ALEXANDRE R. TARSEY Titanium Metals Corporation of America, Henderson, Nevada
THERE
is an adage that one picture is worth a thousand words. It applies well t o chemistry. Thus there is still a general interest in slight rearrangements of the periodic chart, although that chart is well understood in principle. Similarly, a visual approach will help in correlating the various concepts pertaining t o oxidation and reduction potentials. The following is the description of a chart which may serve that purpose, inasmuch as it brings forth a graphical representation of a number of interesting- relationships. CONSTRUCTION OF CHART
An example of the chart is shown in Figure 1, which revresents the elements of G r o u ~I-B. Simiiar charts can be made for other groups & individual elements. The X-axis represents the various oxidation states. The lines from the point representing the elemental states to the points representing the +l states are drawn so that their slopes are equal t o the half-cell potentials of the Mo-M+' couples. Similarly, the lines
connecting the + 1 aud +2 states of each element show by their slopes the oxidation potentials of these couples. The Y-axis was theu graduated using '/2a.ass times the scale of the X-axis, as shown on the left margin of Figure 1. It was furthermore graduated on the right margin a t I/,, or 0.059 times the scale of the X-axis. PROPERTIES
This chart will show the En of anv half-cell bv the slope of the line connecting the couple. This i s true not only for the lines with which the chart was constructed, but for any line that is drawn between two noints renresentine oxidation states of an element. ~ h u as line connecting Cno and CuO+' would show the oxidation potential of that half-cell, and would demonstrate why this potential is not the sum of the CUO-C~+~ and the Cu+'CuO+l couples, but rather a weighed average of the two, i. e., the slope of the vector sum.
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Another property of this chart follows from the Nernst equation: that the AF, in calories, of any halfcell can be seen as the difference of the Y-coordinates of the couple, using the graduations on the left margin of the chart. This chart should furthermore eliminate any confusion regarding the sign of the half-cell potential. Any 'Luphill" reaction is relatively difficult because of the necessary increase in free energy, whereas "downhill" reactions will tend to occur the more readily, the steeper the path.
0
1 2 Oxidation state Rgur. 1. Group 1-8
3
One of the most important properties of this chart, which is not readily brought forth by other means, is its indication of the relative stability of the various oxidation states. Now it is obvious and needs no graph t o expound that metallic gold is less readily oxidized than metallic copper. That follows from the numerical values of their oxidation potentials-if the sign convention is given. But the chart goes further. Look at the copper curve. Any e. m. f. powerful enough to push CuOup the steep step to the +1 state is sufficiently powerful to continue the oxidation to a higher state, since there is a crestlike break in the curve ~ a t the +1 state. The opposite is true of C U + which is located a t a very definite concave break in the curve. C U +is~ therefore quite stable! The chart thus not only shows the various known oxidation states of each element, but shows also which ones must be the most common. Thus the +2 state of copper, being in a crevice, is a common oxidation state of that metal, as must be the +1 state of silver, even though the latter is seen to be easily reduced. As for gold, we see not only that it is difficult to oxidize, but also that the +2 state is very unstable, and that
even the + I state is not particularly stable since it is not in a crevice. As a matter of fact, Au+' will be located on a slight crest when the straight line from An+' to An+3is drawn in, and can thus undergo autooxidation to the latter state. Furthermore, the chart can bring out periodic relationships. Thus with increasing atomic number the metals of this group become more noble, which is another way of saying that in solution i t becomes more difficult to achieve some higher oxidation state. A study of Figure 1 will show that for Group I-B an increase in atomic number results in somewhat of an increase in the stability of the +1 state, in a definite decrease in the stability of the +2 state, and in a definite increase in the stability of the +3 state. I t must be kept in mind that ordinary electromotive series are either mere lists of the reactivity of some elements in some particular solution, such as 0.1 N HCI, or else lists of the EO's of the most important couples. Similarly, the diagrams discussed so far are limited in that they are constructed by the use of Eo's, representing behavior in solutions so strongly acidic that the hydrogen ion artivity is 1.0 N. When this limitation is not serious, these charts should be used as they are for the sake of simplicity. Nevertheless, it may become desirable to study the effect of a change in conditions. Now a change in hydrogen ion concentration does not change the positions of the points representing either simple monoatomic ions or the elemental states, their half-cell potential not being affected. What do change are the "critical slopes" a t which couples may begin to liberate hydrogen from the solution, and those at the substance itself may be reduced by the process of liberating oxygen. These slopes are shown in Figure 2. (The reader need not be reminded that when the element in question is a metal, an increase in the hydroxyl ion concentration in the presence of an oxidized state may often result in exceeding the solubility product of the hydroxide.) Ions which do contain oxygen, such as CuO+', will change their position on the chart with a change in pH, since the formation of such ions becomes less difficult when there are fewer hydrogen ions competing for the oxygen. The new location of such ions is readily predicted: an increase in pH from 0 to 14 results in a stabilization as indicated by a shift down the Y-axis of the chart through a distance corresponding t o 38,000 calories for each atom of oxygen per atom of the element. This value is the differencein free energy between the reactions and H*O
-
2HC
+ 0--
Another method of stabilizing oxidation states is the formation of complex ions. Such stabilization would again be represented by locating the complex ion on the chart below the corresponding ion of the
JULY, 1954
element in question a t a distance representing the decrease in free energy. Thus the Ag(CN)2- ion may be located in Figure 1 a t a distance of -24,670 calories from the Ag+' ion, this value being its free energy of formation from the monovalent silver ion and aqueous cyanide ions. The potential of various couples involving this complex ion will then be represented on the chart by the slope of straight lines which can be drawn to this new point. Rules governing the stabilization of oxidation states by the formation of insoluble compounds are readily arrived a t by analogous considerations. There is yet another relationship brought out by t,his type of chart: that between concentration a t equilibrium and the other values mentioned so far. Negative logarithms of equilibrium constants, or pK's, may thus be read as differencesof Y-coordinates on the righthand margin of the chart, just as the corresponding differences in free energy may be read on the left-hand margin. Figure l , for example, shows that Ag+ will be reduced to metallic silver by gaseous hydrogen in normal acid solution until the concentration is about 10-l3 N. I t also shows that the corresponding equilibrium value for gold is only and that the reduction of Au+ by metallic silver must cease when
I t follows that a particular ion may be located on the chart when either an EO,a AF, or an equilibrium constant is known. That is perhaps the chart's most instructive property. Thus we have already located
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the Ag(CN)Z- ion below the Ag+ ion by the knowledge of the free energy of formation. The graph now shows that the half-cell potential of the A$-Ag(CN),couple must be 0.29 volt, and that the instability constant of the complex is about 10-18. The knowl-
pH. 7
Reduetionaeeompe.nied by the liberation of oxygen rigan 2.
Oxidation accompanied by the liberation of hydrogen Ctitk.1 Slope.
edge of any one of these values would have been sufficient, of course, to locate graphically the stabilized ion. In conclusion, it should be mentioned that the numerical values used were taken from Latimer's oxidation potentials,' wherein may be found an extensive collection of such data ~ublishedvrior to 1938. 1 LATIMER, W. L., "The Oxidation States of the Elements and Their Potential in Aqueous Solutions," Kentiee-Hall, Inc., New York, 1938.
