In a chemical reaction, reactants that are not use up when the reaction is finished are called excess reagents. The reagent that is completely used up or reacted is called the limiting reagent, because its quantity limit the amount of products formed.
2 Au + 3 Cl2 → 2 AuCl3
(10.0 g Au) / (196.967 g Au/mol) = 0.05077 mol Au
(10.0 g Cl2) / (70.9064 g Cl2/mol) = 0.14103 mol Cl2
0.05077 mole of Au would react completely with 0.05077 x (3/2) = 0.076155 mole of Cl2, but there is more Cl2 present than that, so Cl2 is in excess and Au is the limiting reactant.
((0.14103 mol Cl2 initially) - (0.076155 mol Cl2 reacted)) x (70.9064 g Cl2/mol) = 4.60 g Cl2 left over