when a central atom of a molecule has 6 electron domains coming off of it (none of which are lone pairs of electrons), it is considered octahedral

The answer to this question can be determined by drawing a Lewis structure of the molecule. The S atom is central, with an O atom on each side. Adding in double bonds to each O atom and placing lone pairs on the O atoms give them each an octet, which leaves 2 more lone pairs of electrons to go on the S atom, creating a bent shape.

Molecules with three atoms around a central atom such as BF₃ are trigonal planar because electron repulsion is minimized by positioning the three attachments toward the corners of an equilateral triangle.

Multiple bonds, although they may be stronger, are not necessarily favored in a Lewis structure. It is dependent on the atoms involved. Thus, this is not a criterion used in determining a preferred Lewis structure.

In the reactant, , the carbon is bound to three hydrogens and one oxygen, and it has no lone pairs, so it has a tetrahedral geometry. In the product, , the carbon is bound to two hydrogens and one oxygen, so it must be double bonded to the oxygen in order to have a complete octet. Therefore, it has a trigonal planar geometry.

Ammonia exhibits a tetrahedral electron pair geometry. It has three bonded pairs (between nitrogen and each hydrogen), and one lone pair (on nitrogen). This combination forms a trigonal pyramidal molecular geometry.

The molecular geometry refers to the shape of the molecule's atoms, while the electronic geometry refers to the shape of the molecule's atoms and lone pair electrons. PCl₃ has a trigonal pyramidal molecular geometry and a tetrahedral electronic geometry. All other answers have no lone pairs, and therefore have the same molecular and electronic geometries.

This answer relies on remembering that ammonia has a lone electron pair in order to fill its valence shell. Without this lone pair, trigonal planar would be correct, however, since this electron pair is present, it repels the three hydrogens further away from a planar configuration. This results in a trigonal pyramidal shape.

The only answer choice that works is platinum hexafluoride. The platinum molecule is able to bind six fluorine molecules due to the availability of d orbitals in its valence shell. The octahedral shape looks like two pyramids with four sides each that have been stuck together by their bases. We can imagine the platinum at the middle with the six fluorines at each of the vertices of the pyramids. To have the octahedral shape, a molecule must have a central atom and six constituents.

In order for the five chlorine atoms around phosphorus to be distanced from one another, they will orient themselves in a trigonal bipyramidal fashion. This results in trigonal planar geometry in the x-axis. There is also one chlorine atom sticking up out of the plane, and one chlorine atom sticking down out of the plane. This results in the chlorine atoms in the trigonal planar geometry being 120^o away from each other, and the chlorine atoms in the y-axis being 90^o away from the chlorine atoms in the trigional planar geometry.