$n_{OH^-}=0,5(mol)$
$n_{Al(OH)_3}=0,1(mol)$
Vì $3n_{Al(OH)_3}<n_{OH^-}$
$\to $ có muối $AlO_2^-$
$Al^{3+}+3OH^-\to Al(OH)_3$
$Al^{3+}+4OH^-\to AlO_2^-+2H_2O$
Ta có: $3n_{Al(OH)_3}+4n_{AlO_2^-}=n_{OH^-}$
$\to n_{AlO_2^-}=0,05(mol)$
$\to n_{Al^{3+}}=0,05+0,1=0,15(mol)$
Vậy dung dịch có $0,15$ mol $AlCl_3$