Table of Contents
Lab work depends on getting concentrations right - a small error can ruin an entire experiment. Molarity is the most common way chemists express concentration because it links amount of substance (moles) to volume in litres. This guide explains the core formulas (M = mol/L and M1V1 = M2V2), shows how to move between mass and moles, covers common lab and household concentrations, and gives practical examples from medicine doses, pools, and cleaners. You'll also get quick tricks and a worked example to practice.
1Molarity: Definition and core formulas
Molarity (symbol M) measures moles of solute per litre of solution: M = mol / L. It's a concentration based on amount of substance (moles), so converting mass to moles needs the molar mass (g/mol). Common companion formula: mass (g) = M (mol/L) × molar mass (g/mol) × volume (L).
The basic formula: M = mol/L
Write molarity as M = n / V where n is moles and V is solution volume in litres. Example: 0.5 mol in 1 L gives 0.5 M. If you have mmol or mL, convert first: 1 mmol = 0.001 mol, 100 mL = 0.1 L.
Mass ↔ moles conversion
To go from grams to moles: n (mol) = mass (g) / molar mass (g/mol). Then use M = n / V. For example, to prepare 0.1 M NaCl in 0.25 L: mass = 0.1 × 58.44 × 0.25 = 1.461 g (NaCl molar mass ≈ 58.44 g/mol).
2Dilutions: planning and calculations
Dilution connects a concentrated stock with the final working solution via M1V1 = M2V2. It's a conservation of moles statement: moles before dilution = moles after dilution. Use consistent units (litres) and watch decimal places.
M1V1 = M2V2 explained
M1V1 = M2V2 means (concentration of stock)×(volume of stock) = (concentration desired)×(final volume). Solve for the unknown: V1 = M2V2 / M1. Example: to make 250 mL (0.25 L) of 0.1 M from 1.0 M stock, V1 = 0.1×0.25/1.0 = 0.025 L = 25 mL of stock, then add solvent to 250 mL.
Preparing and handling stocks
Make concentrated stocks (1 M, 10× buffers) to save time. Label stock molarity and date. When measuring small V1 volumes, use calibrated pipettes; when V1 is very small (<0.1 mL) consider preparing a less concentrated intermediate stock to reduce pipetting error.
3Common lab concentrations and real-world examples
Labs and industries use a narrow set of concentrations repeatedly: 1 M, 0.1 M, 0.01 M, physiological solutions (e.g., 0.154 M NaCl), and percent w/v or v/v for household items. Knowing typical values helps spot mistakes quickly.
Typical lab and buffer strengths
Buffers and reagents often come as 1 M or 0.1 M stocks. Phosphate buffers used in biochemistry commonly are 0.01–0.1 M. Physiological saline is ~0.154 M NaCl (0.9% w/v). Agarose gels use percent w/v (0.5–2%).
Medicine, pools and cleaners (real-world)
Medicine: IV solutions and drug preparations rely on precise molarity—pharmacists convert mg doses to molarity to check stability. Pools: free chlorine is often reported in ppm; 1 ppm ≈ 1 mg/L, relevant when calculating additions from concentrated chlorine. Cleaning products: household bleach is typically 5–6% NaOCl (w/v) which labs or pool techs dilute to working levels; converting % to molarity needs density and molar mass.
4Common mistakes, quality control and a famous failure
Small unit or calculation slips break experiments. Common errors include mixing up mL and L, forgetting to convert mmol to mol, and using mass of solute without accounting for hydrate water. Implement checks and write steps before mixing.
Three frequent lab errors
1) Using mL where L is required (1000× error). 2) Confusing % w/v with molarity. 3) Pipetting tiny volumes from viscous stocks without pre-wetting tips. Each causes systematic concentration errors; cross-check with a second calculation or colleague.
A costly conversion story
The Mars Climate Orbiter (1999) was lost after a units mismatch between teams — one used imperial and the other metric. While not a molarity error, it shows how small conversion oversights can cause major failures. In a lab, similarly small calculation slips can invalidate weeks of work.
5Practical tricks, worked example and checking your math
Use mental shortcuts and a step-by-step routine to avoid mistakes: always convert to base units, write the equation, substitute numbers with units, check orders of magnitude. Keep a calculator and reference molar masses handy.
Mental math shortcuts
To move between mol/L and mmol/L: multiply or divide by 1000. Rough checks: 0.1 M of a 58 g/mol salt in 1 L is about 5.8 g (0.1×58). For ppm ≈ mg/L when density ≈ water. Halving concentration implies doubling final volume if moles constant.
Worked example: make 250 mL of 0.1 M NaCl
Step 1: Target: 0.1 M, V = 0.25 L. Step 2: mass = M × MW × V = 0.1 × 58.44 × 0.25 = 1.461 g NaCl. If starting from 1.0 M stock instead, use M1V1 = M2V2: V1 = 0.1×0.25/1.0 = 0.025 L = 25 mL stock; add water to 250 mL. Label and mix thoroughly.
Pro Tips
- 1Always convert volumes to litres and amounts to moles before plugging into M = mol/L.
- 2Quick mass formula: mass (g) = M (mol/L) × molar mass (g/mol) × volume (L).
- 3For dilution: V1 = M2 × V2 / M1 — if V1 is tiny, make an intermediate stock to reduce pipetting error.
- 4Use ppm ≈ mg/L for dilute aqueous solutions; 1 ppm ≈ 1 mg/L when density ≈ 1 g/mL.
Understanding molarity and dilution math keeps experiments reproducible and helps you spot errors before they happen. Keep the two simple formulas M = mol/L and M1V1 = M2V2 front of mind, and always convert units to base SI (mol, L). Try the related converters on this site (grams ↔ moles, litres ↔ millilitres) when you plan a solution. Doing a quick conversion check will save time and materials, and help avoid expensive mistakes.
