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.
Dilution Formula
The property that the amount of solute does not change on dilution and concentration gives us a way to calculate what the new solution volume must be to get the desired concentration of the solute. We know that the molarity of a solution is defined as the number of moles per litre of solvent.
Molarity = (moles of solute) / (Volume of Solution in liters)
M = m / V
Now this equation can be re-written as follows:
Moles of Solute = Molarity × Volume of Solution
m = M × V
As the moles of solute remains the same in the solution during dilution as well as concentration, we can say that the number of moles in the solution before and after dilution remains the same. Let M1 be the molarity of the original solution and V1 be the volume of the original solution, M2 be the molarity and V2 be the volume of the solution after dilution. As the number of moles remains constant:
M1V1 = M2V2
This equation is known as the dilution formula.
Note: In the above equation the volume of the solution before and after dilution should be in the same units.
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.