When one ligating group of didentate ligands (like ethylenediamine) is coordinated with a central atom, then the probability of the other ligating group being coordinated, and hence forming a chelate, is high. This is seems to be because one of the ligating groups is bound to be closer to the central atom when the other is coordinated. Does this always hold true? If so, why?
Speaking in general, when a molecule is in a "energetic" environment (in this case, for instance, the energy comes from the temperature of the room, about 298 kelvins away from the "zero energy" point), the molecule moves A LOT. It bends, rotates, and changes its conformation. When EDTA has no complexed metal, its "two arms" just keep moving randomly, until they catch a cation. When one of the arms "catches" a cation, the arms keep moving randomly. But this time, it's much more likely that the other arm will find the cation, being it so close (the cation won't move too far: the other "arm" keeps it close!). When both arms find the cation, the rigid complex is formed.
To make a stupid example, think about a person with two magnets on his hands, moving randomly in a room in the hope of capturing with both his hands a metal ball: the "first arm" has to search around all the room, but the second one only has to find the first one