Dilution
Diluting a solution means adding solvent. The amount of solute stays the same, but it is spread through a larger volume, so the concentration drops.
Because the moles of solute do not change, and moles = M × V:
M1 × V1 = M2 × V2
The 1 values describe the concentrated starting solution and the 2 values describe the diluted one. The volumes can be in any unit as long as both use the same one.
Worked example: diluting an acid
What volume of 12.0 M HCl is needed to make 500 mL of 3.00 M HCl?
M1 × V1 = M2 × V2
12.0 M × V1 = 3.00 M × 500 mL
V1 = 1500 M·mL ÷ 12.0 M = 125 mL
Measure out 125 mL of the concentrated acid and add water until the total volume is 500 mL.
Common mistake
Reading V2 as the volume of water added. V2 is the final total volume. In the example, the water added is 500 - 125 = 375 mL.