Final answer:
A molecular shape with the formula AX₂E₃ is linear due to two bonding pairs and three lone pairs of electrons. The lone pairs occupy equatorial positions in a trigonal bipyramidal arrangement, resulting in the bonding pairs aligning linearly with 180° angles.
Step-by-step explanation:
The molecular shape described by the formula AX₂E₃ consists of two bonding pairs (AX₂) and three lone pairs (E₃) around a central atom, which results in a linear molecular geometry. This is because the lone pairs occupy the equatorial positions in what would otherwise be a trigonal bipyramidal structure, leading to the absence of bonding pairs in these positions. Consequently, the two bonding pairs align linearly with the central atom at an angle of 180°. In this configuration, all lone pair repulsions (LP-LP and LP-BP) are minimized, as the lone pairs are in the arrangement that is furthest apart from each other, and the linear shape minimizes repulsions between the bonding pairs and the lone pairs.