Congeneric Array Interaction Algebra

Congeneric interactions follow the usual rules of array algebra:

(1 x 1) x (1 x 1)		( 1 x 1)		dot x dot		dot
(5 x 1) x (1 x 1)		( 5x 1)		series x dot		series
(4 x 4) x (1 x 1)		( 4 x 4)		planar x dot		planar
(5 x 1) x (4 x 1)		( 5 x 4)		series x series		planar
(5 x 1) x (4 x 4)		( 5 x 4 x 4)		series x planar		volume

For example, the proton x hydride ion (a dot x dot interaction) gives H2, a congeneric dot. Here is no other chemical species at all like H2 (other than its isotopic homologs D2, T2, HD, etc.):

(1 x 1) x (1 x 1)

( 1 x 1)

H+ + H–

H2

Likewise, the Group 1 cations vs. the hydride ion (a series x dot interaction) gives rise to the Group 1 saline hydrides (a series).

(H^–)   x   (Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺)     (LiH, NaH, KH, RbH, CsH)

We have already seen these interactions with the hydrogen probe experiments, but the logic can be continued to generate a range of ionic and polar covalent materials.

We shall explore three (series x series) interactions to generate corresponding congeneric planars:

• Group 1 cations (Li⁺ to Cs⁺) vs. the Period 2 anions (H3C^– to F^–)
• Group 1 cations (Li⁺ to Cs⁺) vs. the Group 17 anions (F^– to I^–)
• Group 1 cations (Li⁺ to Cs⁺) vs. the methyl to tertiary butyl carbanions

In each of these three cases, the congeneric planars are quantified with respect to the % ionic character of the formed bond as determined by the Pauling eqn., here. This bond character is colour coded.

The (5 x 1) x (4 x 4) Congeneric Array Interaction: A Congeneric Volume

The logic of congeneric array interaction can be continued to produce a congeneric volume:

(5 x 1) x (4 x 4)

( 5 x 4 x 4)

series x planar

volume

One such congeneric volume is discovered when the Group 1 cations, Li⁺ to Cs⁺, are arranged against the anionic Lewis bases of the type H3C^– , F^– and I^–.

The resulting congeneric volume has regular changing bond polarisation properties over the volume:

• Over the set of compounds, the least [Brønsted] basic compound is lithium iodide, LiI. (The iodide ion is the weakest proton abstractor because its conjugate Brønsted acid is hydrogen iodide and that is the strongest Brønsted acid.) Proton abstracting ability increases to lithium fluoride, to methyl lithium and to methyl cesium. Thus, Brønsted base strength increases over three connected vertices of the congeneric volume.
• The Li-Sn bond of LiSnH3 will be the most covalent (21% ionic) and the cesium fluoride bond will be the most ionic (89% ionic). These species are found at opposite corners of the congeneric volume.
• All the Group 1 (and Group 2) halides have excellent optical properties and can be used as lenses and prisms from the UV to infrared. Of these, cesium iodide is often the optimum material because it is able to pass infrared light of the longest wavelengths, to 70 microns, (data here).
• The density of aqueous solutions can be increased by dissolving salts, particularly the Group 1 halides. The aqueous solutions with the highest specific gravity are prepared by saturating water with cesium iodide.

© Mark R. Leach 1999-2009

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