Molarity/Dilution Calculator
Molarity/Dilution Calculator
Calculate mass, molarity, and dilution volumes using the M₁V₁ = M₂V₂ equation.
Loading calculator interface...
Calculator stats
Recent Calculations
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 |
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
M = moles of solute / liters of solution
1M = 1 mole dissolved in 1 liter total volume
1. Convert grams to moles (÷ MW)
2. Convert volume to liters
3. M = moles / liters
Dilution equation: moles before = moles after
Use to find any variable when diluting solutions
1. Calculate volume needed (M₁V₁ = M₂V₂)
2. Add water to flask first
3. Slowly add acid to water (NEVER reverse!)
Concentrations: Both in M (molarity)
Volumes: Can be any unit, as long as both same (mL, L, etc.)
Water to add = V₂ - V₁
Example: 10mL acid to 60mL final = add 50mL water
M (molarity): moles/liter solution
m (molality): moles/kg solvent (different!)
No! Volumes aren't additive
Add solute to water, then dilute to 1L mark on flask
Solution too dilute - can't remove water
Must remake solution or add more solute (calculate amount needed)
% w/v means grams per 100mL
M = (% × 10) ÷ MW. Example: 5% = 50 g/L ÷ MW