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Sulfur trifluoride is a radical, meaning it has an unpaired electron. It is an extremely reactive and unstable compound and as such only fleetingly exists in nature. As a result, its actual molecular geometry has not been experimentally determined so we can only operate on the theoretical level here. Sulfur has 6 valence electrons and fluorine has 7 valence electrons. So the sulfur will share a single bond with all 3 of the fluorine atoms. This leaves 6-3=3 valence electrons in the sulfur left to account for. Two if them will be a lone pair, thus leaving a single unpaired electron (the radical as previously mentioned). This would probably give SF3 as a sp2d2 hybridized compound with the three fluorines in a trigonal plane around the central sulfur, a lone pair on one side of the plane, and the radical on the opposite side of the plane.
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