Molarity/Dilution Calculator
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Molarity/Dilution Calculator
Calculate mass, molarity, and dilution volumes using the M₁V₁ = M₂V₂ equation.
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Last updated: August 10, 2026
Molarity & Dilution: Concentration Math
Molarity (M) = moles of solute / liters of solution. Dissolve 58.44g NaCl (1 mole) in water, add water to 1L total = 1M solution. Dilution uses M₁V₁ = M₂V₂: Take 10mL of 6M HCl, add to 50mL water = 60mL of 1M HCl (6×10 = 1×60). Moles stay constant during dilution, only volume changes.
Three common tasks: (1) Making solutions from solids (grams → moles → molarity), (2) Diluting concentrated solutions (M₁V₁ = M₂V₂), (3) Converting concentrations (M to g/L or ppm). Master these and lab prep becomes straightforward.
Molarity Formulas
Basic Molarity
M = moles / liters
moles = grams ÷ MW
grams = M × L × MW
Dilution Formula
M₁V₁ = M₂V₂
M₁ = initial concentration
V₁ = initial volume
M₂, V₂ = final values
Making Solutions: Step-by-Step
Example: Make 500mL of 0.5M NaCl solution
MW of NaCl = 58.44 g/mol
Solution
- Convert volume: 500mL = 0.5L
- Calculate moles: M × L = 0.5M × 0.5L = 0.25 moles
- Convert to grams: 0.25 mol × 58.44 g/mol = 14.61g NaCl
- Dissolve: Add 14.61g NaCl to ~400mL water
- Dilute to mark: Add water until total = 500mL
Dilution Examples
| Problem | Given | Find | Solution |
|---|---|---|---|
| Find Final Concentration | M₁=6M, V₁=10mL V₂=60mL |
M₂ = ? | 6×10 = M₂×60 M₂ = 1M |
| Find Volume Needed | M₁=12M, M₂=2M V₂=100mL |
V₁ = ? | 12×V₁ = 2×100 V₁ = 16.7mL |
| Find Final Volume | M₁=3M, V₁=25mL M₂=0.5M |
V₂ = ? | 3×25 = 0.5×V₂ V₂ = 150mL |
Key Point: Add concentrated solution to water, not water to acid (can cause violent reaction). "Do as you oughta, add acid to water."
Common Laboratory Solutions
| Solution | Molarity | g/L | Use |
|---|---|---|---|
| NaCl (Saline) | 0.9% = 0.154M | 9 g/L | Physiological saline |
| HCl (Stock) | 12M | 437 g/L | Concentrated acid |
| NaOH (Stock) | 10M | 400 g/L | Concentrated base |
| H₂SO₄ (Stock) | 18M | 1765 g/L | Concentrated sulfuric |
| Glucose | 1M | 180 g/L | Cell culture media |
Unit Conversions
Volume Conversions
- 1 L = 1,000 mL
- 1 mL = 1 cm³
- 1 L = 1 dm³
- 1 µL = 0.001 mL
Concentration Conversions
- M to g/L: M × MW
- g/L to M: g/L ÷ MW
- % w/v: (g/100mL) × 10 = g/L
- ppm: mg/L
Serial Dilutions
Making multiple dilutions from one stock
Example: 1M → 0.1M → 0.01M → 0.001M (1:10 dilutions)
| Step | Take | Add Water To | Final Concentration |
|---|---|---|---|
| 1 | 10mL of 1M | 100mL | 0.1M |
| 2 | 10mL of 0.1M | 100mL | 0.01M |
| 3 | 10mL of 0.01M | 100mL | 0.001M |
Common Mistakes & Tips
Common Errors
- Confusing mL and L (check units!)
- Adding water to acid (dangerous)
- Using wrong molecular weight
- Not dissolving before diluting to mark
- Forgetting to convert % to decimal
Best Practices
- Always use volumetric flask for accuracy
- Mix thoroughly after each addition
- Label solutions immediately
- Store in appropriate containers
- Record preparation date
Frequently Asked Questions
Molarity (M) is a measure of solution concentration expressed as moles of solute per liter of solution (mol/L). A 1 M solution contains 1 mole of dissolved substance in every liter of solution.
C1V1 = C2V2 relates the concentration and volume before and after dilution: C1/V1 are the initial concentration/volume, C2/V2 are the final concentration/volume after adding solvent. Since the moles of solute stay constant during dilution, this equation lets you solve for any one unknown given the other three.
Calculate the required mass using mass = molarity × volume (L) × molar mass, weigh out that mass of solute, dissolve it in less than the target volume of solvent, then add solvent up to the final volume mark (this is called "diluting to volume" and ensures accurate concentration).
Molarity (M) is moles of solute per liter of solution and is temperature-dependent (volume changes with temperature). Molality (m) is moles of solute per kilogram of solvent and is temperature-independent, which is why it's preferred for precise physical chemistry work like freezing-point depression.
Use C1V1 = C2V2 to find the volume of stock solution needed, then add that volume of stock to a container and dilute with solvent up to your target final volume. For example, diluting 10 mL of a 2 M stock to 1 M requires adding solvent up to 20 mL total.
The dilution formula works regardless of whether you use mL or L, as long as V1 and V2 use the SAME unit — the units cancel out in the ratio. This calculator handles the conversion automatically so you can mix units in the input fields.
A serial dilution is a series of sequential dilutions, each diluting the previous solution by the same factor (e.g., 1:10 each time), commonly used to create a range of concentrations for calibration curves or to reach very low concentrations that would be hard to measure directly.
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