Molarity/Dilution Calculator

Calculate mass, molarity, and dilution volumes using the M₁V₁ = M₂V₂ equation.

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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

  1. Convert volume: 500mL = 0.5L
  2. Calculate moles: M × L = 0.5M × 0.5L = 0.25 moles
  3. Convert to grams: 0.25 mol × 58.44 g/mol = 14.61g NaCl
  4. Dissolve: Add 14.61g NaCl to ~400mL water
  5. 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

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