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Chapter 15: Problem 4

Predict the \(\mathrm{C}-\mathrm{C}\) bond length for a molecule with a \(\mathrm{C}-\mathrm{C}\) bond order of \(1.5\).

Short Answer

Expert verified
The bond length for a \(C-C\) bond with a bond order of \(1.5\) should be between \(1.34 \, \text{angstroms}\) and \(1.44 \, \text{angstroms}\), but closer to \(1.34 \, \text{angstroms}\).

Step by step solution

01

Understand the bond lengths

A C-C single bond has a bond length of approximately \(1.54 \, \text{angstroms}\) while a C=C double bond has a bond length of approximately \(1.34 \, \text{angstroms}\) under standard conditions. Since a bond order of 1.5 lies in between a single and double bond, the bond length should also lie in between the bond lengths of a single C-C bond and a double C=C bond.
02

Approximate the bond length

An approach to estimate the bond length for a C-C bond order of 1.5 is to take an average of the bond lengths for a single bond (\(1.54 \, \text{angstroms}\)) and a double bond (\(1.34 \, \text{angstroms}\)). This gives us \(1.44 \, \text{angstroms}\) as an approximate bond length. However, since a bond order of \(1.5\) is closer to a bond order of \(2\) (a double bond), the bond length is likely closer to \(1.34 \, \text{angstroms}\) than \(1.54 \, \text{angstroms}\).
03

Make an accurate prediction

Therefore, it is reasoned that the bond length for a C-C bond with a bond order of 1.5 lies between \(1.34 \, \text{angstroms}\) and \(1.44 \, \text{angstroms}\), but likely closer to \(1.34 \, \text{angstroms}\). The exact value will depend on other atomic interactions within the molecule, but for this exercise, an approximation is sufficient.

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Most popular questions from this chapter

Experimentally, we find that all six \(\mathrm{C}-\mathrm{C}\) bonds in benzene have the same bond strength (or bond energy), \(509 \mathrm{~kJ} / \mathrm{mole}\). Is this fact more consistent with the bond orders predicted by the Lewis structure or with the calculated bond orders for benzene?

How do the calculated bond orders for benzene compare to the bond orders predicted by the Lewis structure?

How do the calculated bond orders for ethane, ethene, and ethyne compare to bond orders predicted by the Lewis structures?
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