Concentration Converter
Convert between molarity, molality, ppm, ppb, mass percent, and more
Concentration Unit Definitions
Molarity (M)
M = moles solute / L solution
Temperature-dependent (solution volume changes with T)
Molality (m)
m = moles solute / kg solvent
Temperature-independent (mass doesn't change)
Mass Percent (%)
% = (mass solute / mass solution) × 100
Parts Per Million (ppm)
ppm = (mass solute / mass solution) × 10⁶
For dilute aqueous solutions: 1 ppm ≈ 1 mg/L
Parts Per Billion (ppb)
ppb = (mass solute / mass solution) × 10⁹
For dilute aqueous solutions: 1 ppb ≈ 1 μg/L
Mole Fraction (χ)
χA = moles A / total moles
Dimensionless, sum of all χ = 1
Normality (N)
N = equivalents solute / L solution
N = M × n (where n = # of H⁺, OH⁻, or charge)
Conversion Formulas
Molarity ↔ Molality
M → m:
m → M:
ρsoln = solution density (g/mL), MM = molar mass (g/mol)
Molarity → ppm
(For dilute aqueous solutions where ρ ≈ 1 g/mL)
Mass Percent → Molarity
ρsoln in g/mL, % as decimal (e.g., 10% = 0.10)
ppm ↔ ppb
Worked Examples
Example 1: Molarity to Molality
Problem: Convert 2.0 M NaCl solution (density = 1.08 g/mL) to molality.
Solution:
MM(NaCl) = 58.44 g/mol
m = (M × 1000) / (ρ × 1000 - M × MM)
m = (2.0 × 1000) / (1.08 × 1000 - 2.0 × 58.44)
m = 2000 / (1080 - 116.88)
m = 2000 / 963.12
m = 2.08 mol/kg
Example 2: Mass Percent to Molarity
Problem: Calculate molarity of 10% (w/w) H₂SO₄ solution (density = 1.07 g/mL).
Solution:
MM(H₂SO₄) = 98.08 g/mol
% = 10% = 0.10
M = (% × ρ × 10) / MM
M = (0.10 × 1.07 × 10) / 98.08
M = 1.07 / 98.08
M = 1.09 M
Example 3: Molarity to ppm
Problem: Convert 0.001 M Ca²⁺ to ppm.
Solution:
MM(Ca) = 40.08 g/mol
ppm = M × MM
ppm = 0.001 mol/L × 40.08 g/mol
ppm = 0.04008 g/L = 40.08 mg/L
40.1 ppm Ca²⁺
Quick Reference Table
| Unit | Symbol | Definition | Use Case |
|---|---|---|---|
| Molarity | M | mol/L | Reactions, titrations |
| Molality | m | mol/kg | Colligative properties |
| Mass % | % | (g/g) × 100 | Commercial solutions |
| ppm | ppm | (mg/kg) or (mg/L) | Environmental, trace |
| ppb | ppb | (μg/kg) or (μg/L) | Ultra-trace analysis |
Common Mistakes
Confusing Molarity and Molality
M uses L of solution, m uses kg of solvent!
Wrong Density Units
Density must be in g/mL for these formulas!
ppm Assumptions
ppm ≈ mg/L only for dilute aqueous solutions!
Pro Tip
Always check if you need mass of solvent or solution!