The balanced chemical reaction is written as follows:
AlCl3 + 3AgC2H3O2 = 3AgCl + Al(C2H3O2)3
We are given the volume and the concentration of the AgC2H3O2 to be used. Also, we are given the concentration of AlCl3 to be used in the reaction. These values will be the starting point of our calculations. We do as follows:
0.500 mol AgC2H3O2 / L (.020 L) ( 1 mol AlCl3/ 3 mol AgC2H3O2 ) / 0.250 mol AlCl3 / L = 0.013 L of 0.250 M AlCl3 needed or 13 mL