Final answer:
The relationship between the two structures depends on whether they are isomers with the same molecular formula but different spatial arrangements and if they are chair conformations of the same molecule, which typically maintain consistent relative spatial arrangements.
Step-by-step explanation:
To determine whether the structures in the pair are chair conformations, we can look for specific features that define a chair conformation. In the context of organic chemistry cyclohexane, a chair conformation is a three-dimensional structure that minimizes the repulsive interactions between the hydrogen atoms and reduces ring strain compared to a planar molecule. This preferred conformation leads to a structure that looks somewhat like a recliner chair, which is why it's referred to as a "chair". Boat conformations are another possible three-dimensional shape of cyclohexane, but they're less stable due to more significant sterical hindrance.
When considering structures with isomers, these compounds have the same molecular formula but differ in their spatial arrangement of atoms. This can lead to different chemical and physical properties. If two structures are isomers, they might not necessarily be different chair conformations; they could be structural isomers, cis-trans isomers, or even conformational isomers that do not involve chair forms.
Based on the given information, if the two structures have opposite configurations with the same sequence of bonds indicating they are isomers, yet if an arrow drawn from #1 to #2 to #3 is in the same direction for both structures, this could indicate that one of them could be misassigned, possibly suggesting they are not chair conformations of the same molecule. Indeed, chair conformations are typically interconvertible flip forms of the same cyclohexane molecule and would maintain consistent relative spatial arrangements, not opposite ones.