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Also, why can some elements such as $\ce{Fe}$ have different ionic forms such as $\ce{Fe^{2+}}$ and $\ce{Fe^{3+}}$? What determines each form?

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    $\begingroup$ Although this is not an explanation, do you know about the octet rule, ionisation energies, etc? We do btw see carbocations, but they aren't very stable. $\endgroup$
    – user1160
    Commented Feb 7, 2014 at 7:28

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Boron: borates, borides. $\ce{MgB2}$ is the highest temperature BCS superconductor by a large margin.

Carbon: carbonates, carbides, hexacoordinate carbon in complexes, organolithiums, Grignard reagents, carbenium ions ($\ce{Ph3C+}$). $\ce{Al4C3}$ hydrolyzes to methane.

Silicon: silicates, aluminosilicates, silicides. Cook up silica gel in ethylene glycol plus potassium hydroxide (NOT in glass) to get pentacoordinate siliconate,

http://patentimages.storage.googleapis.com/WO1994020507A1/imgf000014_0001.png

You asked the second half in the Physics Stack.

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