A Warning for Frost Diagrams Users J e s ~ i M. s Martinez de llarduya and Fernando Villafaiie Departamento de Quimica Inorganica, Universidad de Valladolid, 47005 Valladolid, Spain Frost diagrams ( I ) are widely used to study the redox properties and the behavior in aqueous solutions of the different species of an element. They are shown in most inoreanic chemistrv textbooks to eive a visual remesentation zf the free energy changes assGciated with redox processes. Amoncr the more extended books, those of Greenwood and ~ a r n s h u w(2)and Shriver et al. (3, use them thoroughly for most of the elcmcnts in the periodic table. Acid-solution diagrams are extensively s h o d and unambiguously discussed, but there is some controversy on the basic-solution diagrams, as we show below. Reduction Potentials and References Acid-Solution Diagrams Acid-solution Frost diagrams for nitrogen and chlorine are depicted in Figures l a and 2a, respectively These are the result of plotting the volt equivalents associated with each species against the oxidation state. The volt equivalents are defined as the product of the oxidation state of the element in the compound considered and its reduction potential with respect to the element (nEo).Thus, they are a measurement of its free energy (nEo= -AG"IF). Furthermore, the slope of the line joining any two species in the diagram is the potential associated with this couple. The values of the reduction potential used to construct the diaprams shown in F i m e s l and 2 have been taken from the excellent review inref .?, which shows a complete collection of Larimer dia,qams for all the chemical elements, both in acid and basicsolutions. A Discrepancy in Basic-Solution Diagrams If we take the reduction potentials in basic solutions
(a) from these Latimer diagrams for the same elements,
we can construct a new Frost diagram. The representation thus obtained is shown in Figures l b and 2b for nitrogen and chlorine. In the books cited above, only the chlorine diagram agrees with this representation (ref 2, p 1002; ref 3, p 4161, whereas that of nitrogen is clearly different (ref 3, p 248).
A New Reduction Potential and Reference Explaining this discrepancy requires a look at the reference potential. These diagrams (a and b) have been made from standard reduction potentials, that is, in reference to E O ~ + l l i z=, O
which is represented as an a m w of slope zero in the upper left comer of the diaerams. Phillios and Williams defined a new reduction pt&tial for basic- solution^,^ Eo(OH),as
This definition comes after considering the potential of the couple H20/H2,0H- (-0.828 V) as a new reference, instead of HIM2.The representation of these new reduction potentials for basic solutions gives rise to the diagrams depicted in Figures l c (for nitrogen) and 2c (for chlorine). The slope associated with the couple H20/H2,0H-shown in the upper left corner of the diagrams now has zero value, as can be immediately inferred from eq 1. The diagram obtained in Figure l c coincides with that shown in ref 3 (p 248) and in ref 4 where this element is chosen for the definition of EYOH). Therefore, two different Fmst diagrams for basic solutions can be constmcted and are shown in some textbooks. This would not create any trouble if the type chosen were clearly stated. However, some problems may appear if the reader realizes that both types of diagrams are given in the textbooks, without any indication of which basic-solution potential (Fob or Eo(OH))was used to construct them. In fad, as stated above, in ref 3 Eg is used for halogens but EYOH) for nitrugen. This appears on the page just before the diagram for oxygen, made instead with Eg. Furthermore, the reference H+/H2with slope zero is only shown in the nitrogen diagram, where&: (reductionpotentials in acid solutions) and EO(OH) are depicted, but this
Oxidation state Figure 1. Frost diagrams for nitrogen. (a)Acid solution. (b) Basic solution, from 480
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e.(c)Basicsolution, from ,!?(OH),
Oxidation state Figure 2. Frost diagrams forchlorine. (a)Acid solution. (b) Basicsolution,from P. (c)Basicsolution, from @(OH). can only be used for diagrams constructed fromE0,or Eg, as explained before. On the other hand, ref 2 shows the same diagram with Eg for the halogens (p 1002). However, that of P, As, and Bi (p 673) has been made from ,!?(OH) values. This is not specified in the text, although the reference potentials shown in the upper left comer of the diagrams coincide with the representation chosen. Therefore, because two different Frost diagrams can be constructed for basic solutions, it is important to always use the same criteria. Otherwise, an explicit statement of the diagram type chosen would be very valuable in avoiding erroneous predictions. Correct Use of the Diagrams
Below we illustrate how the use of the correct diagram prevents wrong conclusions, or how some predictions depend on the nse of each type of basic-solution diagram. Is Nitrate Ion a Stmng Oxidant in Basic Media Also?
The h o w n oxidative character of nitric acid is shown by the positive value of the slope associated with the NO-NO couple (consideringNO as the reduced species) in acid solutions. From Figure la, we get
However, the value o~E&;~No) in basic media depends on the diagram used. From Figure lb, we get
From Figure lc, we get
Obviously, these are approximate values because they have been calculated from the diagrams, but they must ful-
fill eq l (0.73 = -0.13 + 0.828). From the value obtained in eq 4, it might be inferred that nitrate is also a good oxidant in basic media. However, the potential obtained in eq 3 indicates that its reduction to form NO is not thermodynamically favored. Then which of these two predictions is true? Obviously, the answer is both, once the reference potentials (shown in the upper left corner of the diagrams) are considered in each case. Figures l b and l c (and eqs 3 and 4) indicate that the potential in basic solution of the couple NOmO is lower than that of HIM2 -0.13 < 0 but higher than that of H20M2,0K
g:4.13 > -0.828arE"(0H):0.73 > 0
Thus, the observation of diagrams l a and l c (or both plotted in the same set of axes, a s depicted in refs 2 and 4) without remembering the reference potentials could lead to the conclusion that the oxidative trend of nitrate is similar in acid and basic solutions. Are the Potentials of the Ch/Cr and NO& Invariable with pH?
Couples
The previous example reflects the well-known fact that most potentials depend on the pH ofthe solution, but some couples do not. The two systems chosen in this example serve to show what "same slope in acid and basic diagrams" means, depending on the type of basic diagram chosen. The couple CI&- shows the same slope in Figures 2a and 2b.
This means that the potential does not change with pH, as seen in the half-reaction. The representation of this reduction potential as a function of pH is thus a horizontal line, as depicted in Figure 3. Volume 71 Number 6 June 1994
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The representation of this potential with respect to pH gives rise to a straight line of slope -0.06, which is the same as that of the reference couple Ht/H2(or H20/H2,0Hfor basic media), as depicted in Figure 3. 2H'
Figure 3. Variation of the reduction potentials of the reference, and of the couples CI&-and NOIN, with pH. The value found in Figure 2-2, P(OH), for this couple is just the result of addine - 0.828 V to the value of P. as follows from eq 1. In contrast to C11lCl-. which shows the same s l o ~ in e diagrams of types a(fro& E:) and b (from ~ g )tde , couple NO/& shows the same slope in diagrams l a and lc, that is, from E: and EYOH).
This value is different from that found in Figure l b (0.8 V) from @, indicating that this potential does change with pH. The variation of the potential ar a function of pH is immediately inferred after applying the Nernst equation (when all the species present except H+are considered 1M or 1atm).
+ 2 e + Hz
Therefore, we conclude that the potential of a couple that shows the same slopes in diagrams of types a and c (from E: and EYOH)) varies with pH as the reference. This also could have been inferred from Figures l a and l c because the slope of the NO/& couple remains invariant with respect to the reference potentials shown in the upper left corners of the diagrams. On the other hand, the maintenance of the slope in diagrams of types a (from g )and b (from @) indicates that the potential of the couple (such as C1&-) does not change with pH. Conclusions It is evident that Fmst diagrams for acid solutions may be interpreted by themselves, allowing us to draw conclusions about the redox behavior of the species represented. However, two different Frost diagrams can be constructed for basic solutions. Their interpretation requires knowing which representation has been chosen, that is, which reference potential was used for the diagram. This can be easily achieved by comparing the value of the slope associated with any couple with the value found in tables or Latimer diagrams for basic-solution reduction potentials. If they coincide, it is a Eg diagram (type b in the figures). If the slope is the result of adding 0.828 V to the value found in tables or Latimer diagrams, it is aEYOH) diagram (type c in the fwres). Liierature Cited 1. Fmst, A. A.J Am. Cbm. Soe. I951,73,2680. 2. Gremwood, N. N.;Eamshaai,A. Cbrnislry~f1bEhrn"te: pe~gamon,19%. 3. Shriuer, D . F.;Atkina, P W:I a n g f d , C. H. Inorganic Cbmiatry; Oxford Univerjity. 7 Lam".
4. Phillips, C. S. G.; Williama,R. J. P Inorganic Cbrnisfri; O x f d Univekq, 119% Vol I. pp 31P321.
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