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, V_1​ = 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.

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.