The coordination geometry of an octahedron is determined by the number of atoms or ions that are bonded to the central atom. In the case of chromium(III) chloride crystals, the chromium atom is surrounded by six chloride ions, which gives it an octahedral coordination geometry.
However, the ratio of chromium to chlorine in the formula of chromium(III) chloride, CrCl3, is not 1:6. The formula indicates that there is one chromium atom for every three chlorine atoms, which would not produce an octahedral coordination geometry if the atoms were bonded directly to each other.
One possible explanation for this discrepancy is that the chromium and chlorine atoms are not bonded directly to each other in the crystal structure.
Instead, the chromium atom may be surrounded by a group of six chloride ions that are bonded to each other, forming an octahedron. This would allow the coordination geometry of the chromium atom to be octahedral even though the ratio of chromium to chlorine atoms in the formula is not 1:6.
Alternatively, the chromium and chlorine atoms may be bonded to each other through intermediate atoms or ions, such as water molecules.
In this case, the coordination geometry of the chromium atom would still be octahedral because it would be bonded to six chlorine atoms, even though the overall ratio of chromium to chlorine atoms in the formula would not be 1:6.
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