1. Dilutions
M1V1=M2V2

2. Dilutions of stock solutions are frequently used to make solutions of any desired molarity.

3. To dilute a solution means to add more solvent without the addition of more solute.

4. The solute (denoted by red disks) is concentrated in the beaker on the left. Adding water dilutes the solution as shown with the beaker on the right. However, note that although the concentration changes upon dilution, the number of solute molecules does not.

5. the number of moles of solute is the same before and after dilution
the number of moles of solute is the same before and after dilution. Since Moles = Molarity x Volume (i.e., moles= M x V) we end up with the following equation relating molarity and volume before and after dilution:
M1 x V1 = M2 x V2

6. M1V1=M2V2
“1” refers the situation before the dilution and the “2” refers to after the dilution
M refers to the molarity
V refers to the volume

7. Example #1
You have 53 ml of a 1.5 M solution of NaCl, but 0.8 M solution is needed. How many ml of solvent should you have?

8. Example #2
50 ml of a solution are diluted to a volume of 100ml. The concentration of the diluted solution is 2M. What is the concentration of the original solution?