Final answer:
The true statement about a molecule with a bond order of 1 is that it has a single bond - option b. Bond order, as described in molecular orbital and Lewis structure theories, indicates that a single bond is a pair of bonding electrons between two atoms.
Step-by-step explanation:
The statement that is true about a molecule with a bond order of one is: the molecule has a single bond (b). Bond order is defined in molecular orbital theory as one-half the net number of bonding electrons in a molecule. When using Lewis structures to describe the distribution of electrons, a single bond has a bond order of 1, which corresponds to the presence of a pair of bonding electrons between two atoms. This result agrees with molecular orbital theory where a single covalent bond containing two electrons results in a bond order of 1.
Furthermore, this bond order is an indication of bond strength, where a bond becomes stronger as the bond order increases. Therefore, a molecule with a bond order of 1 would not be as stable as molecules with bond orders of 2 or 3 (d), and the presence of a single bond does not preclude electrons in antibonding orbitals (c). Also, the formation of pi bonds and pi antibond orbitals alone does not determine the bond order (a).