G. P. Haight, Jr. University of Illinois Urbana 61801
Energy Cytles
In recent years it has become fashionable (and instructive) to use energy cycles to show the atomic and molecular energy factors which may influence an observable chemical property. Thus, from energy cycle considerations beginning students learn such things as: The crystal energy of sodium chloride is perhaps as important a factor in the reactivity of sodium with chlorine as the "desire" of sodium atoms to form sodium ions and of chlorine atoms to form chloride ions each with magic, inert gas structures (see Fig. 1). The relative solubilities of salts are influenced by both crystal energies and ionic solvation energies, and these two effects may be in opposition when comparing solubilities of two salts (Fig. 2). Valuable insight can be obtained from energy cycles, especially in seeing why trends in observable periodic properties are seldom "smooth" functions. However, great care must be used in order to avoid errors and misconceptions when teaching with the aid of energy cycles. Since the AH, AS, and AG values for a given process
Figure 1.
obove, Born-Hober cycle for
Enerav .. level diosram for Na and CI. Q = energy of reaction. S = energy of rublimotion of Nm.
Na
+ 'I2Clz
-
NoW:
right,
D = ditsaciotion energy of Ch. I.P. = ionirotion potential of N. E.A. = electron mffinity of CI. U = crystal energy of NafCI-. Q = rum of other energies. Cycle is valid if all energier are free energies or if all are enthalpier. Too often Q, S, and D ore heats or enthalpier while U, I.P., and E.A. ore internal energies.
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Journal of Chemical Education
are additive properties, cycles consisting of a series of simple processes adding up to the process under consideration may be drawn up for each thermodynamic parameter if data are available. The free energies would be most useful for determining directions of reactions, but enthalpies are employed often because they are most readily available. Trouble may arise when one finds some free energy changes, e.g., from cell potentials; some internal energy changes from crystal energies, ionization potentials, etc.; and some enthalpy changes used in the same cycles. Limitations of Cycles
Since the individual terms in an energy cycle are differences in thermodynamic functions, an energy cycle gives no information on mechanisms of reaction. Instead, they provide information on energy differences between states of the system. Thus, Figure l b tells only how the enthalpy of a system containing sodium
Figure 2. Born-Hober cycle for the solution of a soh in water. The binding energy lU1 plus the hydration energy (HI equals the free energy of solution (SI. Since U and H are of opposite sign ond of comparable mognitudes. voriotions in S s m be very erratic. In o particular series M+F- ~olubilitiesincrease with increasing radius d M ? In onother series M ~ + S 0 4 ~ - , ~ ~ I u b i l idecrease ties with increasing rod;". of M2+. The effects of radii on U H provide insight into the phenomena of hydration and ionic crystal formotion or well a$solubility trends.
+
and chlorine in various states of aggregation differs from the enthalpy of the two elements in their standard states a t 25'C. Moreover, diagrams of euthalpies do not indicate the direction a proposed reaction might take although the enthalpy diagram in Figure l b is often used to explain "why Na(s) hums in Cl,(g) to give NaCl(s)." Such an "explanation" assumes enthalpy terms dominate free energy changes which they often, in fact, do. However, spontaneous endothermic processes are well known. Some Pitfalls t o Avoid Energy States for the No-CI System
Referring to Figures l a and l h and the manner in which they are usually discussed, one finds the following tendencies: The endothermic character of processes such as the sublimation of metallic sodium, the ionization of sodium atoms, and the dissociation of chlorine is shown to be greater than the exothermicity of the electron affinity of chlorine atoms. Thus, it is implied that the real reason for the reaction 2Na C1, 2Na+CIproceeding as it does is the large exothermicity of formation of crystals by Na+ and C1- ions. One might well ask why Na2+(C1-)2or Na2+C12-do not form. The latter would have roughly four times the crystal energy as Na+Cl-. The answer is, of course, that the increased crystal energy would not he sufficient to overcome the highly endothermic process
+
N a W
+ C1-(g)
-
-
+ CIa-(g)
Naa+(g)
in which both ions lose their inert gas configurations. Thus the importance of inert gas structures camot be ignored in the search to include all factors responsible for reactivity of sodium and chlorine. Most texts give Figure Ib without showing the ion pair Na+Cl-(g) state. (It is used in essentially that form by the CBA high school course). This omission could cause the reader, led on by discussions in the vein ahove, to suspect that reaction of sodium vapor with chlorine gas a t temperatures of, say, 1500°C where sodium chloride is vaporized, would not occur or that sodium chloride would dissociate into atomic sodium and chlorine a t 1500°C. However, should the reader plan to experiment with vapor mixtures of sodium and chlorine atoms a t 1500°C, one can only hope that the experimenter is safety conscious. A very important state low on the diagram, and thus very stable a t temperatures above the boiling point of sodium chloride, is that of Na+Cl- ion pairs in the gas phase. The binding energy of a mole of Na+C1-
ion pairs is -Ne2/r (plus the repulsion term for impinging electron clouds). This is over half the crystal energy which for Na+Cl- is -1.75 Ne2/r. In this expression, N is Avogadro's number, e is electronic charge, r is the Na-Cl internuclear distance, and 1.75 is the Madelung constant for the NaCl structure. One might also expect ;ion quartets in the gas phase which would have binding energy of about 1.3 Nez/r per mole of Na+Cl-.
+
Limit Cycles to One Kind of Term
Errors in presentation of energy cycles often arise due to failure to distinguish between available thermodynamic energy terms such as enthalpy changes (AH) (e.g., heats of fusion, vaporization, and sublimation), free energy changes (AG) (e.g., electrode potentials), and internal energy changes (AE). Such terms often are used indiscriminately in cycles which appear complete except for one of the terms which is not accessible experimentally. That term is then determined by difference, completing the cycle, which, as commonly presented, may include a mixture of enthalpy (AH), free energy (AG), and internal energy (AE) terms. This sort of error is made the more likely by the absence of complete thermodynamic data. If different kinds of energy must be used, discussion should be properly qualified. For instance, in some textbooks the energy cycles for formation of alkali halides (Fig. 1) have been shown as means of finding the electron affinities of halogen atoms which are difficult to measure. Q = DE + AH8 + I.P. + E.A. + U Calculation of the crystal energy, U , from the electrostatic theory equation given ahove makes it possible to evaluate E.A. by difference from other terms which are measurable. The dissociation energy of C4, DE, and the sublimation energy of sodium, AH,, are easily found as enthalpies, as is the heat of reaction, Q. The ionization potential for the metal, I.P., and the electron affinity for the nonmetals, E.A., are also enthalpies, but U is an internal energy change. As a result, values for the electron affinity calculated in this way are suspect if not completely erroneous. In some cases, however, AE and AH may be of nearly the same magnitude, and if the entropy change is very small the free energy and the enthalpy changes may be nearly the same. Salt Solubilities
Discussion of relative salt solubilities based on Figure 2 are often greatly over-simplified. Two common errors in making comparisons of salt solubilities are to neglect the fact that salts of similar formula have different crystal structures, e.g., NaCl and CsC1, or MgF, and CaF,, and to neglect different degrees of hydration in the solid phase when making comparisons. These differences make simple discussions of solubility change with changing ionic radius in a series such as LiC1, NaC1, ICCI, RbC1, and CsCl largely irrelevant, LiCl in equilibrium with Li+&-a, is a dihydrate. CsCl is a body-centered cubic crystal compared with face-centered cubic crystals for the others. A useful rule here might be to compare only what is comparable, that is, salts with the same structure. Volume 45, Number 6, June 1968
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421
Thermodynamic Data for Electrode Processes Involving Elements. (All energies in kcal/mole a t 298°K) -80"-.-*tron Donor
Product
I.P.
D
Plane and Hesterl have called attention to the quantity represented by 2 by assigning an energy difference to electrons in their "standard state" versus electrons in the gas phase. (Unfortunately, a misprint gives -25.8 kcal as the value for AGhyd of H + rather than -258 kcal.) The authors give this energy difference as 5.08 ev or 117 kcal. This value is higher than the value indicated in Figure 3 (about 110 kcal). The table shows values of 2 for several different electrode processes. It is difficult to tell whether 2 is really constant or varies somewhat with different electrode material. If it varies, it is important that the standard state for an electron be defined so as to take this into account. It is interesting to note that if 2 is calculated from free energy data for the reactions: FeP+(aq) Cra+(aq)
Cydes for Oxidation Potentials
Cycles such as those in Figure 3 have long been used in qualitative discussion of factors affecting electrode potentials. Thus, one can demonstrate the fact that a large AGhvbterm makes the standard electrode potential for lithium very large. Similarly, the low sublimation energy of zinc is an important factor because it is much more active than copper. However, quantita tive consideration of these cycles in textbooks is inhibited by the failure of tabulated values of the free energies, enthalpies of formation, and S for hydrated ions to agree with values calculated theoretically. For example, NBS Circular 500 gives 361 kcal for the hydration energy of H + while most calculations give about 260 kcal. The difference is the quantity 2 in Figure 3, the difference in the free energy of gaseous electrons and electrons in electrodes.
Figure 3. Born-Haber cycles for redox potentials. D is the dissociation energy of the goleovr molecule, I.P. is the ioniration energy, E.A. is the eleebon offinity, E is the electrode potential, ond AGbPd, the hydratiw free energy of the species at the tail of each orrow. Z is tho energy difference of goreous electrons and eleoronr in their "standard state" in a p1otinum wire.
Z = 0-48.6-313f
-X = -31.3
251 = -110.6 84.8 = +I133
- 25.2 + 85.3 f
Although I.P. and E.A. are entholpies above abrolute zero, the os$ociatod entropy term is indeed negligible here.
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Journal of Chemical Education
--
Fe"(aq) Cre(aq)
++ e-e-
the values are -136 and -161 kcal, respectively. Harvey and Porter2 give data indicating that the third ionization potential and the difference in hydration energy for M2+ and M3+ are about the same for each element, yet the electrode potentials differ by more than a volt suggesting that the hydration energies given are seriously in error. A new standard electrode potential which would give the accepted value of AGhvd for H + as 251 rather than 367 would make the use of tabulated thermodynamic quantities for ions much easier for the non-specialist. Alternatively, one can define a standard state for electrons which gives non-zero values for the enthalpy, entropy, and free energy changes for electrons a t the hydrogen electrode. One can sympathize with the reluctance of thermodynamicists to change the base of standard potentials or to be too concerned over thermodynamic data for single ions in solution when they cannot be experimentally determined. However, these quantities are being determined with the aid of theory and are being used. One feels, therefore, that standards making all available AHo, ASo, and AGO values additive should be set. Thermodynamic Cycles and Mechanism
Although thermodynamic cycles have nothing, per se, to say about mechanisms, they do give energetics of
-
individual reactions a t the atomic level which can provide mechanistic clues. For instance, the electrode potential of lithium (Li Li+ e-) is larger than that for sodium, yet lithium reacts much more slowly with water than sodium. In the Born-Haber cycle for these processes it is seen that a large difference in sublimation energy exists with lithium being the more difficult to sublime. This suggests that separation of metal atoms from the solid is the slow step in oxidation of metals. However, one cannot rule out a contribution from the higher ionization potential for lithium to the slowing effect. Comparison of energy diagrams with activation energies can rule out certain postulated mechanistic paths, but seldom, if ever, can they provide real evidence for a particular path.
+
'PLANE,ROBERT A,, AND H E S T ERONALD ~ E., "Elements of Inorganic Chemistry," W. A. Benjamin, New York, 1965. Z H ~ ~K.,vAND ~ PORTER, ~ , G., "Introduction to Physied Inorganic Chemistry,'' Addison-Wesley, New York, 1963.
