Final answer:
To dilute a 1.5 L of a 20% w/v solution to a 12% w/v concentration, you must add 1000 mL of water to the original solution.
Step-by-step explanation:
To determine how many milliliters of water should be added to 1.5 L of a 20% w/v solution to prepare one containing 12% w/v of solute, we can use a dilution calculation assuming the mass of solute does not change. First, we calculate the mass of the solute using the initial concentration:
Mass of solute = Volume of solution × Concentration (% w/v)
= 1.5 L × 20% = 1.5 L × 0.20 g/mL
Mass of solute = 300 g (since 1 L = 1000 mL)
Next, we use the target concentration to find the final volume of the solution:
Volume of solution needed = Mass of solute / Desired concentration (% w/v)
= 300 g / 12% = 300 g / 0.12 g/mL
Volume of solution needed = 2500 mL
Finally, we subtract the initial volume from the final volume to find how much water to add:
Volume of water needed = Final volume - Initial volume
= 2500 mL - 1500 mL
Volume of water needed = 1000 mL (or 1.0 L).
Therefore, to prepare a 12% w/v solution, you must add 1000 mL of water to the 1.5 L of a 20% w/v solution.