Final answer:
A molecule with the general formula AX2E3, according to VSEPR theory, will have a linear molecular shape because three lone pairs occupy the equatorial positions of a trigonal bipyramidal structure, leaving the two bonded atoms in axial positions at 180 degrees to each other.
Step-by-step explanation:
According to Valence Shell Electron Pair Repulsion (VSEPR) theory, the molecular shape of a compound is determined by the repulsive forces between electron pairs around the central atom. For a molecule with the general formula AX2E3, where 'A' is the central atom, 'X' is a bonded atom, and 'E' is a lone pair of electrons, the basic electron group geometry would be that of a trigonal bipyramidal structure.
However, with three lone pairs (E3), these pairs will occupy the equatorial positions of the trigonal bipyramid because these positions afford more space, reducing electron pair repulsion. Thus, the two bonded atoms (X2) will be located in the axial positions, leading to a linear molecular shape. The molecules with a linear shape minimize the repulsion between electron pairs as this arrangement places them at 180 degrees from each other. An example of such a molecule is Xenon difluoride (XeF2), which also adopts a linear shape due to the presence of three lone pairs on the central xenon atom occupying equatorial positions.