In the Classroom
Melting Point, Density, and Reactivity of Metals Michael Laing School of Pure and Applied Chemistry, University of Natal, Durban 4041, South Africa;
[email protected] In today’s typical freshman text, the chapter on the periodic table and chemical periodicity follows the presentation on atomic structure and electron configuration (1, 2). For each of the metals, values of atomic and ionic radii are given along with ionization energies, electron affinities, and even electronegativities. This wealth of numbers is important, but one must ask: what link is there between these values for atoms in the gas phase and the reality of the student’s everyday experience of the metals themselves? Are there alternative physical properties of metals that a student is familiar with—data, simple to understand, straightforward to measure—that can give guidance about the relative reactivities of the metals? The answer is clearly “yes”: the bulk physical properties, melting point and density. There are clear periodic trends in these values going from left to right in the periodic table, beginning with group 1. This was evident to Lothar Meyer when in 1869 he drew up his graph of atomic volumes, equivalent to the reciprocals of the densities (3, 4). He observed that the least dense metals, those with the largest atomic volume, were the most reactive; the most dense were the most inert. Reactivity of a Metal It is not easy to get agreement on what we understand by the word “reactivity”: the term is difficult to define. We
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have an intuitive picture of a piece of potassium bursting into flames when it is dropped into cold water, whereas a piece of silver appears not to change even when heated in steam. Some books use the term “active”, some talk of an “electromotive” or “activity” series and some of “affinity”, and others list the metals in order of relative strength as reducing agents to displace other metals from solution (5). But the word “reactivity” is more than a semantic problem, as is discussed by Mellor (3). The importance is emphasized by Kotz and Treichel, who devote more than 250 pages of their textbook to nine chapters with the common title “Principles of Reactivity” (6 ). In practice we typically class metals as reactive or not, depending on the “rate”, “vigor”, or “violence” of the reaction of the metal in three different processes (reaction of the metal with oxygen, reaction of the metal with water, and the tendency to displace other metals from aqueous solution) and the temperature that is required for the reaction to take place. Reactivity is a Janus because what we see and experience in each of these processes has within itself two aspects, often contradictory: the stability of the products that are formed, which is thermodynamic, and the rate at which the reaction takes place to form the products, which is kinetic (7 ). The thermodynamics of each of the chemical processes can be described by a Born–Haber cycle.
Journal of Chemical Education • Vol. 78 No. 8 August 2001 • JChemEd.chem.wisc.edu
In the Classroom
M2+(g) + nH2O → M2+(hyd); ∆Hhyd (exothermic)
Born–Haber Cycles for the Three Thermodynamic Criteria for Reactivity
1. Reaction of Metal with Oxygen to Give Metal Oxide A large negative enthalpy of formation, ∆Hf , is taken to indicate high reactivity of the metal. The metals of immediate interest are from groups 1 to 4; hence the oxides will have the formulas M2O, MO, M2O3, and MO2, respectively. For convenience, we will do the Born–Haber cycle for the case of a divalent metal. M(s) + ⁄2O2(g) → MO(s);
∆Hf (exothermic)
1
M(s) → M(g);
∆Hsub (endothermic)
M(g) – 2e → M (g);
1⁄
2O2(g)
2+
IE1 + IE2 (endothermic)
→ O(g);
1⁄
O(g) + 2e → O2 (g);
2D
(endothermic)
EA1 + EA2 (endothermic)
M2+(g) + O2(g) → MO(s);
LE (U ) (exothermic)
∆Hf = ∆Hsub + IE1 + IE2 + ⁄2D + EA1 + EA2 + U 1
The reaction will be favored if the enthalpy of sublimation and ionization energy are small and the lattice energy is large. For metals in group 1, low ∆Hsub and IE dominate and lead to high reactivity. For metals in group 4 it is the large value of U that overcomes ∆Hsub and IE and yields the large favorable exothermic ∆Hf ; for example, for TiO2 ∆Hf is 945 kJ/mol owing to a favorable Madelung constant and large charge on the cation.
2. Reaction of Metal with Water to Give Metal Oxide and Hydrogen In practice the “less reactive” metals require the water to be at a high temperature (i.e., steam) to react to form hydrogen, so the Born–Haber cycle will be given for this case. M(s) + H2O(g) → MO(s) + H2(g); M(s) → M(g);
∆Hsub (endothermic)
M(g) – 2e → M (g);
2+
IE1 + IE2 (endothermic)
H2O(g) → 2H(g) + O(g); 2H(g) → H2(g); O(g) + 2e → O (g);
2
2BE (endothermic)
D (exothermic) EA1 + EA2 (endothermic)
M (g) + O (g) → MO(s); 2+
∆Hreact (exothermic)
2
E ° ∝ ∆Hsub + IE1 + IE2 + ∆Hhyd The smaller the sublimation and ionization energies are and the larger the enthalpy of hydration is, the more powerful a reducing agent will be the metal. Commonality These three Born–Haber cycles were given for the case of a divalent metal, but in practice the cation formed could be M+, M2+, M3+, or M4+ depending on the group to which the metal belongs. The total energy involved in the ionization of the metal atom is thus ∑ IE n, where n, the group number, is 1 n to 4. The first ionization energy, IE1, is always involved. Thus there is a commonality among these three reactions for all metals: the energy terms ∆Hsub (the enthalpy of sublimation) and IE1 (the first ionization energy). Whether reactivity of a metal is thought of in terms of ease of formation of a stable oxide or of the metal’s having a large negative electrode potential is not important because both measures involve the same two energy processes characteristic of the metal: the enthalpy of sublimation ∆Hsub and the ionization energy IE1. These two energy terms, characteristic of the metal, are reflected qualitatively in the melting point and the density of the metal. Melting Point and Enthalpy of Sublimation The enthalpy of sublimation describes the energy required to tear the atoms from the solid and put them into the gas phase. It is simple for a student to understand that the metal– metal bonds in the solid must be broken to achieve this end, and that the first step would be equivalent to melting and the second, to boiling. It is evident that the stronger the metal–metal bonding, the higher must be the melting point. It follows therefore that the higher the melting point, the larger will be the enthalpy of sublimation. The correlation between melting point and enthalpy of sublimation is good, close to linear (8). The implication therefore is that a low melting point should lead to high reactivity, and the higher the melting point the lower will be the reactivity. The melting points of two series of metals, potassium to titanium in period 4 and rubidium to zirconium in period 5, are given in Table 1. (Although tabulations of
LE (U ) (exothermic)
∆Hreact = ∆Hsub + IE1 + IE2 + 2BE – D + EA1 + EA2 + U Again, the reaction will be favored if the sublimation energy and ionization energy are small and the lattice energy is large.
Table 1. Some Physical Properties of Metals in Groups 1 to 4, in Periods 4 and 5 Density/ ∆Hsub / IE1/ E °(Mn+/M)/ Z Metal mp/°C (g/cm3) (kJ/mol) (kJ/mol) V 2.93 19 K 64 0.86 90 419
3. Standard Electrode Potential
20
Ca
850
1.54
178
590
2.87
For ease of comparison with the other reactions, this reaction will be written as a loss of electrons from the metal.
21
Sc
1539
2.99
378
631
2.08
22
Ti
1668
4.54
470
658
1.63
37
Rb
39
1.53
86
403
2.92
38
Sr
770
2.60
164
550
2.89
39
Y
1509
4.47
423
616
2.09
40
Zr
1852
6.45
609
660
1.55
M(s) – 2e → M (hyd); E ° (negative relative to hydro
2+
gen for the reactive metals)
M(s) → M(g); ∆Hsub (endothermic) M(g) – 2e → M2+(g); IE1 + IE2 (endothermic)
JChemEd.chem.wisc.edu • Vol. 78 No. 8 August 2001 • Journal of Chemical Education
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In the Classroom
melting points of metals are not uncommon [9, 10], graphical presentations are relatively rare [11–13]; see Figure 1.) Our experience confirms that potassium reacts violently with cold water, whereas titanium is used for the turbine blades in turbojet motors for aircraft. The trend of decreasing reactivity with increasing melting point is evident. The value of E ° for titanium (Ti4+/Ti) implies that the metal should react with water. It is here that kinetic factors play their important role in making titanium so inert under normal conditions; as in the case of aluminum, it is an inert surface oxide layer that prevents reaction at room temperature (7 ). Density and Ionization Energy If a metal is to be chemically reactive then its atoms must easily lose at least one electron to become a cation, at the cost of the ionization energy. The more easily the electron is lost, the more reactive will be the metal. The electron is held to the atom by electrostatic Coulombic forces of attraction; thus the further away from the nucleus, the weaker will be the attraction. For adjacent metals of similar atomic number and positive nuclear charge in the same period of the periodic table, the larger the atomic radius (or atomic volume) the lower will be the density. One may conclude therefore that the lower the density, the lower the ionization energy will be and the greater will be the ease of removal of the electron, hence the greater the reactivity (which is effectively the correlation observed so long ago by Meyer for atomic volume [4 ]). The data in Table 1 show this effect for the series of metals in periods 4 and 5. The reactivity decreases with increase in density: the least dense metal in each period is the most reactive (Fig. 2). Rubidium, the least dense in period 5, explodes into flame when dropped into water. Zirconium, the most dense, is used as cladding for the uranium fuel rods in nuclear reactors because of the corrosion resistance of the metal and its inertness to attack by water and oxygen. Once again kinetic effects play an important role in rendering the metal inert; but at 1000 °C zirconium will react with steam to produce hydrogen, which is the reaction that occurred at the Three Mile Island disaster (1).
Figure 1. Melting points (䊏) and enthalpies of sublimation (䊐) of the elements in groups 1 to 4 in period 4. The correlation between mp and ∆Hsub is evident.
Figure 2. Density (䊏) and ionization energy (䊐) of the elements in groups 1 to 4 in period 5. The trend of increase in IE1 follows the increase in density.
The Importance of Discontinuities The examples of the metals of groups 1 to 4 that have been considered so far show regular trends in the periodicity of reactivity that correlate well with the regular trends in their physical properties. Of greater interest are the cases where there is a sharp discontinuity in the physical properties of metals in the middle of a period, because this points to anomalous, unexpected, or irregular chemical properties. Examples of this effect can be seen both in the 3-d transition metals and in the lanthanides.
Manganese and the 3-d Metals The pertinent physical data for manganese and its congeners are given in Table 2 (14, 15) and Figure 3. The melting point of manganese is dramatically less than those of its neighbors, iron and chromium. This hints that manganese will have anomalous chemical reactivity that will not be simply intermediate between the reactivities of iron and chromium. Examination of the trend in the values of E ° (M2+/M) for these metals shows that they begin very negative (1.18 V 1056
Figure 3. Melting points of the 3-d metals showing the sharp minimum for manganese.
Journal of Chemical Education • Vol. 78 No. 8 August 2001 • JChemEd.chem.wisc.edu
In the Classroom Table 2. Physical Characteristics of Some 3-d Transition Metals Z Metal
mp/ °C
ResisE° E° ∆Hsub / Density/ 2+ 3+ 2+ tivity/ 3 (M /M)/ (M /M )/ (kJ/mol) (g/cm ) µΩ cm V V
23
V
1890
515
6.11
1.18
0.26
24
Cr
1875
397
7.19
0.91
0.42
13
25 Mn
1244
281
7.43
1.18
1.51
136
26
Fe
1527
418
7.87
0.44
0.77
10
27
Co
1493
425
8.90
0.28
1.92
6
20
Table 3. Physical Properties of Some Lanthanides Showing the Anomalies for Europium and Ytterbium Z
Element
mp/ °C
Density/ (g/cm3)
E° E° ∆Hsub/ (M3+/M)/ (M3+/M2+)/ (kJ/mol) V V 2 . 3 2 328 —
60
Nd
1024
7.00
61
Pm
1050
7.20
301
2.29
—
62
Sm
1072
7.53
207
2.30
— 0.35
63
Eu
826
5.25
178
1.99
64
Gd
1312
7.89
398
2.28
—
65
Tb
1356
8.25
389
2.31
—
68
Er
1497
9.04
317
2.32
—
69
Tm
1545
9.32
232
2.32
70
Yb
824
6.97
152
2.22
— 1.05
71
Lu
1652
9.84
428
2.30
—
Experience tells us that chromium is used for plating because of its hardness and inertness, while iron is probably the most widely used metal for construction. We never see artifacts made of manganese owing to its high chemical reactivity and low tensile strength. Both the low melting point and the very high electrical resistivity of the metal reflect an unusual electronic arrangement in the solid, which is linked to the s2d5 electron configuration of the Mn atom in the gas phase.
Europium and the Lanthanides The physical properties of the lanthanides are given in Table 3 (9, 16 ) and the melting points are shown graphically in Figure 4. Overall there is a regular increase in density and melting point as the atomic number increases, but there are marked discontinuities at europium and ytterbium. The very low density and melting point of europium warn us that its chemical properties will be anomalous. They are. The lanthanides are characterized by a common oxidation state of +3. Europium is unusual in having an easily formed oxidation state of +2 both in solution and in relatively stable solid compounds such as EuSO4. This unexpected chemical behavior is reflected in both the low melting point and density of europium metal compared to those of its neighboring lanthanides. One can further pursue discontinuities in melting point and density among the heavier lanthanides, and it is immediately evident that the properties of ytterbium too are out of line. These values correctly point to a chemical anomaly: the unexpected ease of formation of the Yb2+ species, which is well known in compounds such as YbS and YbCl2 (17). The properties of europium and ytterbium are similar to those of barium: mp 727 °C, density 3.62 g/cm3, E ° (M2+/M) 2.91 V, as a direct result of their low melting points and consequent low enthalpies of sublimation. The unexpected stability of the Eu2+ and Yb2+ cations is due to their having half-filled and filled f shells: Eu2+ f 7 and Yb2+ f 14. The weak M–M bonding between the atoms in the solid metal (18) is a direct consequence of the electronic configuration of the atoms. Link to Electron Configurations
Figure 4. Melting points of the lanthanide metals showing the large discontinuities for europium and ytterbium. As may be expected, ∆Hsub of these two metals are minima also.
for vanadium) and become steadily less negative (to 0.28 V for nickel). The large negative value for manganese is anomalous. Conversely, the value of +1.51 V for E ° (M3+/M 2+) for manganese is anomalously large compared with the values for Cr and Fe. These data confirm our observations in the laboratory: Mn2+ in solution is stable, whereas both Cr2+ and Fe2+ are reducing agents; the species Fe3+ and Cr3+ are stable oxidation states, whereas Mn3+ is a very powerful oxidizer.
The striking discontinuities in melting point and density that lead to the apparent anomalies in the chemical reactivity of Mn, Eu, and Yb can be linked to the electron configurations of the atoms in the gas phase. In each case these are “spherically symmetrical” with a filled s 2 shell: Mn d5s 2, Eu f 7s 2, and Yb f 14s 2. Why these particular configurations should lead to the observed chemical properties of the metals requires sophisticated arguments because they would also have to account for the physical and chemical properties of other metals with filled s 2 shells such as Be, Mg, Zn, Cd, and Hg. Such a discussion is outside the realm of this paper. Qualitative or Quantitative? One must ask: is it possible to make the correlations quantitative? The answer is “definitely no”. Melting is not subliming; neither melting point nor even boiling point can be equivalent to the energy of sublimation. Melting point can only give guidance.
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In the Classroom
The ionization energy of a species is related in a complex manner to the electron configuration of the species and its effective nuclear charge as well as to its radius. The density of the metal cannot take into account all these properties, yet it still gives useful information about trends in ionization energy. The quantitative thermodynamic measures of reactivity of a metal, ∆Hf of the metal oxide, and the standard reduction potential E °, are dictated by energy factors remote from the metal itself: the lattice energy U of the oxide which depends on the packing pattern of cations and anions (the Madelung constant A) as well as on the charge on the cation; and the hydration energy of the cation, ∆Hhyd, which in turn depends on coordination number, the mode of bonding, and both the charge and the electron configuration of the cation. Correct application of Born–Haber cycles with the appropriate energy values can allow us to estimate correctly the numerical values of E ° for the metal and ∆Hf of its oxide. Yet these thermodynamic data still cannot give a true measure of what we see or feel, because these data cannot give information about kinetics, which so often dictates the reactivity that we actually experience. Aluminum, whose E ° (and electronegativity) is close to those of titanium and zirconium, is another simple everyday example of a metal that is anomalously inert. Our aim should be simplicity, to help the student correctly predict what to expect from the minimum of easily obtained and understood information. Taken together, these two simple bulk properties of a metal, melting point and density, can give a useful qualitative guide to its chemical reactivity and properties because they bridge the macroscopic and atomic worlds. We should tell freshman students about the periodic trends in melting point and density of metals and what information they can give about the chemical reactivity of the metal. High melting point, high density, low reactivity; low melting point, low density, high reactivity. We should discuss the trends in the physical parameters such as enthalpy of sublimation and ionization energy, and by using appropriate Born–Haber cycles, give an understanding of why melting point and density should give such useful information. Linking the trends in atomic-scale parameters to the trends in these two simple macroscopic properties is a challenge to the teacher. The order in which to present the information about melting point and density—before or after discussing the atomic parameters of ionization energy, electron affinity, etc.—must remain the personal preference of the instructor. I prefer to first visit the real world of macroscopic properties and then to introduce the atomic scale after, which is the historical order of discovery. But you must teach as you believe.
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Acknowledgment I thank one of the referees for the many detailed criticisms and constructive comments. Literature Cited 1. Whitten, K. W.; Davis, R. E.; Peck, M. L. General Chemistry with Qualitative Analysis, 5th ed.; Saunders: New York, 1996; pp 140, 208–221, 951. 2. Hill, J. W.; Petrucci, R. H. General Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1996; pp 242–268. 3. Mellor’s Modern Inorganic Chemistry; Parkes, G. D., Ed.; Longmans, Green: London, 1951; pp 121, 564. 4. Kleinberg, J.; Argersinger, W. J.; Griswold, E. Inorganic Chemistry; Heath: Boston, 1960; p 7. 5. Bodner, G. M.; Pardue, H. L. Chemistry, 2nd ed.; Wiley: New York, 1995; pp 316–335. 6. Kotz, J. C.; Treichel, P. Chemistry and Chemical Reactivity, 3rd ed.; Saunders: New York, 1996. 7. Wulfsberg, G. Principles of Descriptive Inorganic Chemistry; Brooks/Cole: Monterey, CA, 1987; pp 153–159, 200, 215– 221, 371, 372, 420–423. 8. Parish, R. V. The Metallic Elements; Longman: London, 1977; pp 208, 211. 9. Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon: Oxford, 1984; pp 1430, 1447. 10. Sanderson, R. T. Inorganic Chemistry; Reinhold: New York, 1967; p 58. 11. Dasent, W. E. Inorganic Energetics, 2nd ed.; Cambridge University Press: London, 1982; pp 36, 38, 42. 12. Phillips, C. S. G.; Williams, R. J. P. Inorganic Chemistry; Oxford: London, 1966; Vol. 1, pp 87, 89; Vol. 2, pp 20–22, 98. 13. Moeller, T. Inorganic Chemistry; Wiley: New York, 1982; p 122. 14. Jolly, W. L. Modern Inorganic Chemistry; McGraw-Hill: New York, 1984; pp 292, 303. 15. Johnson, D. A. Some Thermodynamic Aspects of Inorganic Chemistry, 2nd ed.; Cambridge University Press: London, 1982; pp 152, 164, 165, 175, 180. 16. Douglas, B. E.; McDaniel, D. H.; Alexander, J. J. Concepts and Models of Inorganic Chemistry, 3rd ed.; Wiley: New York, 1994; pp 706, 733, 739, 748; 17. Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 5th ed.; Wiley: New York, 1988; pp 956, 957, 962, 977, 978. 18. Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry, 4th ed.; Harper Collins: New York, 1993; pp 600, 601.
Journal of Chemical Education • Vol. 78 No. 8 August 2001 • JChemEd.chem.wisc.edu
