Solution Concentration
Concentration expresses how much solute is dissolved in a given amount of solution or solvent. The right unit depends on whether you're doing colligative properties, reactions, or lab dilutions.
Molarity (M)
M = n / V
n = moles of solute
V = volume of solution (L)
25g NaCl (M=58.44) in 500mL:
n = 25/58.44 = 0.428 mol
M = 0.428/0.5 = 0.856 MDilution Formula
C₁V₁ = C₂V₂
C₁ = initial concentration
V₁ = volume taken
C₂ = final concentration
V₂ = final volume
Dilute 10 mL of 6M HCl to 0.1M:
V₂ = C₁V₁/C₂ = 6×10/0.1 = 600 mL
(Add 10mL stock to 590mL water)Other Concentration Expressions
Molality: m = n / mass_solvent (mol/kg) (temp-independent)
% w/v: g solute / 100 mL solution × 100
% w/w: g solute / g solution × 100
ppm: mg solute / L solution (dilute aqueous)Calculate concentrations: Free Concentration Calculator
Concentration Units Quick-Reference Table
| Unit | Definition | Typical Use | Example |
|---|---|---|---|
| Molarity (M) | mol solute / L solution | Chemistry reactions | 1 M NaCl = 58.44 g/L |
| Molality (m) | mol solute / kg solvent | Colligative properties | 1 m glucose = 180.2 g/kg water |
| % w/v | g solute / 100 mL solution | Pharmacy, biology | 0.9% saline = 0.9 g NaCl/100 mL |
| % w/w | g solute / 100 g solution | Food, industrial | 5% acetic acid (vinegar) |
| ppm | mg solute / L (water) | Trace analysis | 1 ppm = 1 mg/L |
| ppb | μg solute / L | Contaminant limits | Lead limit: 10 ppb (WHO) |
How Concentration Works
Concentration expresses how much solute is dissolved in a given amount of solvent or solution. The most common unit in chemistry is molarity (M = n/V), convenient because balanced equations use moles. Dilution calculations use C₁V₁ = C₂V₂ — a straightforward relationship when diluting a stock solution. Serial dilutions (each step 1:10) quickly reach very low concentrations (10⁻⁶ M and below) used in microbiology and pharmacology.
In environmental science, ppm (parts per million) and ppb (parts per billion) quantify trace contaminants. In medical settings, % w/v is standard for IV fluids and drug preparations. Accurate concentration calculations prevent medication errors, ensure reproducible chemical reactions, and maintain quality control in manufacturing.
Common Mistakes
- Molarity vs. molality confusion: Molarity (M) uses volume of solution (changes with temperature); molality (m) uses mass of solvent (temperature-independent). Use molality for boiling point elevation and freezing point depression calculations.
- Forgetting units of ppm in water: For dilute aqueous solutions, 1 ppm ≈ 1 mg/L ≈ 1 μg/mL (because water density ≈ 1 g/mL). For gases or non-aqueous solutions, ppm = parts per million by volume or mass — specify which.
- Dilution direction errors: Always add concentrated acid or base to water, never the reverse — rapid heat generation in concentrated acid can cause spattering.
Frequently Asked Questions
Calculate mass: 1 mol NaCl × 58.44 g/mol = 58.44 g. Dissolve in roughly 800 mL of distilled water, then transfer to a 1 L volumetric flask and top up to exactly 1 L. Adding solid to a full litre of water would give slightly more than 1 L and underestimate the true concentration.
A serial dilution performs successive dilutions by the same factor. A 1:10 serial dilution starts at, say, 1 M, then transfers 1 mL into 9 mL solvent → 0.1 M, repeats → 0.01 M, etc. After 6 steps you have 10⁻⁶ M. This technique is used to count bacteria (colony counting), measure antibody titres, and prepare calibration curves.
0.9% w/v saline = 9 g NaCl per litre = 154 mmol/L Na⁺ + 154 mmol/L Cl⁻. This is approximately isotonic with human blood plasma (~290 mOsm/L), meaning it neither causes cells to swell (hypotonic) nor shrink (hypertonic) when infused intravenously. It is the standard IV fluid for fluid replacement and medication dilution in hospitals worldwide.