William L. Jolly University of California Berkeley, California
The Use of Oxidation Potentials in horgank Chemistry
I n teaching a vast, complicated subject like inorganic chemistry, it is important to acquaint students with effective methods for summarizing and systematizing chemical reactions. Thermodynamics provides several such methods; one of the most effective of these is the use of oxidation-reduction (redox) potentials in quantitatively summarizing the driving forces of oxidation-reduction reactions in aqueous solutions. Unfortunately, it is quite common for students to be unfamiliar with the methods of applying these potentials to practical chemical problems,' even though they may be well versed in the thermodynamics of galvanic cells. I n this paper I try to show, with a minimum of thermodynamics, how oxidation potentials can be used to predict the products and driving forces of oxidation-reduction reactions. Thermodynamic Limitalions and Conventions
First a few words about the limitations of thermodynamics. Thermodynamic data give information only Recent textbooks on inorganic chemistry differ widely in their treatment of this subject. Dav and Selbin ( 1 ) have a verv hrief. incomplete discussion of the application of oxidation pot&tials: Cotton and Wilkinson ( 8 ) quote oxidation potentials in various places throughout their text, apparently with the assumption that the reader is familiar with their significance. Both Sienko nnd Plane ( 8 ) and Douglas and McDtlniel (4) have fairly complete discussions of the application of oxidation potentials, although Sienko and Plane's discussion is very brief, and neither text points out that the course of a reaction often depends on the molar ratio of react,ant,s.
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regarding the extent to which reactions can go, not regarding the rates at which they go. For example, although both of the following disproportionation reactions have large equilibrium constants, only the first proceeds at an appreciable rate under ordinary conditions. 2N09
+ ?OH-
--
2N2O
+ KOl- + H.0 NS + 2NO
NOn-
(fast) (slow)
The science, or art, of predicting the rates of chemical reactions is in a developmental stage. At present, often the best that can be done is to rlassify roughly certain classes of compounds as fast-reacting and others as slowreacting. However, sometimes thermodynamic data are useful even in the absence of kinet,ic information. Thus, when thermodynamics tells us that a reaction cannot go, me are saved the trouble of trying the reacti~n.~ I shall use the sign convent,ion adoptcd by Latimer and the International Union of Pure and Applied Chemistry for oxidation potentials and reduction potentials One must he cautious in such applications of thermodynamirs. Consider the reaction of a non-volat,ile phase (or phases) to yield a volat,ile p r o d ~ ~(or c t products) for which AG' >> 0. Reactions of this type often can be carried to completion by pumpingon the reactants or by continuous sweeping of the non-volatile phase with an inert carrier gas. The reaction of a gas with a non-volatile phase to yield a volatile product (for which AG" >> 0)often e m be carried to rompletion by sweeping the non-volatile phase with the reactant gas.
(5,6). In accordance with Latimer's practice, I shall write half-reactions so a s to correspond to oxidation potentials; thus Of course there is no difficulty in applying the same methods, after taking account of the sign change, to reduction potentials: Obvioudy, in order to use any potential, it is necessary to know whether it is an oxidation or reduction potential, and whether or not the above sign convention is used. Particular care must be taken when using potentials from different sources. All the potentials cited in thii, article refer to 25'. I t should be remembered that the potentials are expressed in volts (a difference in electrical potential). Therefore a potential is a constant which does not change when the coefficients of the half-reaction are changed. Thus both of the following half reactions have the same potential. I-
=
+ +
'/*I?
8-
21- = 1% 2e-
E'
=
-0.54
Eo
=
-0.54
The Use of Tabulated Potentials
Table 1 is an example of the familiar table of "halfreactions" and their standard potent,ials. The reducing agents are listed in order of decreasing strength (and consequently the oxidizing agents are listed in order of increasing strengbh) on going from the top to the bottom of the table. An oxidizing agent should be able to oxidize a11 reducing agents lying above it in the table, and a reducing agent should be able to reduce all oxidizing agents lying below it in the bable. However, because t,he potentials are standard potentials, this statement is strictly correct only when all the species are a t unit activity. As will he shown later, exceptions to this rule can be effected by appropriate adjustment of product and reartant concentrations. Because from any pair of oxidation potentials one can calculate the driving force for a complete, unique reaction, it is clear that a table of this sort summarizes an enornlous amount of
Table 1.
information in a small space. One calculates that a table of 100 oxidation potentials would yield the equilibrium coastants for 4950 different reactions. A more extensive tabulation of potentials than that shown in the table would be very handy when looking for oxidizing agents or reducing agents having certain specified strengths. However, a chemist often wishes to know whether a particular reaction can go, or what its equilibrium constant is. For such purposes it is more useful to have the half-reactions listed according to the elements whose oxidation states ~ h a n g e . ~Thus, if one wishes to know the driving force for the reaction one looks under arsenic for and under iodine for 31- = 4-
+ 2e-
Eo
=
-0.536
By subtracting the second half-reaction from the first, one gets the desired reaction. Whenever half-reactions are added or subtracted, one should not add or subtract the corresponding Eo values (since they are intensive quantities), but rather the appropriate number of electron-volts, or nEo d u e s (where n is the number of electrons appearing in a half-reaction). For the reaction under question, nEo = 2[-0.559 - (-0.536)] = -0.046. From this one can calculate AGO (in calories/ mole) or I< using the relations -AGO = 23060.nE0 and nE"
=
0.05916 log K
AG" = 1,060 cal./rnole K
=
0.17
From these results one must not draw the conclusion that the reaction cannot proceed quantitatively in either direction. Indeed there are volumetric methods of analysis based both on the quantitative oxidation of arsenious acid by triiodide and on the quantitative reduction of arsenic acid by iodide. (7) These are accomplished by appropriately adjusting the hydrogen ion concentration of thesolution. At pH7, we substitute [H+] = lo-' in the equilibrium constant expression:
Oxidation Potentials in Aqueous Solutions at 25'
Half-Reaction
E". Volts 2.71 1.66 0.76 0.50 0.47
Thus arsenious acid can be titrated with triiodide or vice versa. In 6 M HCI,
0.14
non
and consequently arsenic acid can be quantitatively reduced by an excess of iodide. (The liberated triiodide can be titrated with thiosulfate.) Dependence of Potentials on pH
The general problem of the pH-dependence of oxidation potentials is of considerable importance. The a Generally there is no ambiguity in this r ~ p e c t . However, in 2e; one the case of a hzlf-reaction such as 2 S O F = % O F might be justified in a double listing.
+
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potential of any half-reaction changes with the concentration of the species involved according to the Nernst equation, 05916 E = EO - L n log Q
where Q has the same form as the equilibrium constant but refers not to the equilibrium state but to the actual activities of the reactants and products. If the hydrogen ion or hydroxide ion appears in the half-reaction (and the corresponding ionic activity appears in Q), the potential will change with pH. Thus for the hydrogen-hydrogen ion half-reaction, '/lH1=H++e-
E"=O
we write E
=
-0.05916 log ([H+I/Pn:/a)
and for the water-oxygen half-reaction, HtO =
+ 2HC + 28-
E"
+
'/IHsO = L / 4 0 ~H +
or
=
-1.23
+ e-
-1.23 - 0.05916 log ([HtI.Po,'/+)
The potentials for these half-reactions are plotted versus pH in Figure 1. Theoretically no oxidizing agent whose oxidation potential falls below the HxO-02 line and no reducing agent whose oxidation potential lies above the H,-H+ line can exist in aqueous solutions. Actually, for kinetic reasons, these lines can be extended about 0.5 v, and the dotted lines in the figure are more realistic boundaries for the region of stability of oxidizing and reducing agents in aqueous solutions.
Figure 1.
The HrHC and H20-02 oxidation potentials as o function of pH.
One must take care to use oxidation potentials only in the pH ranges for which they arevalid. For example, the iron-ferrous ion oxidation potential, Fe = Fez+
+ 2e-
E'
=
0.41
has little significance in alkaline solutions because the 200
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n
RS
One adds the electron-volts (not the potentials!) for each step to obtain the electron-volts corresponding to the new half-reaction. The potential for the new halfreaction is then obtained by dividing by n, the number of electrons. Thus, E o = 1.7112 = 0.86. Oxidation Potential Diagrams
=
we write E
ferrous ion f o r m an essentially insoluble hydroxide. I n order to calculate the appropriate potential for alkaline solutions, one must know the solubility product for ferrous hydroxide (8 X 10-16). Note that by adding the Fe-Fez+ half-reaction to the reaction for the precipitation of ferrous hydroxide, we get the Fe-Fe(OH)z halfreaction:
If an element can exist in several oxidation states, it is convenient to display the oxidation potentials corresponding to the various half-reactions in diagrammatic form, as shown below for iron and oxygen.
One of the most important facts which can be learned from an oxidation potential diagram is which oxidation states, if any, are unstable with respect to disproportionation. If a given oxidation state is a stronger oxidizing agent than the next higher state, disproportionation can occur. (This is the situation when an oxidation potential on the left is more negative than one on the right.) It will he noted that both Fez+ and FeS+ are stable with respect to disproportionation, and that H202 is unstable with respect to disproportionation. Thus the following reactions proceed spontaneously.
The latter reaction is very slow under ordinary conditiom, but rapid in the presence of certain catalysts. Oftentimes species which are thermodynamically unstable with respect to disproportionation are intermediates in oxidation-reduction reactions and are the cause of slow reactions. Hydrogen peroxide is such a species. Most oxidations by molecular oxygen proceed with intermediate formation of hydrogen peroxide. Thus, although any reducing agent with an oxidation potential more positive than that of the H20-0%half reaction (- 1.23 v) can theoretically be oxidized by oxygen, those with oxidation potentials more negative than that of the H202-O2 half-reaction (-0.68 v) generally react slowly. In agreement with this rule, bromide (Br- - Brs; E" = -1.05) is oxidized very slowly, and iodide (I- - 1 ~; Eo = -0.54) is oxidized rapidly. Sometimes it is not immediately obvious from an abbreviated oxidation potential diagram that a particular species is unstable with respect to disproportionation.
Consider the diagram for phosphorus in basic solution (1 M OH-) :
cern to us, because its oxidation potential is far too positive for Mu to have any stability in acid solution. Therefore we may justifiably consider only the simplified diagrams
Hypophosphite (H2POz-) is stable with respect to disproportionation into phosphorus and phosphite. But if we consider the phosphine-hypophosphite half-reaction as shown in the more complete diagram,
we see that hypophosphite is unstable with respect to the formation of phosphine and phosphite. This reaction takes place when solid hypophosphites are heated, but in hot aqueous solution the principal reaction is the reduction of water to give hydrogen (8): HsP02-
+ OH-
-
HPOax-
+ H2
It is appropriate at this point to show how one calculates potentials when adding or subtracting two halfreactions to form a third half-reaction. As shown below, the phosphine-phosphorus and phosphorus-hypophosphite half-reactions may be added to give the phosphine-hypophosphite half-reaction. 30H++ 20H-
+ + + 3ePHs + 50A- = HsPO1- + 3H20 + 4e-
PHa '/rP4
= =
1/4P4 3H.O HzPOz e-
nEO 2.67 2.05 4.72
We divide the sum of the electron-volts by the number of electrons in the new half-reaction to get the new potential. Thus, E" = 4.72/4 = 1.18. I t can be seen that the new potential is a weighted average of the other two. One of the nicest applications of oxidation potential diagrams is the prediction of the products of reactions involving elements having several oxidation states. Let us consider the reactions of iodide with permanganate in acid solution. The pertinent diagrams are shown below.
If the reaction between iodide and permanganate is carried out with iodide in excess (as when permanganate is added by drops to a hydriodic acid solution), then the products of the reaction must be compatible with the presence of iodide ion. Thus under these conditions iodate cannot be formed, because iodate would react with excess iodide to form triiodide. Similarly, manganese dioxide cannot be formed because it is capable of oxidizing iodide. The observed net reaction is 151-
+ 2MnOn- + 16H+
-
51a-
+ 2MnZ+ + RHIO
If the reaction is carried out with permanganate in excess (as when iodide is added by drops to an acidic permanganate solution) then the prodncts of the reaction must be compatible with the presence of permanganat,e. Thus manganous ion cannot be formed, because it would react with permanganate to form manganese dioxide. The iodide would not be oxidized just to triiodide, because triiodide is capable of reducing permanganate. The fact that the 103-- HJOe and Mn02 - Mn0,- half-reactions have pot,entials of similar magnitudes complicates the problem. I t turns out that iodide is not cleanly oxidized to either iodate or periodic acid, but to a mixture of these products:
Notice that entirely different products are obtained when the reactant in excess is changed. The principle employed in the preceding paragraph may be summarized as follows: The final products of a reaction must be incapable of reacting with themselves or with any reactants that are in excess. Acknowledgment
This work was supported by the Atomic Energy Commission through the Inorganic Materials Research Division of the Lawrence Radiation Laboratory. Literature Cited
I n this case we may correctly assume that the reactions are "thermodynamically controlled1'-that is, that equilibria are fairly rapidly a ~ h i e v e d . ~We notice that there are three species in these diagrams which are unstable toward disproportionation: HOI, Mn3+ and MnOp2-. These are therefore eliminated from consideration. The Mn-Mn2+ half-reaction is of no con-
' The oxidation of water by HdOs and MnO1- is slow under ordinary conditions. The potent,ids for these oxidizing agents barely fall between the dotted lines of Figure 1.
(1) DAY,M. C., JR., AND SELBIN,J., "Theoretical Inorganic Chemistry," Reinhold Publishing Corp., New York, 1962. F. A,, AND WILKINSON, G., "Advanced Inorganic (2) COTTON, Chemistry," Interscience, New York, 1962. (3) SIENKO,M. J., AND PLANE,R. A,, "Physical Inorganic Chemistry," W. A. Benjamin, Inc., New York, 1963. (4) D o u c ~ s ,B. E., AND MCI)ANIEL,D, H., "Concepts and Models of Inorranic Chemistry," Blaisdell Publishing Co., New York, 1965. (5) LATIMER, W. IM., "Oxidation Potentials," 2nd ed., PrenticeHall. h e . . Enelewood Cliffs. N. J.. 1952. (6) LATIMER, W. I\I; J. Am. ~ h e ~ko c . ; 76, 1200 (1954). (7) VOGEL,A. I., "A Textbook of Quantitative Inorganic Analysis," 3rd ed., John Wiley & Sons, h e . , New York, 1961. (8) YOST,D. M., AND RUSSELL,H., JR., "Systemat,ic Inorganic Chemktry," PrenticsHall, Inc., Englewoad Cliffs, N. J., 1944, p. 192. Volume 43, Number 4, April 1966
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