Solved Examples on Dilution Formula
Example 1: A 10 litres solution of 5M HCl is diluted to 1M HCl solution. What is the volume of the 1M HCl solution formed?
Solution:
Given,
M1 = 5M, M2 = 1M, V1 = 10l, V2 = ?
Using dilution formula: M1V1 = M2V2
5 ×10 = 1 × V2
V2 = 50l
Thus the volume of 1M HCl formed is 50 litres.
Example 2: A person added some water to 500 ml of 10M to make a solution of 5M solutions. How much water was added to the solution?
Solution:
Given,
M1 = 10M, M2 = 5M, V1 = 0.5l
Now Using dilution formula:
M1V1 = M2V2
10 × 0.5 = 5 × V2
∴ V 2 = 1l
Thus the volume of 5M HCl formed is 1 litres but the initial volume was 500 ml.
So the amount of water added to the solution
= V 2 − V 1
= 1 − 0.5
= 0.5l
Example 3: What volume of water should be added to 1l of 2N H2SO4 needed to make it 0.5M H2SO4?
Solution:
We know that for H2SO4,
Normality = 2 × Molarity
Thus the concentration of 2N H2SO4 is 1M.
Now M1 = 1, V1 = 1, M2 = 0.5, V2 = ?
Using dilution formula we get,
M1V1 = M2V2
1 × 1 = 0.5 × V2
V2 = 2 liters
Thus 2 litres of water should be added.
Example 4: How much solution of 3M KCl is needed to make 10 litres of 2M KCl solution?
Solution:
Given,
M1 = 3, V1 = ?, M2 = 2, V2 = 10
Using dilution formula,
M1V1 = M2V2
3 × V1 = 2 × 10
V1 = 6.67 liters
Thus, 6.67 litres of 3M KCl is needed to make 10 litres of 2M KCl solution.
Example 5: A chemist added 5 litres of water to 5 litres of 5M HCl solution. What is the molarity of the resulting solution?
Solution:
Given,
M1 = 5, V1 = 5, M2 = ?
If 5l of water was added to 5l solution then V2 = 10
Using dilution formula:
M1V1 = M2V2
5 × 5 = M2 × 10
M2 = 2.5 M
Thus the molarity of the resulting solution is 2.5 M.
Dilution Formula
The concentration of a solution depends upon the amount of solute present in the solution. The higher the amount of solute, the more concentrated is the solution. Dilution refers to a decrease in the concentration of a solution. It is generally done by increasing the content of the solvent in the solution. For example, adding more water to sugar syrup leads to a decrease in the concentration of the solution and the solution is said to be diluted.
Thus we can define dilution as:
Dilution is the process of decreasing the concentration of a solution by adding more solvent to it. Dilution may also be defined as the decrease in the pH of a chemical which may be solution, vapour or a gas. Concentration is the reverse of dilution.
Note that the amount of solute does not change in the dilution and concentration process. Only the amount of solvent changes.