1. Making Dilutions from Solutions
Think about what the word “dilute” means. What must be added to make a solution more dilute?

2. Making Dilutions
It is very common to make a more dilute solution by diluting a small amount of more concentrated solution (called the stock solution).
Calculations to determine the amount of concentrated solution needed are based on a simple idea: the number of moles of a solute does not change when a solution is diluted.

3. Therefore: M1V1 = M2V2 Where
M1 describes the molarity of the stock (more concentrated) solution
M2 and V2 describe the molarity and volume of the more dilute solution you’re making
V1 is unknown; it’s the amount of stock solution you have to measure out and then dilute

4. Making a dilution is also a simple process:
Determine volume of concentrated solution needed (calculate using M1V1 = M2V2) and measure in a graduated cylinder or volumetric pipet
Pour more concentrated solution into the proper size volumetric flask
Add enough distilled water to make the necessary amount of solution
Cover the volumetric flask and mix completely by inverting

5. Example
0.10 M HCl is needed for a lab. How would 250 mL of 0.10 M HCl be prepared from 6.0 M HCl stock solution?
Step 0.5 (before step 1 ) – identify your variables:
M1 = concentration of stock solution = 6.0M
V1 = volume of stock solution = unknown (what we are solving for)
M2 = goal concentration = 0.10M
V2 = goal volume = 250 mL = L

6. Example, continued 1. Solve for V1 Original equation: M1V1 = M2V2
Plug in numbers: 6.0M x V1 = 0.10M x 0.250L
Solve for unknown: V1 = L = 4.2 mL of concentrated stock solution required to make final desired solution

7. Example, continued
2. Briefly describe the process of making the solution.
Calculate the required amount of stock solution (M1V1=M2V2).
Measure out that much stock solution using a graduated cylinder or volumetric pipet.
Put stock solution in appropriate size volumetric flask.
Add distilled water to reach desired final volume.
Cover volumetric flask and mix completely by inverting.

8. Practice
0.2 M CuSO4 is needed for a lab. You have a stock solution of 1.5 M CuSO4. How much stock solution do you need to make 250 mL of the desired solution? (first identify your variables!)
M1 = 1.5 M
V1 = ??
M2 = 0.2 M
V2 = 250 mL = 0.25 L
1.5 M x V1 = 0.2 M x 0.25 L
V1 = L = 30 mL of 1.5 M CuSO4