on first thought, it might seem the reaction might be like that. However, sulphide ions hydrolyses readily to produce H2S, so the actual reaction mechanism is:
1. Na2S + 2H2O -> 2NaOH + H2S
2. 3NaOH + FeCl3 -> Fe(OH)3 + 3NaCl
so the overall reaction is:
3Na2S + 6H2O + 2FeCl3 -> 2Fe(OH)3 + 6NaCl + 3H2S
since water is always excess in an aqueous system, we need not consider it to be the limiting reagent. From the above equation, we can tell that 1 mole of FeCl3 reacts with 1.5moles of Na2S.
given we are considering 200ml 0.5M Na2S and 200ml 0.45M FeCl3 whereby there are 0.1mole of Na2S and 0.09mol of FeCl3, we can conclude FeCl3 is in excess and thus Na2S is the limiting reagent. Being the limiting reagent, all Na2S is consumed during the reaction. This should be the basis of your calculation for the number of moles of reactant and product present after the reaction has completed.