Concentration and dilution calculations template

Molarity, mmol, equivalents, C₁V₁ = C₂V₂, % w/v and ppm on one card, with three worked examples: a 0.100 M solution, an acetylation set-up in mg and mL, and a stock dilution with saline in mol/L and ppm.

What the template shows

• Concentration and dilution
• The six formulas used every day at the bench, with worked examples
• Molarity: c (mol/L) = n (mol) / V (L) · n (mmol) = c (M) × V (mL)
• Moles from mass: n (mmol) = m (mg) / MW (g/mol) · neat liquid: V (mL) = m (g) / d (g/mL)
• Equivalents: n(reagent) = equiv × n(limiting reagent)
• Dilution: C₁V₁ = C₂V₂ (same units on both sides)
• % w/v = g solute per 100 mL solution (1% w/v = 10 g/L) · % w/w = g per 100 g
• ppm (dilute aqueous) = mg/L = µg/mL; ppb = µg/L · 1% w/v = 10 000 ppm
• Example 1 · make 250 mL of 0.100 M NaCl
• n = c × V = 0.100 mol/L × 0.250 L = 0.0250 mol
• m = n × MW = 0.0250 mol × 58.44 g/mol = 1.461 g NaCl; dissolve and make up to the mark in a 250 mL volumetric flask.
• Example 2 · acetylate 2.00 mmol benzylamine (limiting reagent)
• Acetyl chloride
• mmol = equiv × 2.00 mmol; mg = mmol × MW; mL = mg / (1000 × d). For Et₃N: 1.5 × 2.00 = 3.00 mmol; 3.00 × 101.19 = 303.6 mg; 303.6 / 726 = 0.418 mL.
• Example 3 · dilute a stock, and convert % w/v to M and ppm
• C₁V₁ = C₂V₂: V₁ = C₂V₂ / C₁ = (100 µM × 2.00 mL) / 10000 µM = 0.0200 mL = 20.0 µL of the 10.0 mM stock + 1.98 mL diluent.
• 0.9% w/v saline = 9.0 g NaCl per litre; 9.0 g/L ÷ 58.44 g/mol = 0.154 M; 9.0 g/L = 9000 mg/L = 9000 ppm (w/v).
• Work in mmol, mg and mL at the bench: the factors of 1000 cancel (mmol = mg / MW = M × mL).
• Base equivalents on the limiting reagent, and use the purity or titre on the bottle (e.g. 60% NaH, titrated n-BuLi).
• Weigh liquids under about 0.1 mL by mass rather than volume; syringes are least accurate at small volumes.
• Make a stock solution when you need less than about 5 mg of a reagent, then take an aliquot.
• Keep units identical on both sides of C₁V₁ = C₂V₂: 10 mM = 10 000 µM.
• Every number in the worked examples is recomputed by the template check · every part of this card is editable

Drawn with 23 atoms, 1 arrow, 9 shapes – every one editable in MolDraw.

Sources

• CRC Handbook of Chemistry and Physics, 104th ed., CRC Press 2023 Textbook