How to Calculate Dilution in Mixture Problems?
Dilution is the process of reducing a solution’s concentration by adding a solvent, usually water. In aptitude questions, the amount of solute generally remains constant when water is added. Use C₁V₁ = C₂V₂ to connect initial and final concentration and volume, and apply the replacement formula when part of a solution is removed and replaced.
What Is Dilution?
Here, C₁ and V₁ are the initial concentration and volume, while C₂ and V₂ are the final concentration and volume. If a solution of 20% concentration is diluted to 5%, then its volume becomes four times the original volume because V₂ = (20 × V₁) ÷ 5 = 4V₁. The volume of water added is V₂ − V₁ = 3V₁.
Dilution Video Lessons
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Dilution and Concentration Problems
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Dilution Formula & Tricks
Important Formulas
The amount of solute remains constant when solvent is added. Concentrations may be expressed as percentages, fractions or any common unit.
Use this when the initial concentration, initial volume and required final concentration are known.
This gives the quantity of solvent required after calculating the final volume.
If x units are removed from a vessel of volume V and replaced with water n times, A is the initial amount of solute.
C₀ is the initial concentration, x is the quantity removed each time and V is the constant total volume.
Quick Tricks
When only water is added, first equate the initial and final amounts of solute. This avoids calculating the amount of water separately at the beginning.
If x/V of the solution is removed each time, the fraction left after every operation is 1 − x/V. Raise this fraction to the number of operations.
Dilution Concepts
Using C₁V₁ = C₂V₂
Convert percentages to the same form on both sides. If 8 L of a 25% solution is diluted to 10%, then 25 × 8 = 10 × V₂, so V₂ = 20 L. Therefore, water added = 20 − 8 = 12 L.
Finding the quantity of water required
The direct formula is water added = V₁(C₁/C₂ − 1). This applies when the final concentration is lower than the initial concentration and the solvent is added without removing solution.
Repeated removal and replacement
For a vessel of volume V, removing x units leaves the fraction (V − x)/V of the original solute. After n operations, the remaining amount is A[(V − x)/V]ⁿ. The total volume remains V after each replacement.
Concentration expressed as a percentage
For volume-based aptitude questions, concentration percentage can be written as C = (solute volume/solution volume) × 100. When water is added, the numerator remains fixed but the denominator increases, so the percentage falls.
Dilution Data Table
Use the structured data below while following the explanation and examples.
Common dilution cases
Rules for adding water and replacing removed solution
| Case | Solute change | Useful relation |
|---|---|---|
| Water added to solution | Amount of solute remains constant | C₁V₁ = C₂V₂ |
| Water added to reach a target concentration | Amount of solute remains constant | Water added = V₁(C₁/C₂ − 1) |
| Solution removed and replaced with water | Original solute decreases each time | Remaining fraction per operation = 1 − x/V |
| n repeated replacements | Original solute is multiplied repeatedly | Remaining amount = A(1 − x/V)ⁿ |
Note: Use consistent units for all volumes. The replacement formula assumes the total volume is restored after every operation.
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Dilution Revision Points
Formulas and rules for solving dilution questions
- Dilution lowers concentration by adding solvent, usually water.
- For simple dilution, use C₁V₁ = C₂V₂.
- Water added equals final volume minus initial volume.
- Direct water formula: V₁(C₁/C₂ − 1).
- In repeated replacement, the remaining fraction per operation is 1 − x/V.
- After n replacements, original solute left is A(1 − x/V)ⁿ.
- Keep concentration units and volume units consistent.
Dilution FAQs
What is the dilution formula?
The dilution formula is C₁V₁ = C₂V₂, where C₁ and V₁ are initial concentration and volume, and C₂ and V₂ are final concentration and volume.
How much water should be added to 5 L of a 40% solution to make it 10%?
Final volume = (40 × 5) ÷ 10 = 20 L. Therefore, water added = 20 − 5 = 15 L.
What happens to the amount of solute when water is added?
The amount of solute remains unchanged, while the total volume increases. Therefore, concentration decreases.
How do you solve a dilution question when the final volume is given?
Use the initial and final solute equality: C₁V₁ = C₂V₂. If water added is required, subtract the initial volume from the given final volume.
What is the formula for repeated dilution by replacement?
If x units are removed from a total volume V and replaced with water n times, the original solute left is A(1 − x/V)ⁿ.
What is the difference between dilution and replacement?
In direct dilution, solvent is added and the original solute amount stays constant. In replacement, part of the solution containing solute is removed, so the original solute amount decreases before water is added.