you have 57.0 mL of a 2.00 M stock solution that must be diluted to 0.500 M. how much water should you add?

since .500M is 1/4 the concentration of 2.00M, you need 4 times the volume

So add 3*57.0 = 171.0 mL of water.

To find out how much water should be added to dilute the 2.00 M stock solution to 0.500 M, you can use the dilution formula:

C1V1 = C2V2

Where:
C1 = initial concentration of the stock solution (2.00 M)
V1 = initial volume of the stock solution (57.0 mL)
C2 = final concentration of the diluted solution (0.500 M)
V2 = final volume of the diluted solution

Rearranging the formula to solve for V2:

V2 = (C1V1) / C2

Now let's substitute the given values into the formula:

V2 = (2.00 M * 57.0 mL) / 0.500 M

Simplifying the equation:

V2 = (114.0 mol/L * 0.057 L) / 0.500 mol/L

V2 = 11.4 mL

Therefore, you should add 11.4 mL of water to the 57.0 mL of the 2.00 M stock solution to achieve a final concentration of 0.500 M.