How do you calculate dilution using M₁V₁ = M₂V₂?

Short Answer

Dilution using the formula M₁V₁ = M₂V₂ means calculating the new concentration or volume of a solution after adding solvent. Here, M₁ and V₁ are the initial concentration and volume, while M₂ and V₂ are the final concentration and volume after dilution.

To calculate dilution, rearrange the formula depending on what is needed. For example, if you want the volume required for dilution, use V₁ = (M₂V₂) ÷ M₁. This formula helps prepare accurate solutions in laboratories and industries.

Detailed Explanation

Calculation of Dilution Using M₁V₁ = M₂V₂

The formula M₁V₁ = M₂V₂ is one of the most common equations used in chemistry to perform dilution calculations. It helps determine how much of a concentrated solution (called a stock solution) is needed to prepare a weaker or less concentrated solution. This method is important in preparing solutions for experiments, medicines, chemical manufacturing, and many laboratory procedures.

The formula ensures that the total amount of solute remains the same during dilution. When solvent is added, the concentration decreases, but the solute does not change. The relationship between initial and final concentration and volume is expressed through this equation.

Meaning of each term in the formula

  • M₁: Initial molarity (concentration before dilution)
  • V₁: Initial volume taken from the stock solution
  • M₂: Final molarity (concentration after dilution)
  • V₂: Final volume of solution after adding solvent

The formula is based on the idea that:

Amount of solute before dilution = Amount of solute after dilution

Because molarity × volume gives the number of moles of solute, the equation becomes:

M₁V₁ = M₂V₂

This means the moles of solute remain constant during dilution.

How to use the formula step by step

Performing a dilution calculation requires only three known values. The fourth value is calculated using the dilution formula. Below are the steps:

Step 1: Identify the known values

You will be given three of the following:

  • Initial molarity (M₁)
  • Initial volume (V₁)
  • Final molarity (M₂)
  • Final volume (V₂)

Choose the appropriate rearranged formula depending on what you need to find.

Step 2: Rearrange the equation if needed

Examples:

To find V₁:
V₁ = (M₂ × V₂) ÷ M₁

To find M₁:
M₁ = (M₂ × V₂) ÷ V₁

To find V₂:
V₂ = (M₁ × V₁) ÷ M₂

To find M₂:
M₂ = (M₁ × V₁) ÷ V₂

Step 3: Substitute values and calculate

Insert the known values into the equation and solve for the unknown.

Examples to understand dilution formula

Example 1: Finding V₁ (how much stock solution to take)

How many millilitres of a 2 M stock solution are needed to prepare 500 mL of a 0.5 M solution?

M₁ = 2 M
V₁ = ?
M₂ = 0.5 M
V₂ = 500 mL

Use V₁ = (M₂V₂) ÷ M₁

V₁ = (0.5 × 500) ÷ 2
V₁ = 250 ÷ 2
V₁ = 125 mL

This means you need 125 mL of the stock solution, and then add water until the total volume becomes 500 mL.

Example 2: Finding M₂ (new concentration after dilution)

If 50 mL of a 1 M solution is diluted to 200 mL, what is the final concentration?

M₁ = 1 M
V₁ = 50 mL
V₂ = 200 mL
M₂ = ?

Use M₂ = (M₁V₁) ÷ V₂

M₂ = (1 × 50) ÷ 200
M₂ = 50 ÷ 200
M₂ = 0.25 M

Example 3: Finding V₂ (final volume needed)

If you want to dilute 10 mL of 3 M acid to a concentration of 1 M, what is the final volume?

M₁ = 3 M
V₁ = 10 mL
M₂ = 1 M
V₂ = ?

Use V₂ = (M₁V₁) ÷ M₂

V₂ = (3 × 10) ÷ 1
V₂ = 30 mL

This means water must be added until the total volume reaches 30 mL.

Why this dilution formula works

The formula works because dilution does not change the number of moles of solute. Only the solvent quantity changes. Therefore, the product of molarity and volume (which represents moles) should be equal before and after dilution.

This principle helps create precise solutions for:

  • Chemical reactions
  • Titrations
  • Medical preparations
  • Laboratory experiments
  • Industrial processes

Practical uses of dilution

  1. Preparing laboratory solutions:
    A strong stock solution is diluted to obtain required concentrations.
  2. Medical dosage adjustments:
    Strong drug solutions are diluted for safe administration.
  3. Cleaning and disinfection:
    Disinfectants and acids are diluted before safe use.
  4. Food and beverage industry:
    Juices, syrups, and flavours are diluted to required strengths.
  5. Environmental studies:
    Water and soil samples are diluted before testing pollutant levels.

Important points to remember

  • Always add solvent to reach the final volume (do not add volume directly).
  • Use consistent units—convert mL to L if required.
  • Mix well after dilution.
  • The solute amount remains constant.
Conclusion

Dilution using the formula M₁V₁ = M₂V₂ allows us to calculate how the concentration of a solution changes when solvent is added. It ensures that the number of moles of solute remains the same before and after dilution. By identifying the known values, rearranging the equation, and substituting the numbers, accurate dilution calculations can be easily performed. This method is essential in laboratories, medicine, industry, and many scientific fields.