Problem 4 - Chemistry A Guided Inquiry

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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 \(1.54 \, \text{angstroms}\).

Step 3: 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.