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.

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, 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.

FAQs on Dilution Formula

Question 1: What do you mean by dilution? Give one example.

Answer:

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.

 For example, adding more water to sugar syrup leads to decrease in concentration of the solution and the solution is said to be diluted.

Question 2: State dilution formula?

Answer:

Dilution formula can be expressed as follows:

M₁V₁ = M₂V₂

where,

M₁ is Initial molarity of the solution
M₂ is Molarity of solution after dilution
V₁ is Initial Volume of the solution
V₂ is Volume after dilution

Question 3: Why does a solution become less conducting when diluted?

Answer:

When a solution is diluted, the amount of solvent increases and the amount of solvent remains same. Thus the number of solute particles per unit volume of the solution decreases. The conductivity of solution is a property of solute particles, the conductivity decreases on dilution.

Question 4: Why molality is not considered a unit for concentration in the dilution formula?

Answer:

Molality is defined as the number of moles of solute per kg of solvent. In chemistry we generally deal with liquid quantity in litres and to calculate the weight of solvent in kg, we will require density of the liquid. Thus we will need to calculate the weight for each type of solvent as different solvents have different density.

Question 5: What is serial dilution?

Answer:

Serial dilution is the dilution of a solution in stepwise manner. The dilution factor in each step is a constant.

Related Resources

• Concentration of a Solution
• Difference Between Molarity and Molality
• Molar Concentration Formula