Research: Science and Education
Silver(II) Oxide or Silver(I,III) Oxide? David Tudela Departamento de Química Inorgánica, Universidad Autónoma de Madrid, 28049-Madrid, Spain;
[email protected] An article published in this Journal uses pattern recognition and simple rules to make the formulas of oxides and hydrides (1). Nevertheless, it contains a small mistake that can be used to promote a discussion on different topics of interest for the teaching of inorganic chemistry, such as coordination geometries and electron configurations, magnetic properties, thermochemical cycles and lattice energies, and ionization energies of transition metals. It is stated that Ag2O is the highest oxide of silver because AgO is a peroxide (1) and this statement needs to be corrected in two ways. On the one hand, the highest oxide of silver is Ag2O3, a well-characterized solid prepared by anodic oxidation of aqueous silver(I) solutions (2), although it is less stable than Ag2O. On the other hand, although there are many references to silver peroxide in the literature, AgO (actually Ag2O2) is not a silver(I) peroxide because it does not contain the O22– anion, but it is an oxide. Nevertheless, AgO is not a silver(II) oxide but a mixed oxidation state silver(I,III) oxide (3, 4). Coordination Geometries and Magnetic Properties of Silver Oxides Two polymorphic forms of AgO have been crystallographically characterized (3, 4) and both are actually AgIAgIIIO2 with linear coordination for Ag(I) and square-planar for Ag(III). The same coordination geometries are found for Ag(I) in Ag2O (5) and Ag(III) in Ag2O3 (6). It is interesting to correlate the coordination geometry of the silver ions in these inorganic solids with the geometry of coordination compounds and the electron configurations usually associated with linear (d10) and square-planar (d8) complexes (7). Another well-characterized silver oxide is Ag 3O4, a mixed-valence oxide with square-planar coordination for both Ag2+ and Ag3+ ions (8). Although less common than for d8 species, square-planar complexes are also found for some d9 ions such as Ag2+ (7). As far as the magnetic properties is concerned, Ag2O, Ag2O3, and AgIAgIIIO2 are diamagnetic, as expected for Ag+ (d10) and square-planar Ag3+ (d8) ions, while Ag 3O4 is paramagnetic because of the presence of Ag2+ (d9) ions (9). If AgO had been a silver(II) oxide, it would have been paramagnetic in the absence of long-range magnetic order, while if it had been a silver(I) peroxide, it would have been diamagnetic as the silver(I,III) oxide is.
While the silver oxides Ag2O, Ag2O2, Ag 3O4, and Ag2O3 are well-known, in the case of copper, Cu2O (10), Cu4O3, a mixed oxide with Cu+ and Cu2+ ions (11), and CuO (12) have been structurally characterized, and the three compounds show the same correlation between coordination geometry and electron configuration as their silver counterparts: linear for Cu+ (d10) and square-planar for Cu2+ (d9). In the case of gold, only Au2O3 has been characterized (13) and the existence of Au2O is still doubtful (9). Indeed, theoretical calculations indicate that Au2O would be thermodynamically unstable with respect to both metallic gold and Au2O3 (14). The crystal structure of Au2O3 (13) shows that it is isostructural with Ag2O3 (6) with the expected square-planar coordination for the Au3+ (d8) ions. Among the silver oxides that have been crystallographically characterized, the most surprising is probably Ag2O2, which is a mixed silver(I,III) oxide (3, 4) and not a silver(II) oxide. Thus, we may wonder why silver(II) oxide does not exist. Thermochemical cycles are useful to understand some apparently surprising facts in inorganic chemistry (15), and a thermodynamic cycle can answer the above question. The Stability of AgIAgIIIO2 Some thermodynamic properties of the mixed oxide AgIAgIIIO2 (Ag2O2) are displayed in Table 1 along with those corresponding to the single oxidation state oxides Ag2O, Ag2O3, Cu2O, and CuO (16). The data in Table 1 show that the stability of silver oxides decreases as the oxidation state increases, and both Ag2O2 and Ag2O3 are not thermodynamically stable with respect to decomposition into Ag2O and oxygen, while for copper, CuO is more stable than Cu2O. We can also see that AgIAgIIIO2 is stable towards the segregation of Ag2O and Ag2O3, because its Δ f H° and Δ f G° values are more negative than the average of those corresponding to the single oxidation state oxides. Table 1 also contains the lattice energies (Ulat) and formula unit volumes (Vm), because the discussion will be performed in the framework of “volume-based thermodynamics” (15, 17–21). From the point of view of Δ f H°, Ag2O2 is stable with respect to Ag2O and Ag2O3, because its lattice energy is higher than the average of the other two compounds.
Table 1. Thermodynamic Properties and Formula Unit Volume of Some Silver and Copper Oxides o
a
o
a
o
c
Oxide
∆fH /(kJ mol–1)
∆fG /(kJ mol–1)
S /(J mol–1)a
U lat/(kJ mol–1)b
Vm/nm3
Ag2O
–31.1
–11.2
121.3
3029
0.0526
Ag2O2
–24.3
+27.6
117.0
9421
0.0534
Ag2O3
+33.9
+121.4
100.0
15761
0.06182
Cu2O
–168.6
–146.0
93.1
3301
0.03885
CuO
–129.7
42.6
4163
0.0203
a
–157.3 b
o
c
Data taken from ref 16. Calculated from ∆fH by a thermochemical cycle (see text). Calculated from crystallographic data (3–6, 10, 12) as the ratio between the unit cell volume and the number of formula units in the unit cell.
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Research: Science and Education
Lattice energies in Table 1 have been calculated by a Born– Haber thermochemical cycle, because Δ f H° for each oxide equals the addition of the standard enthalpies of formation of the gaseous metal and oxide ions, with the appropriate coefficients, minus the lattice enthalpy. The relationship between the lattice energy Ulat and the lattice enthalpy ΔHlat has been carefully described (22) and, in the case of monoatomic ions, is expressed as
% H lat U lat
1
2 nRT
% rxnH 2U lat Ag II O U lat Ag I Ag IIIO 2 IE 3 Ag IE 2 Ag
(2)
While the ionization energies are shown in Table 2, the lattice energy of AgIAgIIIO2 is included in Table 1. Therefore, we just need to estimate the lattice energy of the hypothetical compound AgIIO. The “volume-based” thermodynamic approach usually gives good results for a broad range of ionic compounds (17–21), with eqs 3 and 4 for lattice energies smaller and higher, respectively, than 5000 kJ mol‒1
1 /3 U lat 2I B Vm C
2I U lat A I Vm
(3)
1 /3
(4)
IE1/ (kJ mol–1)b
Cu
337.4
745.5
1957.9
3554
Ag
2Ulat(AgO) 2RT
IE2/ (kJ mol–1)b
IE3/ (kJ mol–1)b
284.9
731.0
2074
3361
a
From ref 16. From ref 7.
b
where α and β are empirical coefficients appropriate for each stoichiometry (15, 21), A = 121.39 kJ mol‒1 nm, and I is the ionic strength, I = ½Σ ni zi2, where ni is the number of ions of type i and charge zi in the formula unit. The units for Ulat and Vm are kJ mol‒1 and nm3, respectively. Unfortunately, these equations do not give good results for most of the oxides included in Table 1. For example, the application of eq 3 to Ag2O, with α = 165 kJ mol‒1 nm and β = ‒30 kJ mol‒1 nm (21), gives Ulat = 2462 kJ mol‒1, 567 kJ mol‒1 (19%) lower than the value shown in Table 1. Also, the application of eq 4 to AgIAgIIIO2 gives Ulat = 7603 kJ mol‒1, 1818 kJ mol‒1 (19%) lower than the value calculated by the Born–Haber cycle. These poor agreements are probably due to the high covalent character of the oxides. For example, Ag2O has been reported to have only 20% ionicity (24). Nevertheless, although the coefficients normally used in eqs 3 and 4 do not work well for most of the oxides included in Table 1, the lattice energies of related compounds must be inversely proportional to the cubic root of the formula unit volume. Therefore, it is expected that for isostructural copper and silver oxides
U lat Ag oxide U lat Cu oxide
{
Vm Cu oxide Vm Ag oxide
1
3
(5)
If we apply eq 5 to calculate the lattice energy of Ag2O, from that corresponding to Cu2O, we get 2984 kJ mol‒1, only 45 kJ mol‒1 (1.5%) lower than the value calculated from the Born– Haber cycle (see Table 1). Consequently, we could estimate the lattice energy of a hypothetical AgIIO compound, isostructural to CuO, from the lattice energy of the copper oxide, if we can estimate its formula unit volume.
ΔrxnH
2 AgIIO(s)
2Ag2 (g) 2O2 (g)
∆Hatom/ (kJ mol–1)a
Metal
(1)
where n is the number of ions in the formula unit. On the other hand, the enthalpy of formation of the gaseous oxide ion, using the ion convention, is 950 kJ mol‒1 (21), while the enthalpy of formation of the gaseous metal ions can be calculated with the data included in Table 2. It must be taken into account that ionization enthalpies are higher than ionization energies by 5/2RT = 6.197 kJ mol‒1 at 298 K (23). In this way, Δ f H values for the gaseous cations are 1022.1, 3102.3, 6469.5, 1089.1, 3053.2, and 6613.4 kJ mol‒1 for Ag+, Ag2+, Ag3+, Cu+, Cu2+, and Cu3+, respectively, and the lattice energies for the metal oxides are those included in Table 1. To understand the existence of AgIAgIIIO2 instead of II Ag O, a thermochemical cycle for the solid-state transformation of two moles of AgIIO into AgIAgIIIO2 is shown in Figure 1. For that reaction
Table 2. Atomization Enthalpies and Ionization Energies of Cu and Ag
AgIAgIIIO2(s) Ulat(Ag2O2) 2RT
IE3(Ag) IE2(Ag)
Ag (g) Ag3 (g) 2O2 (g)
Figure 1. Thermochemical cycle for the transformation of AgIIO into AgIAgIIIO2.
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The formula unit volume of AgIIO can be estimated from the values corresponding to Ag 3O4 (AgIIAgIII2O4), 0.08985 nm3 (8), and Ag2O3, 0.06182 nm3 (6), according to
Vm AgO
Vm Ag 3O4 Vm Ag 2 O 3
(6)
If the value Vm (AgIIO) = 0.02803 nm3 is used in eq 5 with the Ulat and Vm values corresponding to CuO, we can estimate that Ulat (AgO) = 3739 kJ mol‒1. Finally, by applying eq 2, we get that ΔHlat for the solid-state transformation of two moles of AgIIO into AgIAgIIIO2 is about ‒656 kJ mol‒1, thus explaining the nonexistence of AgIIO.1 As an additional interesting exercise, students could be asked to develop a Born–Haber cycle for the transformation of silver(I) peroxide into silver(II) oxide or silver(I,III) oxide, although an accurate quantitative solution would need a reliable lattice energy for the peroxide. Ionization Energies A thermochemical cycle identical to that shown in Figure 1 can be used to understand why CuO is a stable copper(II) oxide instead of a mixed oxide CuICuIIIO2. Nevertheless, the lattice energy calculated for the hypothetical compound has a significant uncertainty because of the incertitude associated with its formula unit volume.2 In any case, when analyzing the factors responsible for the different stability of CuIIO and AgIIO, in terms of eq 2 and the data shown in Table 2, we can see that while the third ionization energy is higher for Cu, as expected, the second ionization energy is higher for Ag, that is, the ionization energy corresponding to the removal of one electron from the filled 4d subshell. Indeed, there is a frequent increase in the first and second ionization energies on going from the first to the second transition series elements (7). This fact is not often accounted for in textbooks and it can be explained by the small size of 3d orbitals that leads to a high electron repulsion for the first transition series elements, thus making it easier to remove electrons. The small size of 3d orbitals also accounts for the increased bond strength on going down a transition metal group (31). Notes 1. Of course it is the Gibbs energy, rather than the enthalpy change, that should be considered, but entropy changes are small for solid-state reactions. Indeed, the standard absolute entropy is related to the formula unit volume (25),
S°298/( J K‒1 mol‒1) = 1360 (Vm/nm3) + 15
and the formula that works well for CuO (see Table 1), gives S °298= 53 J K‒1 mol‒1 for AgO. Therefore, for the reaction shown in Figure 1, ∆S is about 11 J K‒1 mol‒1, and G about – 659 kJ mol‒1 at 298 °K. 2. The formula unit volume of CuICuIIIO2 could be estimated from the values corresponding to a series of alkali cuprates MCuO2 (26–29) and oxides M2O (30), as well as Cu2O. Nevertheless, the standard deviation is rather high because the values obtained from LiCuO2 (26, 27) and NaCuO2 (27, 28), which share the same monoclinic structure, differ significantly from those obtained from the K, Rb, and Cs salts, which have the same orthorhombic structure (28, 29).
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