How do you calculate bond lengths? and 40 Bond

How do you calculate bond lengths?

For the molecule Carbonate (CO3-2) there are 2 single bonds and 1 double bond. How do you calculate the bond lengths for these?


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Answer by Stephen McNeil
Short answer: you don't. You look them up.

Bond lengths are experimentally determined properties, not theoretical abstractions. Somebody has determined the C-O bond length in carbonate, so you look it up. Carbonate is tricky, because it's an ion, so it cannot exist by itself and the solid state C-O bond lengths will differ from compound to compound. About 130 pm is typical.

Longer answer:
Lewis theory isn't designed for the kind of quantitative rigour that would let you predict bond lengths to that kind of precision. You can determine an effective bond order between pairs of atoms, and compare that to other "typical" bond lengths, but even then it's only going to be approximate. For example, Lewis structures cannot distinguish between any two C-H bonds in any two compounds, but there are large (and systematic) variances in C-H bond lengths and strengths that other, more sophisticated theories can rationalize and even predict. But not Lewis.

Incidentally, there are NOT two single bonds and one double bond in carbonate. All three bonds are identical. Three resonance structures give you an overall resonance hybrid in which the second bond of the double bond is delocalized equally over all three O atoms, giving an effective net bond order of 1 and 1/3. You would therefore expect a bond length between that of a typical C-O single bond (like in methanol) and a C=O double bond (like in formaldehyde). And it is. C-O are usually around 143 pm and C=O are around 120. But anything more precise than that broad, qualitative reasoning is beyond the Lewis model.

And again -- you don't use theories to make blind predictions, you use theories to rationalize experimental observations. If your question is "what's the bond length in such and such a compound", the answer is always "this value, as experimentally determined by such and such a measurement", never "this, because my theory says so." The theory helps you understand WHY it's like that -- why does carbonate have three identical C-O bond lengths between those of methanol and formaldehyde? -- but not what that length is.

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