JOURNAL OF CHEMICAL EDUCATION
Figu. 1.
Enarm Relatbnship Which Determine the Activity of a Metal (at 2S0C.)
formation. It is the heat of the reaction forming a mol of hydrated ions from a mol of the metal in its standard state. Data of this type is presented in Table 1 and graphically in Figure 1. A representative list of metals was chosen for which complete data were available. They are arranged in Figure 1 so that the metals decrease in activity going from left to right. The horizontal axin in units of decreasing electrode potential toward the right can be thought of as an "activity" axis in a manner similar to the usual vertical representation of the series from top to bottom. The usual thermodynamic convention has been employed of designating the heat ahsorbed by a reaction as positive; negative values imply the release of energy. The values are, of course, rela tive to the assigned value of zero for the heat involved in the over-all reaction producing hydronium ions from elemental hydrogen gas. The horizontal axis of the figure represents the normal electrode potentials as tabulated by Latimer.5 The heats of reaction for each step were calculated for one gram equivalent weight of L * n m ~ ,W. M., "Oxidstion Potentials," Prentice-Hnll, Ine., New York, 1938.
the metal from the data (all at 25%) in the National Bureau of Standards Tables.= The manipulation of the data for cadmium can he used for illustration. The tables give the AH of formation from the crystalline metal of Cd(g) as 26.97 kg.cal./mol; Cd++(g) as 627.1 kg.-cal./mol; and Cd++ (aq.) as - 17.3 kg.-cal./mol. Each of these values is divided by two to give figures for one gram equivalent weight. The 13.5 kg.-cal. for sublimation is subtracted from half of 627.1 to give 300.1 kg.-cal. as the heat absorbed in producing one gram equivalent weight of cadmium ions from that weight of cadmium gaseous atoms. The heat of hydration is calculated as the heat evolved to supply the 313.6 kg.-cal. necessary for sublimation and ionization and still allow for the evolution of - 8.7 kg.-cal. of heat which is the heat of formation of one gram equivalent weight of Cd++ (aq.). It will he noted that when the sum of these three energy steps for a gram equivalent weight of each of the metals is plotted against the normal electrode potential for that metal a straight line can he drawn which very nearly includes all points. A somewhat more detailed discussion of the location of points off the line will follow later. The approximately linear relationship has the followingimplications: (1) To a first approximation, the net exothermic character of the reactions producing ions in solution from crystalline metals is a measure of the "activity" of that metal. This loose equating of exothermic reaction energy to reaction tendency is ordinarily an easy concept for the beginner. Indeed, he has a historical prerogative from the early workers in thermodynamics. It should he emphasized that the true quantitative measure of a reaction's tendency to proceed is the free energy decrease rather than the total energy as here described. This relationship is dealt with later. However, realizing that the electrode potential is thermodynamically valid as a measure of the spontaneity of a reaction (free
' "Selected Values of Chemical Themodynmnic Properties," Series I, National Bureau of Standards, Washington, 1950. TABLE 1 Energy Data for Metals i n the Activity Series (Kilocalories oer Gram Eouivalent Weioht at 2SDC.) -N m l SublzI n i z a - Hydmttma Total electrode mation tion enenerqy (net) potential energy Metal energy .-229.4 -66.6 Li 3.02 37.1 K 2.92 21.5 -183.1 -60.0
-
~
Bs
Sr CR Na. Mg Al Zn Fe Cd Co Ni Pb
c,,
2.90 2.89 2.87 2.71 2.34 1.67 0.76 0.44 0.40 0.28 0.25 0.13 -0.34
21.0 19.6 23.0 26.0 18.0 25.0 15.6 48.3 13.5 52.5 50.8 23.2 40.8
~
-262.2 -279.1 -296.7 -203.3 -336.1 -477.6 -350.7 -335.5 -322.3 -351.9 -358.1 -283.2 -357.3
-64.3 -65.2 -64.9 -57.3 -55.2 -41.8 -18.2 -10.5 8.7 8.0 - i.7 0.2 7.7
-
DECEMBER, 1950
energy decrease), the approximate linearity demonstrated by the graph does lend strength to the qualitative argument. (2) All of the usual corollaries of the activity-series concept can be retained and further amplified. For example, predicting the amount of energy evolved or the vigor with which a displacement reaction will occur has a meaning in terms of the difference between the vertical positions of the two elements on the solid line. (3) If the exothermic nature of the over-all reaction is allowed as a measure of a metal's relative "activity," it should be possible to examine each of the contributing steps in terms of structural concepts to gain some understanding of why the metals are arranged in the list as they are.
1°-
25.
20.
lo-
s 'o
"
,
3.0
rigursa.
2.0
I0
.I0
volt."
potenti& of ~ . t a l sin tho ~ ~ t r h.ie. n t ~
ATOMIC STRUCTURE INTERPRETATIONS
Iar. For example, zinc has the highest potential r e The concepts of atomic structure which usually quired for ionization, yet it is still to be considered as a are employed in discussions of the periodicity of relatively actjive met,al. The absence of any consist,ent atomic properties are the ionization potentials, atomic and ionic size, and the arrangement of the electrons 20which contribute most to the atom's interactions with other atoms, the valence electrons. This pertinent in-. formation for the metals of this series is collected.in . Table 2, following the order established in Table 1. 8. The ionization potential data are fmm Herzberg7 and ,,o. the atomic and ionic radii are from Wyckoffs. These data are presented graphically in Figure 2 and Figure 3, ., cu using a horizontal axis identical with that employed in $ 5Figure 1 to facilitate comparisons. d . Many general chemistry textbooks present a plot of 30 Po 10 (I -1.0 V~JI. the first ionization potential of the elements against Fi9"m 3. Atomicand Ionic Si- of Met& in the Actmty Serb. their atomic number, Students frequently associate "metallic" properties with the fact that an element oc- feature in this plot indicates that any implied criterion cupies a valley in such a graph. This conclusion is in of low ionization potential for pronounced metallic acharmony with the observation that these same elements tivity in the usual chemical sense certainly must be are also foundtoward the left side and toward the bottom modified. The line connecting the second ionization of the periodic table, where low ionization potential is potentials for the divalent metals with the first for the predictable from electron TABLE 2 configurations. For the metals of the series under Atomic ~tructureData for the Metals i n the Activity Series discussion here, it can be Distribution of I a i z a t i m Atomic Ionic seen from Figure 2 that the Atomic vnlenee electronsa potentials, radius, radius, first ionization potential Metal nurnbcr volts s P d A. A. only very qualitatively Li 1.51 0.70 shows the expected upK 1; 5.3 4 4 2.25 1.33 ward trend in proceeding Ba. 56 5.2,lO.O 2.17 (TJ) 1.38 5 . 7 , l l . O 2.13 (71) 1.18 across the activity axis to6.1,ll.g 1.96 1.05 ward the less active metals N, 11 5.1 1.85 1.00 12 on the right. Such a Mg 7.7,15.0 1.60 0.75 (11) A1 13 6.0,18.8, 1.43 0.55 (1) (f) trend is by no means regu28.4
[I]
Fa ii zn
'HERZBERG,G., "Atomi~ Spectra and Atomic Structure," 2nd. ed., Dover Publications, New York, 1944, p. 200. WYCKOIF,R. W. G., "Crrstal Structures," Interscience Publishers, Inc., New York, 1948, Ch, 11, Table p, 14, Ch. 111, Table p. 15.
Fe Cd Co ~i Pb Cu Ag
30 26 48. 27 28 82 29 47
(a)
I ! ! !( T l )
(~1)
Arrowsin parentheses indicate electronslost inionization. Thisvelue for Cu+is listed since nonifor.Cu++was available.
9.4,ls.o 7.9,16.2 9.0,16.9 7.9,17.4 7.6,lS.Z 7.4,15.0 7.7,20.2 7.6
1.37 1.24 1.54 1.25 1.32 1.74 1.27 1.44
0.83 0.80 0.99 0.78 0.74 1.18 (0.58)& 0.97
JOURNAL OF CHEMICAL EDUCATION
662
monovalent and the third for trivalent aluminum repre- ions and is seen to be the most energetically hydrated sents the potential required to produce the ions which of that family, followed in order by calcium, strontium, actually exist and has a contour like that of the upper and barium. line in Figure 1. This further emphasizes the necessity The tendency to hydrate as evidenced by the exofor the consideration of other factors, since these data thermic character of the reaction is also influenced by alone would predict a much higher place in the series for factors other than ionic size. Two factors which are silver and conversely place aluminum far toward the inherent in the electron configurations of the atoms are the magnitude of the positive valence of the ion and the bottom. An examination of the contour of the second line of orbital distribution of its electrons. These are illusFigure 1, the representation of the sublimation energy, trated by comparisons of the electron distribution data is illuminated by a comparison with the upper line of of Table 2 with the hydration energies graphically Figure 3 which shows the variations in atomic radius of shown in Figure 1. The metals which lose a single a the metals under consideration. The sublimation en- electron to form monovalent ions do not hydrate very ergy requirements for the metals show less pronounced extensively. This can be considered as due to the low variations than the corresponding ionization energies. ion-dipole attractions which singly charged particles Notable are the relatively high values for silver and the would be expected to exert toward water molecules. transition trio of iron, cobalt, and nickel. The generali- Such attractions would be greater for the di- and trization, in light of the data in Figure 3 is that the rela- positive ions. Even lithium's apparent eagerness to hytively smaller atoms can be packed into the crystal more drate as a consequence of its small size is not as energetic tightly and consequently require more energy for their as those of more highly charged ions. sublimation. This is subject, of course, to the modificaThe other structural correlation between electron tion of the kinetic energy demanded by the weight of distribution and hydration is to note that ions which the atom. This further increases the requisite energy have available orbitals of types which can combine to for silver, for instance. It should he mentioned further form spatially symmetrical coordination structures are that such a generalization is valid only if all the crystals energetically hydrated. This is the same as making under consideration are of similar characteristics. This the broad generalization that the metallic ions which is the ease for the metals here listed. The majority are are often encountered as complex ions of other types either face-centered cubic or hexagonal close-packed can be expected to give evidence of extensive hydrawith the maximum coordination number of twelve. tion. The term "available orhitals" implies either that Lithium, potassium, barium, sodium, and iron have the electrons have been removed from an orbital to form slightly looser body-centered cubic configuration. This the ion (as in the case of the s orbital in Zn++) or that type involves each atom with only eight nearest neigh- half-filled orbitals can rearrange their electrons so that bors, but, since the six next nearest neighbors are only completely vacant orbitals can be opened up (as in the about 15 per cent more distant, the effectiveenviron- case of the d orbitals of Ni++). These vacant orhitals, ment for each atom is virtually the same as for those in and others of nearly the same energy in the ion, are then the close-packe'd symmetries. The cases of zinc and particularly attractive as electron-receptor sites for the cadmium are somewhat unique. Although these met- coordinate covalencies, established by water molecules als crystallize in a hexagonal close-packed form, they attaching to the ion, to make it the center of a spatially have a unit cell which does not. have the regular axial symmetrical hydration complex. Some of the generaliratios, hut is extended somewhat in one ~lirection.~zations relating types of coordinate structure with elecAccord'mgly, the figure given for the atomic radius of tron distribution have been presented previously.I0 these two metals in Table 2 is a weighted average com- Among the metals under discussion here it can be noted promising the two internuclear distances which Wyckoff that the ions of zinc, aluminum, and cadmium have gives. This qualitatively, a t least, places these two on available one s and three p orhitals which interact to form a spatially oriented tetrahedron about the ion a size scale relative to the others. The very significant hydration energy which can be when filled by electron pairs from donor molecules. seen from Figure 1 to play such a deciding role in deter- I n a similar fashion, the ions of nickel and copper can mining a metal's position on the activity scale can re- utilize one open d, one s, and two p orhitals to estabceive some structural interpretation in terms of ionic lish a stable square configuration. Iron, cobalt, and size and electron configuration. The lower lime of Fig- possibly aluminum ions probably utilize an available s, ure 3 shows the variations in ionic radius which are seen three p, and two d orbitals to orient water molecules to follow the same pattern as the lowest line of Figure 1, into octahedra about them. This conjecture is also the hydration energy. The quite apparent generaliza- supported by the tendencies of these ions to form hytion is that the relatively smaller ions hydrate more ener- drated salt crystals, notably sulfates. The relatively getically. This is particularly illustrated by the behav- low hydration energy of lead can be interpreted in terms ior of lithium, aluminum, and copper. Likewise, of these considerations. Plumbous complex ions are magnesium is the smallest of the alkaline earth metal encountered rarely, whereas complexes of other metals of comparable activity are common. The lead atom's
* I%-Romar, W., "The Structure of Metals and Alloys," The Institute of Metals, London, 1947, p. 28.
lo
KIEFPER, W. F., J. CHEM.EDUC., 25,537 (1948).
DECEMBER, 1950
663
ionization to the divalent state removes the p electrons but retains the full s orbital. This does not make possible any of the more stable orbital combmations such as are utilized by the other more vigorously hydrated ions. The difference between the behavior of copper in losing two electrons, one from the filled d orbitals, and silver's adherence to losing only the s electron to establish the contrasting monovalence is not readiiy explained. The cupric state is certainly stabilized by the establishment of the hydration complex. It may be that a similar dsp2 square configuration is less likely for the silver because of its increased size. Although silver readily forms linear complexes such as Ag(NH&+, it is apparently less likely to do so with the less basic HpO mole cules. The foregoing analysis seems to offer the following advantages as a supplement to the usual discussions relating an element's chemical characteristics to its position inthe periodic table. (1) It has summarized the way in which the energies of sublimation, ionization, and hydration are balanced to account for the relative position of a metal in the familiar activity or electromotive force series. It shows further how it is possible to interpret the relative magnitudes of these energies in terms of differences in the atom's electron distribution, its size, and the size of its ion. The discussions following from a recognition of the relative sizes of these units serve to emphasize the conclusions summarized by Campbell1' as pertinent for the presentation of general chemistry. (2) Lithium's apparent anomalous position ahead of potassium hm a strnctural interpretation. This illustrates the application of the generalization too often overlooked in discussions of periodicity of atomic properties that the first members of the A families as designated by the periodic table behave in a unique manner relative to the other members of the family. These elements, lithium to fluorine, have only one filled s orbital beneath their valence electrons, whereas the others have an octet of electrons filline s and u orbitals next to their outer electrons. This strnctural difference can he considered responsible for most of the atypical properties. For example, fluorine's behavior sharply contrasts with that of the other halogens. (3) Agreements with the order of properties predicted by the periodic table for the typical members of the A families are apparent. Potassium leads sodium; barium, strontium, calcium, and magnesium are in line. Similarly, the expected order is found in the period: sodium, magnesium, and aluminum. This implies that each of the factors involved in determining a metal's activity varies in comparable order relative to its position in the periodic table. (4) There is some basis for interpreting the puzzling order of metallic activity noted when comparing metals diagonally located in the I A and I1 A families of the table. Potassium is just about the equal of barium and strontium, yet calcium is definitely ahead of so-
-
dium. The contrasting energies of ionization and hydration are seen to account for the established order of activity. The entropy contributions to the energy balance discussed in the following section are also pertinent, particularly in the case of potassium as compared with the more hydrated alkaline earth metals. (5) A4 understanding of the relative chemical activities of the common heavy metals is possible. The "noble" behavior of silver is seen to be due primarily to its firm binding in the solid metal and its low degree of hydration. The interesting order in which the hard, high melting metals-iron, cobalt, and nickel-re situated with respect to the softer, lower melting zinc, cadmium, and lead similarly can be accounted for by the balance between the energetic factors due mainly to atomic and ionic size. THE FREE ENERGY AND ENTROPY RELATIONSHIP
This discussion should not conclude without some more accurate, if qualitative statement about the thermodynamic relationship between the heat of a reaction and the electromotive force which it can develop. Although the following discussion is undoubtedly beyond the understanding of the student in a general chemistry course, it may help the more mature student to connect some of the familiar chemistry of the beginning course with theoretical concepts usually encountered later. The previous discussion has dealt with AH, the total heat energy change for a reaction. This total actually involves two types of energy change. One of these energy terms, the "free energy" change, designated as AF, is the measure of the energy available for harnessing into useful work. The electromotive force is proportional to the maximum amount of such useful work. The other term is the "unavailable energy," designated as T AS. This energy is soaked up or squeezed out of the reacting system by changes in its store of internal energy. The equation relating these is AH = AF
+ TAS
(1)
It is also true by thermodynamic conventions that: -AF = (n X F) X (e. m. f.)
(2)
where n X F represents the number of faradays of electricity involved and e. m. f. is the electromotive force developed by the reaction. Combining these two relationships, there results the equation: -AH = (F) (e. m. f . )
- TAS
(3)
for the react.ions involved when 1 g. equivalent weight of a metal is changed into hydrated ions. The straightline relationship between AH and e. m. f., shown in Figure 1,implies that all the reactions whose data have been used must have a TAS energy term of the same sign and magnitude. The fact that the points fall nearly, but not exactly, on such a line obviously shows that such a situation is only approximately realized. A word of definition and explanation of the TAS term is in order. In this expression, T has the usual connotation of absolute temperature, and AS represents the
664
JOURNAL OF CHEMICAL EDUCATION
change in the property known as the "entropy" of the system. Since the temperature is the same for all the reactions compared here, differences in the magnitude of the TAS term must be due to differences in the entropy changes involved. Any attempt to set forth a complete treatment of the entropy concept would be out. of place here. However, some insight to the present discussion can be gained by considering one aspect of the idea of entropy. I t is correct to think of an increase in entropy (positive AS) as associated with the easing of restrictions or the establishment of a randomness or lark of orientation in the system being investigated. This mould mean, for example, that all of the sublimation processes referred to above would occur with an increase in entropy. The precise ordering of the atoms in the crystal would cease to exist. Conversely, a negative AS would imply that as a consequence of the reaction, the system ended up in a more restricted, less random involvement. This second circumstance would be illustrated by the cases previously mentioned in which t,he ions add water molecules to become hydrated into definite, spatially oriented, coordination complexes. The ions, free and at random in the gaseous state before entering the water, become very much restricted. A reconsideration of Figure 1 along with equation (3) reveals that if a point lies below or to the right of the solid line, as drawn on Figure 1, there has been more of an entropy decrease (-AS) in the over-all process than in a similar reaction for a metal represented by a point. on or above the line (to the left). The entropies listed in Table 3 are the thermodynamically accurate values for the over-all process of changing 1 g. equivalent, weight of a metal into ions in aqueous solution. The units are the usual "entropy units" of calories/degree. The values are calculated from the entropies of metals and ions a t 25% given in the Bureau of Standards table^.'^ The value - 15.6 entropy units for hydrogen has been included in Table 3 to facilitate detailed calclculations by equation (3). It also serves to indicate that the line drawn on Figure 1would not be expected to go through zero on the electrode potential axis. Zero would be the position of hydrogen assigned in the same way as the points for the metals. The line was drawn to give the best fit with the most points, rather than beine located on anv standard value. Thermodvnamir conventions assign"the value zero to both the total energy change and the free energy change for the process l2
See footnote 6.
of producing hydronium ions from a mol of hydrogen gas, yet the same conventions establish the entropy change for that reaction as - 31.2 cal./mol, deg. The consequence of this is to make the value of 15.6 an arbitrary additive constant to all the entropies of Table 3 when using them in calculations by equation (3). It means, for example, that when employing the values for silver from Table 1, e. m. f., -0.80 and AH, 25.3 kg.cal., the AS for the reaction must be chosen as 21.1 to obtain agreement. Similarly, the 2.34 volts and - 55.2 kg.-cal. for magnesium agree with an entropy change assigned the value - 2.4 cal./deg. Calculations of this type would make possible a large-scale plot analogous to Figure 1 with a straight line showing the true linear relationship between the quantity (AH - TAS) and the e. m. f. of the reaction. TABLE 3 E n t r o-. ~ vChanoes for Reaotions of Mstals in t h e Activitv Series
Metal
Cal./g. ep. ?ul.,
Metal
dey.
Li
- 3.3
Zn
Cal./g. ey. tot., deg .
-17.2
When the entropy contributions are thus calculated the conclusions of the previous qualitative representation are substantiated. A comparison of the figures in Table 3 with the relative positions of the points near the solid line of Figure 1 bears this out. The metals for which an increase of entropy for the over-all process is indicated are those which are not very energetically hydrated. Potassium, sodium, and silver are examples. For these there is little orientation of water molecules into definite complexes. The ions which do prefer to form tight hydration complexes, such as aluminum, zinc, or copper are listed with relatively large negative entropy changes. ACKNOWLEDGMENT
Acknowledgment should be made of the assistance of Miss Marjorie Hulett who examined this subject for a portion of her Junior year's work in the Independent Study Program a t the College of Wooster.
