How much water must be added to 440. mL of 0.204 M HCl to produce a 0.139 M solution? (Assume that the volumes are additive.)

To answer this question, we need to use the concept of dilution. Dilution is a process of reducing the concentration of a solute in a solution by adding more solvent. The formula to calculate dilution is:

C1V1 = C2V2

Where:
C1 = Initial concentration of the solution
V1 = Initial volume of the solution
C2 = Final concentration of the solution
V2 = Final volume of the solution

In this problem, we know the following values:
C1 = 0.204 M (initial concentration)
V1 = 440 mL (initial volume)
C2 = 0.139 M (final concentration)

We need to find V2 (final volume), which represents the total volume of the solution, including the added water.

Substituting the known values into the formula:

0.204 M x 440 mL = 0.139 M x V2

Solving for V2:

V2 = (0.204 M x 440 mL) / 0.139 M

By solving this equation, we can determine the required final volume of the solution, which includes the added water.