magnitudes of all the equilibrium constants existing between the various species in solution are usually sought. The equilibrium constants arise from equilibria involving formation of complexes of the type ML,(X-ny)+ from interaction of metal ion species Mx+with ligand LY-. For simplicity, the equilibria present in solution can be represented by a general equation of the type
NIX+
+ nLY-
e Bn
J/lLn(X-nY)+
(1)
I n this equation, pn is the equilibrium constant, usually referred to as the "stability constant," and n represents the number of ligands of LY- attached to the central metal ion !VIx+ to give the metal ion complex 14Ln(x--"y) +. pn, the stability constant, is mathematically related to the activities of each of the species represented in eq 1 by an expression fin =
(activity MLn(X-"Y)+) (activity &!Ix+) (activity L Y - ) ~
(2)
I n terms of concentrations of the various species [ ]
and activity coefficients y, this expression in eq 2 becomes
or by rearrangement
It can be seen therefore that pn can be measured if either the activities are known or alternatively both activity coefficients and concentrations are known. Jf any analytical or instrumental techniques used to measure stability constants, however, measure or indicate concentration only. Furthermore, the activity coefficients are generally not known nor can they be calculated easily and reliably except a t low ionic strengths, so that in many cases and especially a t high ionio strength, the stability constant pn cannot, strictly speaking, be evaluated. However, a related quantity, which may be designated on', can be evaluated using concentrations instead of activities and neglecting activity coefficients. This quantity pn' appears frequently in the literature, although it is quite often mistakenly referred to as a pn value. The relationship between pn and fin' and the procedure of neglecting activity coefficients and using Volume 7.4, Number 2
January Z2?1970
332
A. M. BOND
concentrations instead of activities can be seen as follows. Rearrangement of eq 3b leads to
Since the activity coefficients are a function of ionic strength I , then it follows that pn’ is related to pn by a function of ionic strength, F ( I ) ,i.e.
pn’
F(1)pn (5) Equation 5 implies that On’ values should be quoted =
a t the particular ionic strength a t which they were measured to be of any thermodynamic significance. I n the special case where the ionic strength is low and approaches zero, pn and pn‘ will be equal, as with these conditions activity coefficients approach unity and concentration equals activity. Under other conditions, which are usually the case in practical measurements, pn and pn’ values are quite different in magnitude, and calculated pn‘ values to be of any significance need to be reported with the ionic strength a t which they were measured. I n many of the common techniques for measuring stability constants, for instance electroanalytical methods such as potentiometry and polarography, the ligand concentration L Y - is varied over quite a wide concentration range while the analytical metal ion concentration is maintained a t a considerably lower value relative to the ligand concentration. Graphical plots, statistical methods or other numerical methods of calculation, of functions of potential, current or some other variable, us. concentration of ligand, allows pn‘ to be evaluated. The ionic strength for evaluation of pn’ can be maintained constant for all ligand concentrations by always adding sufficient calculated, additional electrolyte to bring the ionic strength up to a particular value after allowing for contribution by the species AIx+, Ly-, lIL(x-Y)+ etc., already present in solution. I n this manner on’ can be calculated at a particular ionic strength I . Obviously the nature and type of electrolyte added to maintain the ionic strength constant will be critical in calculation of pn’ values and care needs to be made in choosing the particular electrolyte to be used. For instance, if an equilibrium of the type M x + nLy- $ RILn(X-ny)+ is being studied, an important requisite of the added electrolyte AB is that it should be noncomplexing towards Xx+. In most work A is chosen to be Li+, Na+, or K + and B is either CIO1- or AT03-, but unfortunately most often without thought as t o whether the choice is the best possible. It should always be remembered that it is possible that in some complex ion systems, weaker complexes than perchlorate, and certainly nitrate, can exist. If they do, then more reliable answers
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can be obtained for pn‘ values as compared with those obtained by using perchlorate or nitrate. Often, of course, these two will be the best available “noncomplexing” media, but a t least thought should be given to alternatives. As an example of this, the possibility of using fluoride electrolytes to maintain constant ionic strength in studies on thallium(1) complexes was investigated and results are reported using the polarographic method. Consideration is also given to the effect of the contribution of AB to the value obtained for pn‘ in the polarographic method.
Experimental Section All chemicals used were of reagent grade purity. All measurements were made at (30 f 0.1)’. Oxygenfree nitrogen was used t o deaerate the solutions. The concentration of thallium(1) used was approximately 2 X X ; the ligand concentrations and concentrations of added fluoride electrolytes added to maintain constant ionic strength are shown in Tables I-V. All measurements were made on solutions of pH 3.5-6.5. In this pH range it was assumed that both complex formation of fluoride ion by hydrogen ion and thallium(1) by hydroxide ion are negligible. Polarograms were obtained using the Xetrohm Polarecord E.261. Ac polarography was carried out using the Metrohm Ac hIodulator E.393 with an ac voltage of 10 mV, rms at 50 cps. To minimize cell impedance, the modulating ac voltage was applied through an auxiliary tungsten electrode. Rapid polarographic techniques and controlled drop times for the dropping mercury electrode (dme) of 0.16 sec were achieved with a Rletrohm Polarographie Stand E.354. The dme had a capillary constant r n r l a ~ l = B 1.93 (in distilled water a t zero applied potential us. Ag-AgC1 electrode) for drop time t = 4.4 sec. Reversibility of the electrode reaction T1+ e e T1 (amalgam) was verified for each solution as folloms. (i) ac polarograms were completely symmetrical and the ac half band-width was (96 f 2) mV for all drop times between 0.16 and 4.4 sec. (ii) Plots of Ede us. log ( i ) / ( i d i) mere linear with slope (GO f 1) mV for all drop times between 0.16 and 4.4 sec. (iii) Half-wave potentials (Ell2)from ac polarography and summit potentials (E,) from ac polarography coincided. (iv) E,,, and E, values were independent of drop time over the range 0.16 to 4.4 sec. ORION Fluoride Activity Electrode, Model 94-09 was used to measure the concentration or activity of free fluoride ion present in thallium(1) and other solutions.
+
-
Results and Discussions ( a ) Complexes of Thallium(I), Examination of tables’ gives the stability constants ( P I or PI’ values) (1) “Stability Constants of Metal-Ion Complexes,” Special Publication No. 17, The Chemical Society, London, 1964.
333
ELECTROLYTE CHOICEIN STABILITY CONSTANT STUDIES of some typical thallium(1) complexes. It can be seen that in general they are extremely weak as most values lie in the range 1-20. Furthermore, most values have been obtained using perchlorate media to maintain constant ionic strength. However, p1 for the perchlorate complex of thallium(1) has been measured as 1.0.2 In addition, in some of the methods of measurement used, the concentration of perchlorate used to maintain the ionic strength constant is considerably greater than the ligand concentration and results obtained by allowing for perchlorate complexing could be quite different from those in which perchlorate complexing is neglected. Obviously the use of nitrate for which p1 = 2.153 would even be more unsatisfactory than perchlorate for use as a medium to maintain constant ionic strength if effects of nitrate complexing are to be neglected. Solubility measurements4 have shown that the fluoride complex of thallium(I), like perchlorate, is also very weak, with a value of p1 = 1.2 being obtained. On the other hand, potentiometric studies maintaining an ionic strength of 1.0 with NaClOt indicated no evidence of any fluoride complex formation, and analysis of results suggested in fact that the fluoride complexes may be weaker than the perchlorate complexes. Thus, as the results for p 1 for the fluoride and perchlorate complexes were obtained by different methods and under different conditions, then after taking into account the experimental errors and the evidence from potentiometry, it is quite conceivable that the fluoride complex of thallium(1) is in fact weaker than that of the perchlorate complex. In view of the uncertainty as to whether the fluoride or perchlorate complex of thallium(1) is weaker, an investigation was therefore carried out to test the relative complexing effects of fluoride and perchlorate toward thallium(1) and to evaluate results for other complexes of thallium(1) when fluoride media are used to maintain constant ionic strength. The technique used for these measurements was that of polarography, since the electrode reaction T1 e T1 (amalgam) is reversible,6 and the interpretation of results is relatively simple. (b) The Polarographic Method f o r Evaluation of Concentration Stability Constants. Since the electrode reaction for thallium(1) a t the dme was shown to be reversible in this work, the polarographic equation derived by DeFord and Hume7 can be used to calculate the nature and magnitude of thallium(1) complexes formed in solution. The DeFord-Hume equation can be expressed as
+
Fo(X) =
p n ’ C ~ ”= n
nF antilog 0.434 - X RT
{
where the symbol F,(X) is introduced for convenience to represent the experimentally measurable quantity on the right-hand side of the equation, pn’ is the concentration stability constant of the nth complex, CL is the concentration of the complex forming substance and the subscripts f and c refer to the free ion and complexed ion, respectively. Other symbols are those conventionally used in polarography. The function F1(X) = (Fo(X) - p 0 ’ ) / C ~is now introduced by DeFord and Hume, where 00’is the stability constant of the zero complex and is of course, unity. If F1(X) is plotted against CL, and is extrapolated to C L = 0, then the value of K ( X ) at the intercept equals pl’. Likewise, the value p 2 ’ is given by the value F 2 ( X )at the intercept when the function F , ( X ) = ( F , ( X ) - p l ’ ) / C L is plotted against CL and is extrapolated to C L = 0. The formation constants of higher complexes (if present) may be determined similarly. As a consequence of the nature of the F,(X) functions, a plot of F,(X) vs. C L for the last complex will be a straight line parallel to the concentration axis, and this allows the determination of the number of complexes. ( c ) The Effect of the Noncomplexing Electrolyte on the Polarographic Method f o r Evaluation of Stability Constants. Experimentally, the values (El/?)fand (id), are evaluated from the polarogram obtained in the absence of complexing ligand (i.e. when the ionic strength is maintained at I solely by added noncomplexing electrolyte). ( E 1 / J ,and (id)c are evaluated from polarograms obtained when the concentration of ligand is CL and ionic strength I is maintained by added noncomplexing electrolyte. For instance, if 1: 1 electrolytes are used, then concentration of added “noncomplexing” electrolyte will be ( I - CL). If, however, complexing of the socalled ‘Lnoncomplexing” electrolyte is considered, then the values (El,,)m and ( i d ) f used can be shown to be in error slightly and the true values of these quantities and (id)t will be related to the experimentally measured values el/,)^ and (id)f by an equation
{
nF RT
pj’C,j = antilog 0.434 j
-
where j = j t h the complex of noncomplexing ligand, (2) R. A. Robinson and C. W. Davies, J . Chem. SOC.,574 (1937).
(3) V. 5. K. Nair and G. H. Nancollas, ibid., 318 (1967). (4) R. P. Bell and J. H. B. George, Trans. Faraday Soc., 49,619 (1953). (5) R. 0. Nilsson, Arkiv K e m i , 10, 363 (1957). (6) I. M. Kolthoff and J. J. Lingane, “Polarography,” Vol. 11, 2nd ed, Interscience, New York, N. Y., 1952, pp 520-521. (7) D. D. DeFord and D. N . Hume, J . Amer. Chem. Soc., 73, 5321 (1951). Volume 74, Number 2
January 28, 1970
A. M. BOND
334
C, is the concentration of added “noncomplexing” electrolyte, and pj’ is the stability complex of the “noncomplexing” ligand. Similarly, when mixtures of complexing ligand and noncomplexing electrolyte are present, measured values of (EI/Jc and (id), are slightly in error and values actually being measured will be (EI/~)(,I+~~) and (id)( , I + ~ Z ) , where subscript (cl c2) represents a contribution of complexing from ligand L Y - a t concentration CL and “noncomplexing electrolyte a t concentration C,. If the usual case is considered in which the complexing strength of ligand is very much greater than that of the “noncomplexing” electrolyte, then it can be simply shown that calculated values of F o ( X ) will essentially be correct as the measured quantity [(El/,)f(El/p)(c1+c2)] will be almost the same in magnitude as the correct difference which should be used [(El/,)t - (B1,JC]and relative errors will be small. The term log ( i ~ ? ) f / ( i d )is~ normally very small as (id)* and (id)c for a constant concentration of thallium are usually approximately equal and as the term makes little contribution to F o ( X ) , it is often neglected (e.g., ref 8) so that any effects on this term due to the “noncomplexing” electrolyte need not be considered in consideration on F o ( X )values. In the case in which the complexing strength of the ligand is not much greater than that of the “noncomplexing” electrolyte, Le., (El/,)t and (E,,,), are similar, then experimentally measured differences between [(E1/,)f- ( E l / , ) ( c ~ +and c 2 ) ]the correct value for this term [(Bl/Jt- (E,/Jc]will be quite important and large relative errors in calculated values of Fo(X) will be introduced. If the extreme case is now considered in which the overall stability of the complex whose value is being measured is less than the overall stability of the LLnon-complexing”electrolyte then the apparent, experimentally measured values of [(EllJf - ( . . 8 1 / 2 ) C ] J could be negative which would give an undefinable value of F o ( X ) . What needs to be done in this case to calculate a sensible value of F o ( X ) is to reverse the definition of the complexing and “noncomplexing” ligand. For thallium(1) complexes, pn’ values generally fall in the category of weak to very weak complexes, and even the perchlorate complex is not very much weaker than most other complexes. Many polarographic studies of thallium(1) and other metal-ion complexes have been carried out using sodium or lithium perchlorate as the “noncomplexing” electrolyte to maintain the ionic strength constant; however, consideration to contributions of perchlorate to the pn’ value obtained, which could be extremely significant have normally been neglected. AS the activity coefficients of the perchlorate system are generally unknown,g it is difficult to make any quantitative corrections to allow for perchlorate complexing,
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The Journal of Physical Chemistry
but alternative media to perchlorate which could be less complexing than perchlorate could be sought. In the case of thallium(I), as previously mentioned, the nitrate complex is stronger than the perchlorate complex so this rules out the use of nitrate; however, the fluoride complex could well be weaker, so that an improved “noncomplexing medium’’ to perchlorate in which to evaluate thallium(1) complexes may be fluoride. To test whether in fact fluoride is a weaker complex than perchlorate, Ellzvalues for the thallium(1) electrode reaction can be measured in various mixtures of perchlorate and fluoride while the ionic strength is maintained at I . Furthermore, pn’ values for other complexes of thallium(I), such as nitrate and chloride, can be calculated at varying ionic strengths maintained by fluoride. Results from these studies can be compared with those obtained in the literature in which perchlorate has been used to maintain constant ionic strength. (d) Use oj” ac and Rapid Polayographic Measuyements f o r Thallium(1) Complexes. For thallium(1) complexes, which are extremely weak, the shift in half-wave potential [(El,,)f- (E1~J,] due to complex formation is extremely small. Hence relative errors in calculating F o ( X ) values for weak complexes are very large. lo Thus , ac polarographic measurements, in which the summit potential (E,) is used instead of half-wave potential and the wave height ( i d w ) is used instead of diffusion current ( i d ) were used in place of conventional methods. Results from previous worklo showed that the reproducibility of the ac method was higher than the dc method, so that more reliable values of F o ( X ) and hence pn’ could be obtained because ac polarographic measurements improve the precision of measurement of shifts in half-wave potential.’O Ac measurements have also been used previously in studies of complex ions;”-’j further advantages of the method over dc measurements are reported in these studies. The only requisite for use of ac measurements is that the electrode reactions should be reversible. The appearance of an ac wave is not a sufficient criterion for reversibility as was reported quite frequently in the early ac literature, as i t has also now been shown to be possible to get ac waves for quasi(8) J . Heyrovsky and J. Kuta, “Principles of Polarography,” Academic Press, New York, N. Y . , 1966, pp 147-154. (9) J. E. Prue and A. J. Read, J . Chem. Soc., A1812 (1966). (10) A. M. Bond, J . Electroanal. Chem., 20, 223 (1969). (11) S. L. Gupta and M.K. Chatterjee, J . Electroanal Chem., 8, 245 (1964). (12) 9. L. Gupta, J. N. Jaitly, and R. N. Soni, J . Indian Chem. Soc., 42, 384 (1965). (13) S. L. Gupta and M. K. Chatterjee, Indian J . Chem., 4,22 (1966). (14) S. L. Gupta and M.K. Chatterjee, Rev. Polarog., 14, 198 (1967). (15) A. M. Bond, J . Electroanal. Chem., 23, 277 (1969).
ELECTROLYTE CHOICEIN STABILITY CONSTANT STUDIES reversible’6 and irreversible” electrode reactions. The earlier reported advantage made by some workers that it is unnecessary to analyze the ac polarograms for reversibility in studies on complex ions’l is thus, unfortunately, incorrect, as has been pointed out in a recent review article by Hume.’* However, for the thallium(1) electrode reaction, ac as well as dc reversibility has been established by several criteria, as mentioned in the experimental section, and ac measurements will be valid. When ac polarographic measurements are used, eq 6 can be solved as
FdX) = n
nF p n ’ C ~=~ antilog 0.434 - [(E,)f RT
Experimentally, it has been found that for a constant concentration of thallium(1) (id-)f is approximately equal to (id-)c, so that the above expression can be simplified by neglect of the term log (id-)r/ (id-)c to give eq 9, which was used subsequently in some calculations.
Pn’CI,“ =
Fo(X) = n
nF
antilog 0.434 - [(E,)f- (E&] RT
(9)
Rapid polarographpic ac and dc techniques, using short controlled drop times of 0.16 sec and fast scan rates of potential of 0.5 V/min, were also used in this work. This allowed a considerable time saving in recording of polarograms, compared with the conventional polarographic technique using longer drop time and slower scan rates. Furthermore, maxima which were found to be present with conventional dc polarography for the thallium(1) chloride complex system were not observed under conditions of rapid polarography. The uses and advantages of rapid polarographic techniques in studies of complex ions have been investigated recently, l5 and as the thallium(1) electrode reaction was found to be reversible under rapid polarographic conditions, as well as with conventional polarographic conditions, thallium(1) com-
Table I : Analysis of F , ( X ) Funct,ions for Thallium(1)-Perchlorate System. I = 1.0, PI’ [NaClOal
[NaF]
- E , us. Ag/AgCI, V
0.00 0.20 0.40 0.60 1.00
1.00 0.80 0.60 0.40 0.00
0.4220 0.4239 0.4282 0.4274 0.4298
= 0.32 =t0.04
zd-
FA
FO(X)
FI(X)
0.238 0.239 0.242 0.246 0.249
1.00 1.071 1.112 1.190 1.289
0.36 0.28 0.32 0.29
...
335 plexes were conveniently and easily evaluated from measurements using the rapid technique. ( e ) The Thallium(I)-Fluoride-Perchlorate System. Table I shows the values of E, and id- obtained for various mixtures of SaF-NaC104 at an ionic strength of 1.0. These results indicate that the fluoride complex of thallium(1) is in fact weaker than the perchlorate complex (i.e,, fin’ perchlorate < pn’ fluoride at ionic strength 1.0). However, the shift in E , in going from an ionic environment of completely fluoride medium to completely prechlorate medium is only 8 mV. This rather small change for a complete change in ionic environment could well be due to factors other than complex formation. For instance, junction potentials and activity coefficients, which are assumed to be constant for all measurements, could alter slightly with change in ionic e n v i r ~ n m e n t . ~ ,Unfortunately, ’~ the limit of solubility of NaF prevents concentrations greater than 1 M in sodium fluoride being used to determine if larger shifts in E, occur at higher fluoride concentrations. Xixtures of KF-KC104, LiF-LiCIOh, and NH4F-NH4C104,which could possibly have been used as alternatives to SaF-SaCI04 mixtures to provide higher fluoride concentrations, were not usable because of insolubility of KC104, LiF, and NH4C104. Ideally, to confirm n-hether the fluoride complex is weaker than the perchlorate complex, it would have been desirable to conduct an experiment in which E, in say 4 M fluoride could have been compared to E, in 3 M fluoride-1 114 perchlorate, and 2 ;1/1 fluoride-2 M perchlorate. In such an experiment, high concentrations of perchlorate could have been added without altering the ionic environment as drastically as in going from 1 M fluoride-0 M perchlorate to 0 M fluoride-1 M perchlorate. In view of solubility problems, this was not possible and the best mixture that could be obtained was a comparison of E , in 4 M NaC104 and E , in 3 114 NaC104-1 1%’ NaF. At the ionic strength of 4.0, however, pn‘ values of both species would be so small that changes in E , due to complex formation would only be expected to be of the order of experimental error of measurement of E,, so that results are not particularly meaningful. Results of this experiment, which showed a difference in E, of 3 mV, were, however, at least again consistent with fluoride complexes being weaker than perchlorate at an ionic strength of 4.0. The polarographic results, therefore, in agreement with the potentiometric results of Silsson,j suggest that fluoride forms less stable complexes than perchlorate at ionic strengths greater than 1, although (16) D. E. Smith, in “Electroanalytical Chemistry,” Vol. I, A. J. Bard, Ed., iMarcel Dekker, Inc., 1966, Chapter I. (17) D. E. Smith and T. G. McCord, Anal. Chem.,40, 474 (1968). (18) D. N. Hume, Anal. Chem., 38, 261R (1966). (19) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Butterworth and Co., Ltd., London, 1959, Chapter 15. Volume 74, Number
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January $8,1070
A. nt. BOND
336 this point has still to be proved conclusively. The polarographic results, however, do certainly indicate that fluoride formed complexes must be weaker than can be detected polarographically. If any further information on fluoride complexation is to be obtained then a different technique of polarography must be used. To verify that the fluoride complexing of thallium(1) is extremely small and to assess its order of magnitude a series of experiments were carried out with an ionselective fluoride electrode. The potential of an ion-selective fluoride in solution is directly related to the activity of the free uncomplexed fluoride ion present according to an equation
E = E,
- RT - In u p F
where E is the electrode potent,ial corresponding to fluoride activity aF- and E, is a constant. Alternatively, the fluoride electrode can be used to measure the concentration of free fluoride ion using an equation of the form
E
=
RT E,’ - -In F
[F-]
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The Journal of Physical Chemistry
where CTF- and CTMare the analytical or total fluoride and metal ion concentrations, respectively, and CFis the concentration of free or uncomplexed fluoride ion. For the fluoride ion electrode, when a change in potential AE occurs on addition of a large excess of metal ion to the solution containing fluoride then A E is related to pl’ by an expression
AEF 2.303RT
= {antilog ____
which applies for measurements made at constant ionic strength or at low ionic strengths where activities and concentrations are very nearly equal. In this equation E,’ is a new constant different from, but related to, Ec. To test for thallium complexing of fluoride, the potential of the fluoride electrode vs. sce was measured 5 X for each of the solutions: (a) 1 M NaC104 5 X M NaF; il/l KaF; (b) 1 M YaN03 (c) 0.1 111 Sac104 5 X 10-5 M YaF; (d) 0.1 M K a y o 3 5 X 10-E’%1 XaF; and (e) distilled water 5 X 10-5 i W NaF. Thallium(1) was then added to solution (a) up to a concentration of 0.1 M keeping the ionic strength constant. With this two thousand-fold excess of thallium(I), no change in potential of the electrode was observed. This means that within the limits of experimental error ( = k l mV), no change in the activity or concentration of free fluoride ion has occurred and that no detectable thallium(1) fluoride complex formation exists. In this experiment, as distinct from the polarographic work, the ionic environment remains essentially unaltered for all measurements and the junction potentials and activity coefficients would certainly be expected to be constant. The above experiment with the fluoride electrode in 1.0 111 XaC104 and 5 X 10-5 ill NaF was repeated with addition of zinc(II), cadmium(II), magnesium(II), and silver(1) instead of thallium(1). These four metal ions are all known to form weak complexes with fluoride ion1 and addition of these to the solution altered the potential of the fluoride electrode
+
in a manner consistent with the lowering of free fluoride concentration due to complex formation. Addition of vast excesses of thallium(1) to solutions (b), (c), (d), and (e) also left unaltered the potential of the fluoride ion electrode and these results prove conclusively that the fluoride complexes of thallium(I), if they exist, must be extremely weak. It can be shown quite simply that under conditions in which the metal ion concentration is in a vast excess over the concentration of fluoride ion that PI‘ is given by an expression
+
+
+
1
- 1)CTM -
In this work with thallium(I), C T was ~ 0.1 M and the smallest AE that could have been detected would have been 1 mV so that PI’ must be less than {antilog 0.0167 - 1110 ( i e . , less than about 0.4). Thus it can be concluded that the complex T1F must have a stability constant of a very low value and certainly less than 0.4. Therefore it has been shown clearly that thallium(1) fluoride complexes if they exist must be extremely weak. Furthermore, potentiometric5 and polarographic results indicate that at an ionic strength of 1.0, pl’(fluoride) is probably less than Pl’(perchlorate). Thus fluoride could be better than but certainly should be at least as good as perchlorate in the role of a “noncomplexing” supporting electrolyte in which to study thallium(1) complexes. Assuming that the fluoride complexing of thallium(1) is in fact less than that of perchlorate, then the thallium(1)-perchlorate complex system can be evaluated polarographically by the DeFord-Hume method. Table I shows that a value of PI’ = 0.32 0.04 for the complex T1C104 is obtained by analysis of F,(X) functions, if fluoride complexing is neglected and shifts in E , are attributed to perchlorate complexing only. (f) The Thallium(I)-Fluoride-Nitrate System. Tables 11 and I11 show that analysis of F,(X) functions obtained in KN03-KF media give values of PI’ = 0.65 f 0.05 and pl’ = 0.37 rLr 0.04 for the TlNOs complex at ionic strengths of 1.0 and 4.0, respectively. These results indicate conclusively that the fluoride
337
ELECTROLYTE CHOICEIN STABILITY CONSTANT STUDIES I
I
Table I1 : Analysis of Fn(X)Functions for Thallium(1)-Nitrate System. I = 1.0, pl’ = 0.62 f 0.05 [KNOa]
0.00 0.20 0.40 0.60 1.00
[KF]
1.00
0.80 0.60 0.40 0.00
-Em ~ 8 . Ag/AgCl V
id-
0.4233 0.4280 0.4318 0.4348 0.4380
pA
FdX)
FdX)
0.234 0.252 0.258 0.259 0.262
1.000 1.112 1.256 1.402 1.565
0.56 0.64 0.67 0.57
... I 0
I
3
2
El3 ?4 Figure 1. Graphical method of analysis of F , ( X ) functions for the thallium(1)-chloride system. I = 4.0, T = 30”.
Table I11 : Analysis of F , ( X ) Functions for Thallium(1)-Nitrate System. I = 4.0, &’ = 0.37 i. 0.04 [KNOa]
[KFJ
-Em US. Ag/AgCl, V
idPA
Fo(X)
Fi(X)
0.00 0.50 1.00 2.00 3.00
4.00 3.50 3.00 2.00 1.00
0.4349 0.4400 0.4432 0.4504 0.4569
0.212 0.215 0.219 0.220 0.220
1.000 1.199 1.330 1.745 2.239
0.40 0.33 0.37 0.41
.,.
Table IV : Analysis of F,(X) Functions for Thallium(1)-Chloride System. I = 1.0, PI’ = 2.1 i.0.1 [KC11
[KF]
-E~us. Ag/AgCl, V
0.00
1.00 0.75 0.50 0.25 0.00
0.4233 0.4350 0.4433 0.4500 0.4555
0.25 0.50 0.75 1.00
Y
0
idpA
FdX)
P’i(X)
0.234 0.242 0.252 0.250 0.250
1.000 1.514 1.998 2.603 3.214
... 2.06 2.00 2.14 2.21
Table V : Analysis of Fn(X)Functions for Thallium(1)-Chloride System. I = 4.0, PI’ = 1.00 i. 0.02, &’ 0.36 f 0.05 -E8 U B .
id-
[KCII
[KF]
Ag/AgCI, V
ph
FdX)
0.00
4.00 3.50 3.00 2.00 1.00 0.00
0.4349 0.4482 0.4585 0.4772 0.4892
0.212 0.222 0.228 0.232 0.234 0.238
1.000 1.590 2.291 4.618 7.254 10.76
0.50 1.00 2.00 3.00 4.00
0.5000
Fi(X)
FdX)
...
...
1.180 1.291 1.809 2.085 2.440
0.36 0.29 0.40 0.36 0.36
complex of thallium(1) is considerably weaker than the nitrate complex. The literature values of p1 = 1.82.g2”are difficult to compare with the PI’values obtained in this work, as no readily obtainable values of activity coefficients are available to convert 01’ values to p1. However, the order of magnitude observed in which p1 (I = 0) > PI’ (I = 1.0) > pl’ ( I = 4.0) is at least the anticipated result. (g) The Thallium(I)-Fluoride-Chloride System. Table IV shows that analysis of F,(X) functions obtained in KC1-KF media gives a value of ,&’ = 2.1 f 0.1 for the complex TlCl at an ionic strength of 1.0. Table V and the graphicalmethod of evaluationof F,(X), as presented in Figure 1, give values of pl’ = 1.00
I
2
eel-7
3
4
M
Figure 2. Distribution of the various species present in the thallium(1)-chloride system. I = 4.0, T = 30”.
and p2’ = 0.36 for the complexes TIC1 and TIC12-, respectively, at an ionic strength of 4.0. The percentage distribution of the various species present in the thallium(1)-chloride complex ion system shown in Figure 2 indicates that very little TIC&- is present at chloride concentrations up to 1 M , so that it is not surprising that at an ionic strength of 1.0, in which the maximum ligand chloride ion concentration is 1.0 M , no TIC&- is detected. Other studies at an ionic strength of 4.0 maintained by sodium perchlorate or lithium perchlorateJ6t21 have similarly indicated two chloride complexes of thallium(1) , However, polarographic studies maintaining the ionic strength at 1.0 and 2.0 with sodium perchlorate,22,28 reported only T1C1. Consequently, it can be seen that good agreement is obtained for results as to the number of complexes of thallium maintaining ionic strength constant by either perchlorate or fluoride media. Literature values given for pn’ vary over quite a wide rangeJZ4 so that comparison of results using perchlorate and fluoride as the noncomplexing media is rather difficult. However, results do indicate both fluoride and perchlorate complexes of thallium(1) are (20) Same as ref 1, p 174. (21) F. Ya. Kul’ba, V. E. Mironov, and V. A. Fedorov, Zh. Neorg. Khim., 6 , 1586 (1961). (22) 6.J. Nyman, D. K. Roe, and R. A. Plane, J . Amer. Chem. SOC. 83, 323 (1961). (23) D. Banerjea and I. P. Singh, J . Indian Chem. Soc., 39,353 (1962). (24) Same as ref 1, pp 294-296,
Volume 74, Number 8 January 88, 1970
RONALD H. ERLICH AND ALEXANDER I. POPOV
338 extremely weak and that fluoride is most satisfactory as an alternative “noncomplexing” medium t o the commonly used perchlorate. p1 values in the literature vary over the range 3-5,24 so that it can be seen again that the expected result of p,(I=O) > ,&’(I = 1.0) > &’(I = 4.0) is obtained for chloride complexes of thallium(1).
Summary of Polarographic Results Polarographic results have indicated that the fluoride complex of thallium(1) could be weaker than the per-
chlorate complex. Consequently, fluoride electrolytes should be better than or at least as good as perchlorate as a “noncomplexing” electrolyte in studies on concentration stability constants of thallium(1) complexes. The use of fluoride as a noncomplexing” medium to maintain constant ionic strength at 1.O in polarographic studies has given values of PI’ = 0.32, 0.65, and 2.1 for the complexes TlC104, T1N03, and TlC1, respectively. At an ionic strength of 4.0, values of PI’ = 0.37 and 1.00 and pz’ = 0.36 for the complexes T1N03, TlCl and TlClz-, respectively, were obtained.
Basicity Constants of Cyclopolymethylelaetetrazoles in Formic Acid Solutions by Ronald H. Erlich and Alexander I. Popov Department of Chemistry, Michigan State University, East Lansing, Michigan 48828
(Received July $1, 1969)
Electrical conductance measurements have been carried out on six cyclopolymethylenetetrazoles varying from trimethylenetetraaole to undecamethylenetetrazole as well as on 6,6’-dichloro- and 6,6’-dibromopentamethylenetetrazoles in formic acid solutions at 25’. Basicity constants defined by the reaction Tz HCOOH + TzH+ HCOO- as well as limiting equivalent conductances have been calculated by the Fuoss-Shedlovsky method from the conductance data. It is shown that while the above tetrazoles do not have any detectable proton affinity in aqueous solutions the unsubstituted cyclopolymethylenetetrazoles act as fairly strong monoprotic bases in formic acid solutions. The length of the hydrocarbon chain does not influence the basic strength of the tetrazole ring, but the inductive effect of the halogens essentially divests the ring of its proton affinity.
+
Previous studies on cyclopolymethylenetetrazoles have shown that these compounds can form fairly stable
complexes with transition metal and with halogen^.^ The compounds act as unidentate ligands. It is interesting to note, however, that qualitative studies in aqueous solutions indicate essentially complete absence of proton aEnity1-6 although a claim has been made6 for the preparation of a solid complex P M T . HzS04 (PMT = pentamethylenetetrazole). It has also been shown that the tetrazole ring can be protonated in a strongly protogenic solvent such as formic acid and the pKb value for P M T has been determined in this solvent both by potentiometric6 and by conductometric measurements.’ It should be noted that for the study of very weak bases formic acid is a much better solvent than acetic acid since not only does the former have a greater acidic strength, but also, The Journal of Physical Chemiatry
+
owing to its high dielectric constant of 56.1, the formation of ion pairs is minimized. Recently a number of new polymethylenetetrazoles have been synthesized8 with n varying from 3 to 11, as well as two halogenated derivatives of PMT, namely, 6,6‘dichloro- and 6,6’-dibromopentamethylenetetraz01es.~ It was of interest to us to see if the variation in the length of the hydrocarbon chain or the halogen substitution had any influence on the proton affinity of the tetrazoles. (1) A. I. Popov and R. D . Holm, J . Amer. Chem. Soc., 81, 3250 (1959). (2) F. M. D’Itri and A. I. Popov, Inorg. Chem., 5, 1670 (1966); 6 , 597, 1591 (1967). (3) D . M. Bowers and A. I. Popov, ibid., 7, 1594 (1968). (4) A. I. Popov, C. C. Bisi, and M. Craft, J . Amer. Chem. Soc., 80, 6513 (1958). (5) A. Dister, J . Pharm. Belg., 3, 190 (1948). (6) A. I. Popov and J. C. Marshall, J . Tnorg. Nuc2. Chem., 19, 340 (1961). (7) T. C. Wehman and A. I. Popov, J . Phys. Chem., 72, 4031 (1968). (8) F. M. D’Itri and A. I. Popov, J . Amer. Chem. SOC.,90, 6476 (1968). (9) F. M. D’Itri, Ph.D. Thesis, Michigan State University, 1968.
