A colloidal solution of gold nanoparticles is prepared by reduction of $HAuCl_4$. Which of the following methods is MOST EFFECTIVE for purifying this solution from excess reactants and small ionic byproducts?

Weight of ${\rm{FeS}}{{\rm{O}}_4}\left( {{\rm{mol}}{\rm{.wt}}{\rm{.}} = 152} \right)$ oxidized by 200 mL of 1 $N$ ${\rm{KMn}}{{\rm{O}}_4}$ solution is :