#### Answer

$\left[\mathrm{AlCl}_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\right]-$ is the only possibility for a six-coordinate complex that does not conduct electricity and results in no precipitate with $\mathrm{AgNO}_{3}(\mathrm{aq}) .$
There are three possible four-coordinate complexes: $\left[\mathrm{AlCl}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\right] \mathrm{Cl}_{2}$ $\left[\mathrm{AlCl}_{2}\left(\mathrm{H}_{2} \mathrm{O}\right)_{2}\right] \mathrm{Cl} \cdot \mathrm{H}_{2} \mathrm{O},$ and $\left[\mathrm{AlCl}_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)\right] \cdot 2 \mathrm{H}_{2} \mathrm{O} .$ The first two of which can be distinguished by conductivity measurements, where the first is the better conductor. The third cannot be differentiated from the $\left[\mathrm{AlCl}_{3}\left(\mathrm{H}_{2} \mathrm{O}\right)_{3}\right]-$ by Werner's method.

#### Work Step by Step

See answer above.