METALS: INTRODUCTION - REACTIVITY (2)
A healthily critical attitude to reactivity can be acquired from the
careful consideration of the following example of hypothesis testing.
[Li > K > Ca > Na > Mg > Al > Zn > Fe > Sn > Pb > (H) > Cu > Hg > Ag]
Quelle horreur! Hypothesis: 'Within each group of the Periodic Table, the reactivities of the metallic elements (M) increase with increasing atomic number.' Data: A. J. Bard et al., Standard Potentials in Aqueous Solutions, Marcel Dekker, New York, 1985. Results: Standard oxidation potentials derived from this source of data show that the ease of oxidation for the metallic elements of six groups is as follows. Group 1: 3Li > 37Rb 19K 55Cs > 11Na Group 2: 56Ba > 38Sr > 20Ca > 12Mg > 4Be Group 3: 57La > 39Y > 21Sc Group 11: 29Cu > 47Ag > 79Au Group 12: 30Zn > 48Cd > 80Hg Group 13: 13Al > 31Ga > 49In > 61Tl Sources of Error: Surprisingly, reference books reveal a wide variation in the numerical values of redox potentials. Nevertheless, in terms of the ordering within groups, such books are concordant with Bard et al. Conclusion: As adjudged by standard oxidation potentials, in a study limited to the elements in Periods 2 to 6, the data provide no general support for the hypothesis. Thus, Group 1 is irregular; the ease of oxidation does increase as the atomic number increases in both Groups 2 and 3 (i.e., as each group is descended): but, the ease of oxidation decreases as the atomic number increases in Groups 11, 12, and 13. However, the use of different criteria for reactivity may well provide support for this hypothesis. *
After due consideration of the above example of hypothesis testing, a student may well exclaim: "Quelle horreur! Is there no method to this madness?" The answer is yes: if, and only if, one accepts that many patterns in Chemistry are complex, and that they start to emerge only after focusing closely on the details.
Plus horreur? A preliminary insight into some of the variables which determine the reactivity of metals can be gained by placing a specific reaction type 'under the microscope'; e.g., reaction of a solid metal with an aqueous solution of acid to form a hydrated metal cation and dihydrogen gas: M(s) + H1+(aq) 覧覧覧覧覧 M1+(aq) + スH2(g) This reaction can be divided into several ergonic processes; the Table below shows typical values of these processes for four metals known to form uni-positive cations.
           Ergonic process / kJ mol-1 
   Li 
    K 
   Na 
   Ag 
 M(s) 覧覧覧覧覧 M(g)             DH1
  161 
   90 
  109 
  289 
 M(g) 覧覧覧覧覧 M1+(g) + e-       DH2
  520 
  419 
  496 
  731 
 M1+(g) 覧覧覧覧覧 M1+(aq)          DHH
 -523 
 -331 
 -419 
 -464 
 H1+(aq) + e- 覧覧 スH2(g)           DHR
 -432 
 -432 
 -432 
 -432 
 M(s) + H1+(aq) 覧 M1+(aq) + スH2(g) DH 
 -274 
 -254 
 -246 
 +124 
 DH = DHS + DH1 + DH2 + DHR, where: DH1 is the heat of sublimation;
 DH2 is the 1st ionization energy; DHH is the heat of hydration of
 the metal cation; and, DHR is the heat of reduction of the aqueous
 hydrogen ion to molecular dihydrogen.


A complete explanation of these tabulated data is well beyond the scope
of this text: but even a partial explanation should be illuminating ...
Two processes are always endothermic, the heat of sublimation (DH1) and the 1st ionization energy (DH2), whereas two are always exothermic, the heat of hydration of the metal cation (DHH) and the heat of reduction of the aqueous hydrogen ion to molecular dihydrogen (DHR). Because the value of DHR is constant, the differences in the overall heat energy change (DH) depend upon the relative magnitudes of DH1, DH2, and DHH.
The heat of sublimation reflects the strength of metallic bonding in the solid state. However, the relationship between this bonding and ground- state electronic structure of a gaseous atom is very complex indeed. Be that as it may, uniform periodicity is clearly not observed; thus, 3Li > 11Na > 19K (Group1), but 79Au > 29Cu > 47Ag (Group 11).
The 1st ionization energy is the only ergonic process which is directly related the ground-state electronic structure of a gaseous atom. Nevertheless, here also, uniform periodicity is not observed; thus, 3Li > 11Na > 19K (Group1), but 79Au > 29Cu > 47Ag (Group 11).
The heat of hydration reflects the electronic structure of the gaseous cation and its subsequent bonding with a (variable) number of water molecules to form the hydrated cation. Unfortunately, a clear statement of periodicity is precluded because, in contrast to those in Group 1, the metals in Group 11 show variable oxidation states.
And finally, ... These data would support this principle: 'high metal reactivity is favoured by a low heat of sublimation, a low ionization energy, and a high heat of hydration of the metal cation'. The overall heat energy change (DH) is negative for each Group 1 metal, and the relative magnitudes of DH parallel the measured energy changes of their reactions with water (i.e., Li > K > Na); the 'anomalous' position of lithium is attributable to the higher heat of hydration of the lithium cation. In contrast, largely because of silver's much higher ionization energy, DH is positive for this Group 11 metal; this is consistent with the observed lack of reaction between silver and dilute acid or water.
 [Scene.  A court in the state capital of Poppermania]
 Mermaid: Plus horreur! ... M'Lud ... [The judge holds up his hand.]
 Judge:   My Lord is the correct method of address, if you please.
 Mermaid: Sorry, my Lord. These results and explanations are all well
          and good: but, they can have little relevance to solid ionic
          compounds, such as chlorides, oxides, and nitrides, surely?
 Judge:   [He smiles tolerantly at this less-than-humble student.]
          I do admit, strictly speaking, only parts are; for example,
          the DH1 and DH2 terms. However, for other reactants, there
          should be analogous terms to DHH and DHR. Perhaps you would
          care to note the relationship of DHH to the lattice energy?
 Mermaid: Duly noted, M'Lud ... I mean, my Lord. Please no more ...
          My time is valuable! [She states petulantly before glancing
          briefly, but proudly, at her varnished finger-nails.]
 Judge:   Oh dear, in my day ... no, never mind. [He sighs.] Remember,
          Rome was not built in a day: although it may well have burnt
          down in one! [He glances at his fiddle before dabbing some
          eau-de-cologne on his pristine wig.] Mermaid, I ... advise
          you to spend at least part of your free-time giving the grey
          cells some aerobic exercise. [Sighs of relief from the rest
          of the synchronized-swimming team in the public gallery.]
 Mermaid: My Lord, perhaps I should emigrate to Laputa? [... but the
          venerable judge has fallen asleep (bless his silken socks).]
*  The student is encouraged, albeit gently, to consider testing this
hypothesis, or a similar one which focuses on Periods, using different 
physical data (e.g., heats of sublimation, ionization energies, energy 
changes for the formation of solid ionic compounds, ...); such data 
should be abstracted from reference books.
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