Quick Answer
The dilution equation is C₁V₁ = C₂V₂. To make 250 mL of a 2 M solution from a 10 M stock, you need V₁ = 2 × 250 ÷ 10 = 50 mL of stock, then add 200 mL of solvent to reach 250 mL.
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Table of Contents
- Dilution Calculator
- Quick Answer
- Related Calculators
- How This Dilution Calculator Works
- How to Use the Dilution Calculator
- Core Formulas
- Key Terms
- Worked Example
- Real-Life Examples
- Dilution Factor vs Dilution Ratio
- Stock Needed for 100 mL
- Tips for Accurate Dilutions
- Common Mistakes to Avoid
- Frequently Asked Questions
- References & Sources
How This Dilution Calculator Works
Choose the value you want to find, then enter the other three. The calculator rearranges C₁V₁ = C₂V₂, converts the volumes to the same unit, and solves. It also shows how much solvent to add and the dilution factor, so you know exactly how to mix the solution.
Quick explanation: diluting adds solvent but keeps the amount of solute the same.
- C₁ and V₁: the stock solution’s concentration and the volume you take.
- C₂ and V₂: the final concentration and total volume.
- Same solute: C × V stays the same before and after.
How to Use the Dilution Calculator
- Choose which value to solve for.
- Enter the other three values.
- Choose a unit for each volume.
- Press Calculate.
- Read the answer, the solvent to add and the dilution factor.
Core Formulas
- Dilution equation: C₁V₁ = C₂V₂
- Stock volume: V₁ = C₂V₂ ÷ C₁
- Final concentration: C₂ = C₁V₁ ÷ V₂
- Solvent to add: V₂ − V₁
- Dilution factor: C₁ ÷ C₂ = V₂ ÷ V₁
Why it works: the amount of solute is concentration × volume. When you add only solvent, the amount of solute does not change, so the product before mixing, C₁ × V₁, must equal the product after mixing, C₂ × V₂. That is why you can solve for any one of the four values when you know the other three. The two volumes just need to be in the same unit before you divide, which the calculator handles for you.
Key Terms
- Stock solution: a concentrated solution used to make weaker ones.
- Solute: the substance dissolved in a solution.
- Solvent: the liquid that dissolves the solute, often water.
- Concentration: the amount of solute per volume, such as mol/L (M).
- Serial dilution: a series of dilutions, each made from the one before.
Worked Example
You have a 1 M salt solution and need 500 mL at 0.1 M.
- V₁ = 0.1 × 500 ÷ 1 = 50 mL of stock
- Solvent = 500 − 50 = 450 mL
- Dilution factor = 1 ÷ 0.1 = 10×, or a 1:10 dilution
Real-Life Examples
- Lab work: make 100 mL of 0.5 M HCl from 6 M stock: about 8.33 mL of stock.
- Cleaning: dilute a 12% concentrate to 3%: 1 part concentrate to 4 parts total.
- Plant food: mix a liquid fertilizer at the label’s strength from a concentrate.
- Serial dilutions: repeat a 1:10 dilution to go from 1 M to 0.001 M in three steps.
Dilution Factor vs Dilution Ratio
- Dilution factor: final volume ÷ stock volume, such as 10×.
- 1:10 (part to whole): often means 1 part stock in 10 parts total.
- 1:9 (part to part): 1 part stock plus 9 parts solvent, which is the same 10× dilution. Check which style a recipe uses.
Stock Needed for 100 mL
| Dilution factor | Stock volume | Solvent to add |
|---|---|---|
| 2× | 50 mL | 50 mL |
| 4× | 25 mL | 75 mL |
| 5× | 20 mL | 80 mL |
| 10× | 10 mL | 90 mL |
| 20× | 5 mL | 95 mL |
| 50× | 2 mL | 98 mL |
| 100× | 1 mL | 99 mL |
Tips for Accurate Dilutions
- Add solvent up to the final volume in a volumetric flask, rather than adding a measured amount, for the best accuracy.
- Keep units the same for C₁ and C₂.
- For acids, add acid to water, not water to acid, for safety.
- Mix well before using the final solution.
Common Mistakes to Avoid
- Adding V₂ of solvent. V₂ is the total final volume, not the solvent amount.
- Mixing concentration units. Use the same unit for C₁ and C₂.
- Trying to concentrate. Adding solvent can only lower the concentration.
- Confusing 1:10 styles. Part to whole and part to part differ.
- Ignoring volume changes. Some liquids, like alcohol and water, shrink slightly when mixed.
Frequently Asked Questions
C₁V₁ = C₂V₂, where C is concentration and V is volume, before and after.
V₁ = C₂ × V₂ ÷ C₁.
Add solvent to make the total volume V₂. That is V₂ − V₁.
Any concentration unit, as long as C₁ and C₂ match. Volumes can be in mL, L, µL, fl oz or gallons.
Usually 1 part stock in 10 parts total, a 10× dilution.
Yes, if both concentrations are in percent.
Yes. Enter molarity (M) for both concentrations.
Diluting only adds solvent, so the solution gets weaker, never stronger.
How many times weaker the final solution is, C₁ ÷ C₂.
Dilute, then dilute the result again by the same factor. Each step multiplies the factor.
Volumes change slightly with temperature. For precise work, measure at the same temperature.
No. Mixing two solutions of different strengths needs a different formula.
References & Sources
| Source | Used For | Link |
|---|---|---|
| Chemistry LibreTexts, Dilution | How to use M₁V₁ = M₂V₂ and make dilutions. | https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(LibreTexts)/13%3A_Solutions/13.07%3A_Solution_Dilution |
| Wikipedia, Serial dilution | Step-by-step dilutions and dilution factors. | https://en.wikipedia.org/wiki/Serial_dilution |