In the Classroom
In Search of a Deep Understanding of Cu2+/0 and Zn 2+/0 E o Values Steven H. Strauss Department of Chemistry, Colorado State University, Fort Collins, CO 80523;
[email protected] This paper presents an example of an interesting way to introduce periodic trends in undergraduate inorganic chemistry courses. The student, guided by the instructor, “investigates” the significantly different M2+/0 E ° values for two adjacent period-4 elements, copper and zinc, as though the investigation were a research project. The periodic trends and anomalies are “discovered” (or rediscovered) on a need-toknow basis, and the student learns how a deep understanding of chemical reactivity can result only when layer upon layer of complexity is peeled back and examined. A series of three lectures based on this material has been used to begin the onesemester sophomore-level course Basic Inorganic Chemistry at Colorado State University. Since the lectures are integrated and have a common theme, the periodic trends may be more meaningful to the student and may not seem like so many disjointed concepts to be memorized. These lectures on the copper/zinc “problem” can start with a demonstration in which pieces of copper and zinc are dropped into test tubes containing 3 M aqueous HCl. If cobalt and nickel are available, they could be included in the demonstration after the class observes the copper and zinc experiments. Alternatively, the instructor could describe the behavior of the first 12 period-4 elements when they are treated with aqueous acid. The instructor should tell the class that what they have observed is a thermodynamic phenomenon, not a kinetic phenomenon. On the basis of observations that cobalt, nickel, and zinc (as well as calcium through iron) react with aqueous acid and copper does not, the class is asked to decide which element, copper or zinc, is behaving in an unexpected manner. It is likely that most students will conclude that copper is the correct answer to this question. Some students might recall from general chemistry that copper is a “noble” metal, or that it is less electropositive than the other firstrow transition metals, but of course these are just restatements of the observations, not explanations of them. Anomalous vs Unexpected Behavior The instructor should remind the class that, as scientists, they must always regard conclusions as tentative,1 and a tentative conclusion should be treated as a hypothesis to be examined further. Copper is the only element in the series Ca–Zn that does not react with aqueous acid, and in this regard its behavior is anomalous. However, whether the behavior of copper is unexpected depends on how the expectation is formulated. If this were a research project, the observations would constitute the “What happened?” part of the study; the “Why did it happen?” part remains to be investigated. The best place to start the investigation is to quantitatively examine the reaction of the metals Ca–Zn with aqueous acid. Figure 1 is
a plot of M2+/0 standard reduction potentials (E ° values) versus periodic table group number for the elements Ca–Zn (with the understandable omission of scandium). The data for this and the other plots used in this paper are listed in Table 1 (1– 4 ). Students should be encouraged to construct the plots used in this paper from data in their textbook, the Handbook of Chemistry and Physics, other resources, or, as a last resort, Table 1. This process will make the data and the plots more meaningful to them and will be in keeping with the “research project” theme of the copper/zinc lectures. There is an obvious periodic trend displayed in Figure 1: M2+/0 E ° values tend to become less negative from left to right across period 4. On average, the metals Ca–Zn become progressively more difficult to oxidize. The simple explanation of this trend is that the effective nuclear charge of atoms (Zeff) increases from left to right across a period, and a review of the Aufbau principle and shielding is appropriate at this point. However, the Zeff explanation sheds no light on the copper/ zinc problem; in fact, it is inconsistent with it. The straight line of slope 0.306 volt element {1 in Figure 1 is a least-squares fit to the data from calcium to copper. Its only significance is to highlight the overall trend. Nevertheless, it is instructive that the largest deviation from the least-squares line is for zinc (∆E ° = 1.40 V), more than three times larger than the next largest deviation, which is for calcium (∆E ° = 0.45 V). (If a least-squares line is calculated using all ten data points, the slope is 0.236 volt element {1 and zinc still has the largest deviation). The interesting result of this analysis is that zinc, and not copper, behaves unexpectedly when treated with aqueous acid. Put another way, if the M2+/0 E ° values for calcium through copper were known before the value for zinc had been established, the expected E ° value for zinc would probably have been more positive than the value for copper. On the basis of the trend in Figure 1 alone, it would have been reasonable to predict that zinc would be more noble than copper. The student should fully appreciate at this point why conclusions in science must always be regarded as tentative. The fact that zinc is highly electropositive—that is, that the E ° value for the Zn2+/0 redox couple is significantly more negative than the Cu2+/0 couple (and more negative than the E ° values for the Fe2+/0, Co2+/0, and Ni 2+/0 couples as well!)—is quite unexpected at first glance and deserves close scrutiny. As far as I am aware, a plot similar to Figure 1 does not appear in any inorganic chemistry textbook currently in print, although a 1-dimensional plot of the M2+/0 E ° values for the period 4 metals is part of a figure of Frost diagrams in Inorganic Chemistry by Shriver, Atkins, and Langford (5). Interestingly, the Zn2+/0 couple is not included in this figure, but it was included in a similar figure in the classic two-volume text Inorganic Chemistry by Phillips and Williams (6 ).
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In the Classroom
Choosing an Appropriate Thermochemical Model The reaction of metals with aqueous acid to form M2+(aq) ions and hydrogen gas at 25 °C is shown below. M(s) +
1 M H+(aq) 2H+ → 1 atm H2
2+
M (aq) + H2(g)
The thermochemical cycle for the half reaction M(s) → M2+(aq) + 2e{(g) is depicted in Figure 2, which can be presented to the class along with a review of Hess’s law. Since the standard reduction potential for the H+/H2 couple is defined as zero, the cycle in Figure 2 also defines ∆G° for the reaction shown above, and since zinc reacts with aqueous acid but copper does not, ∆Gf°(Zn2+[aq]) must be negative and ∆Gf°(Cu 2+[aq]) must be positive. With Figure 2 and the remaining data in Table 1 in hand, the student is in a position to study the copper/zinc problem in considerable detail in small, more easily understood steps. For reasons that will become apparent, it is preferable pedagogically to discuss the three individual steps in the cycle in the order ∆Ghyd°, I1 + I2, and ∆Gsub°.
Table 1. Relevant Thermodynamic Data for Calcium–Zinc ∆Gsub°(M)/ E °(M2+/0)/ ∆Ghyd°(M2+)/ I1/eV c I2/eV c Element kJ mol {1 b kJ mol {1 c Va Calcium Scandium
{2.87
–1,593
–
–
6.11
11.87
144
6.54
12.80
336
Titanium
{1.63
–
6.82
13.58
425
Vanadium
{1.13
–
6.74
14.65
468
Chromium
{0.90
{1,861
6.76
16.50
352
Manganese
{1.18
{1,832
7.44
15.64
239
Iron
{0.44
{1,910
7.87
16.18
371
Cobalt
{0.27
{2,006
7.88
17.06
380
Nickel
{0.26
{2,068
7.64
18.17
385
Copper
0.34
{2,087
7.73
20.29
299
{0.76
{2,028
9.39
17.96
95
Zinc aData
from ref 1. bData from refs 2 and 3. cData from ref 4.
Analyzing the Experimental Data Figure 3 is a plot of ∆Ghyd°(M 2+) vs period 4 group number for the elements Mn–Zn. The ∆Ghyd°(M2+) values listed in Table 1 and plotted in Figure 3 may differ from values from other sources. This is simply due to different reference states for ∆G hyd°(H+) and is of no consequence here, since our analysis will be based on a ∆∆Ghyd° value. The general trend in M2+ hydration energies from Mn2+ to Zn2+, shown by the straight line connecting the points for these two cations, is of course due to the decrease in cation radius from left to right across the period, which in turn is due to the increase in Z eff. The deviations from the line for iron, cobalt, nickel, and copper are due, in large part, to differences in ligandfield stabilization energy, LFSE. In addition, the more negative value of ∆Ghyd°(Cu2+) relative to ∆Ghyd°(Ni2+) is the consequence of the Jahn–Teller distortion of Cu(H2O) 62+ from Oh to D4h symmetry. Neither LFSE nor Jahn–Teller theory has to be discussed in detail during the copper/zinc lectures. Figure 3 can serve as a reference point if and when LFSE and Jahn– Teller theory are introduced later in the semester. For now, students can be told that the deviations from the straight line connecting Mn2+ and Zn2+ in Figure 3 are the result of factors that do not bear on the copper/zinc problem per se. In other words, the significance of Figure 3 is that the relative free energies of hydration for Cu2+ and Zn2+ (∆∆Ghyd°) = 59 kJ mol{1), regardless of why they are different, favor the reaction of copper metal with aqueous acid relative over the reaction of zinc metal with aqueous acid, and this is not consistent with the observation that zinc is the more reactive metal. In summary, zinc is more reactive than copper in spite of the less negative hydration energy of Zn2+. Note that an instructor can avoid the use of Figure 3 altogether by giving students only the values for ∆Ghyd°(Cu2+) and ∆Ghyd°(Zn2+). Figure 4 displays plots of the first and second ionization energies of Ca–Zn, I1 and I2, respectively, and the sum of I1 and I2 vs period 4 group number. A fruitful discussion of Zeff, electron configurations, and electron correlation can be based on this figure. As far as the reactions of copper and zinc with aqueous acid are concerned, I1 favors copper but I2 favors zinc, and the net result is that zinc is slightly favored 1096
Figure 1. Standard reduction potentials for M2+/0 couples (M = Ca and Ti–Zn). The line is a least-squares fit to the data excluding the Zn2+/0 value. The open square is the calculated value for E°(Zn2+/0) based on the least-squares fit. The data are from ref 1.
Figure 2. Thermochemical cycle for the reaction M(s ) → M2+ (aq) + 2e{(g). I1 and I2 are the first and second ionization energies of the metal atom.
Journal of Chemical Education • Vol. 76 No. 8 August 1999 • JChemEd.chem.wisc.edu
In the Classroom
Figure 3. Free energies of hydration of Mn2+ , Fe2+ , Co2+, Ni 2+, Cu2+ , and Zn2+ , based on the convention that ∆G °hyd(H+) = {1090 kJ mol {1. The data are from ref 2 as quoted in ref 3.
Figure 4. Ionization energies of Ca–Zn. I1 and I2 are the first and second ionization energies. The straight lines are linear least-squares fits to the data. The data are from ref 4.
when the sum I1 + I2 is considered (∆(I1 + I2) = 0.660 eV = 64 kJ mol {1). This almost exactly compensates for the difference in hydration energies of Cu 2+ and Zn2+. Once this compensation becomes apparent, Figure 2 requires that there be a very large difference in sublimation energies for elemental copper and zinc, a difference that is probably underappreciated even by many instructors. Figure 5 is a plot of sublimation energies (atomization energies) vs period 4 group number. The values rise and fall between calcium and manganese, and then rise and fall again between manganese and zinc. Note that zinc has the lowest atomization energy, 95 kJ mol{1, of all eleven metals in the plot. In fact, zinc has a lower atomization energy than all but three elements in period 4, namely potassium (60 kJ mol{1), bromine (82 kJ mol{1), and of course krypton (0 kJ mol{1). The student who may have started the copper/zinc inquiry with the platitude “Copper is a noble metal” now has a deeper understanding of why zinc reacts with aqueous acid but copper does not: the reason is that zinc has a very low sublimation energy. Some students will no doubt realize that low fusion and sublimation energies are a common feature of the group 12 elements, since the liquid state of elemental mercury at 25 °C is one of the best known facts of descriptive inorganic chemistry, even for the lay public. A detailed explanation of the plot in Figure 5 would require a detailed discussion of metallic radii, metallic bonding, and band theory (including density of states), which may be beyond the scope of undergraduate inorganic chemistry courses at some institutions. However, the fact that an understanding of the very low sublimation energy of zinc requires yet additional inquiry is a perfect object lesson in the scientific method: one can understand a set of experimental observations on many levels, and, if one has more time, it is always possible to dig deeper. For those instructors who choose to discuss the underlying reasons for the plot in Figure 5, schematic density of states diagrams for the bulk metals Fe–Zn are given in Figure 6. This figure was adapted from a figure in the Phillips and Williams text (7), which has been reproduced in a more recent inorganic text (8). More realistic density of states diagrams for d-block metals based on modern computational methods are also available (9–11). It is clear from Figure 6 that zinc has a completely filled d band and a nearly completely filled s band. Since the top half of molecular orbital bands are effectively antibonding in character (12), the bonding between zinc atoms in the bulk metal is seen to arise from the small overlap of the s and p bands. The bonding is very weak because only a few of the s-band antibonding levels are empty and only a few of the p-band bonding levels are filled. Conclusions
Figure 5. Free energies of sublimation of Ca(s)–Zn( s). The lines connecting Ca, Mn, and Zn are for illustrative purposes only and have no special significance. The data are from ref 4.
After a set of lectures based on the material in this article, students will understand a great deal about numerous periodic trends as well as a great deal about the copper/zinc “anomaly”. They will also have learned the process of analyzing interesting chemical facts and anomalies by examining relevant data graphically. Finally, since all of the trends examined cannot be completely understood in a given amount of time, the student will appreciate that there is always more that she or he can learn in the future.
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Note 1. The quote “A conclusion is nothing more than an opinion you have when you get tired of thinking” can be paraphrased for scientists as follows: A conclusion is nothing more than an opinion you have when you get tired of thinking or doing more experiments.
Literature Cited
Figure 6. Schematic density of states diagrams for Fe–Zn. The hatched areas represent filled energy levels.
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1. Bard, A. J.; Parsons, R.; Jordan, J. Standard Potentials in Aqueous Solution; Dekker: New York, 1985. 2. Martell, A. E.; Hancock, R. D. Metal Complexes in Aqueous Solutions; Plenum: New York, 1996, p 5. 3. Friedman, H. L.; Krishnan, C. V. In Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 3, p 55. 4. Handbook of Chemistry and Physics, 71st ed.; Lide, D. R., Ed.; CRC: Boca Raton, FL, 1990. 5. Shriver, D. F.; Atkins, P.; Langford, C. H. Inorganic Chemistry, 2nd ed.; Freeman: New York, 1995; p 328. 6. Phillips, C. S. G.; Williams, R. J. P. Inorganic Chemistry; Oxford University Press: Oxford, 1966; Vol. II, p 171. 7. Ibid.; Vol. I, p 205. 8. Miessler, G. S.; Tarr, D. A. Inorganic Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1991; p 173. 9. Saillard, J.-Y.; Hoffman, R. J. Am. Chem. Soc. 1984, 106, 2006. 10. Wang, C. S.; Callasay, J. Phys. Rev. B 1977, 15, 298. 11. Burdett, J. K. Chemical Bonding in Solids; Oxford University Press: Oxford, 1995, p 119. 12. Ibid.; pp 40–44.
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