1. Understand Percent by Mass Concentration

A 15.00% by mass aqueous solution means that 15.00 g of NaCl is present in 100 g of the solution.

2. Set up a Proportion

We know the mass of NaCl (255.0 g) and want to find the mass of the solution (let's call it 'x'). We can set up a proportion:

15.00 g NaCl / 100 g solution = 255.0 g NaCl / x g solution

3. Solve for 'x' (Mass of Solution)

Cross-multiply and solve for 'x':

15.00 g NaCl * x g solution = 255.0 g NaCl * 100 g solution

x g solution = (255.0 g NaCl * 100 g solution) / 15.00 g NaCl

x g solution = 1700 g solution

4. Calculate the Mass of Water

Since the solution is made up of NaCl and water, the mass of water is the difference between the mass of the solution and the mass of NaCl:

Mass of water = Mass of solution - Mass of NaCl

Mass of water = 1700 g - 255.0 g

Mass of water = 1445 g

Therefore, you need to add 1445 g of water to 255.0 g of NaCl to make a 15.00% by mass aqueous solution.