(Polar molecules, Non-polar molecules, etc.)
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ClO2+ will be bent because the central atom chlorine has 2 bonding pairs and one lone pair so its VSEPR formula would be AX2E which corresponds to the bent shape. If the central atom had 3 bonding pairs, then it would trigonal planar but in this case there is a lone pair.
I think the more accurate shape of ClO2+ is bent, but if you were to describe it generally (without taking into account the lone pair on Cl), it would have a trigonal planar shape because there are 3 regions of electron density.
I think the solutions manual shows the shape and then the shape including all of the electronic densities ( which includes lone pairs). Be sure to read the question carefully and see whether or not the lone pairs should be accounted for when identifying the shape.
Trigonal planar would be the shape when taking into consideration the bonds AND the lone pairs, which the textbook calls the "electron arrangement" around the central atom. However, since we name shapes based only on bonds, the final answer would be bent or "angular."
Trigonal planar would be the general arrangement of the structure, because the central atom has 3 electron regions, however, since only 2/3 of those electron regions are bonded and there is one lone pair, the molecular geometry is a bent shape.
The electron geometry of ClO2+ is triganol planar since it has three regions of electron density around the central atom. The molecular geometry is bent since there is one lone pair and two bonded atoms around the central atom.
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