How much water is needed to prepare a.50 molar solution using 0.50 moles of sodium chloride?

  1 Litre of water

Solution:
From the question, what is known is that the molarity of the solution that is trying to be obtained is 0.5 M. So let's begin there: 
   
           ⇒   1 L of the solution contains 0.5 moles NaCl  (1)

Also, known is that the solution is being made with 0.5 moles of NaCl. What needs to be found is the amount of water that is needed to create such a solution. Let that volume of water be y

        ⇒     y L of water contain/ dissolve 0.5 moles of NaCl  (2)

Now, by combining (1) and (2):

                      1 L → 0.5 mol
                        y → 0.5 mol 
 
        ⇒    (0.5 mol) y  = (0.5 mol) (1 L)
      
        ⇒                    y = (0.5 mol · L)  ÷ (0.5 mol)

        ⇒                    y  =   1 L

Thus the amount of water needed to prepare a 0.5 M solution of NaCl is 1 Litre.