how-to · 5 min read
Preparing solutions from a solid or a stock solution
A solution of known concentration is prepared either by weighing a pure solid or by diluting a stronger stock solution. Both routes come down to the same relationship between concentration, volume and amount of solute, but they use it in different directions.
This guide walks through the solid route with m = C × V × M and the dilution route with C1V1 = C2V2, using 250 mL of 0.100 M NaCl and a 1.00 M to 0.100 M dilution as worked examples. It also covers the unit and lab-practice details that determine whether the prepared solution is actually the concentration on the label.
The amount of solute is the anchor
Molarity is moles of solute per liter of solution, so the amount of solute in a volume V is n = C × V. If the solute comes from a solid, that amount is weighed as a mass using its molar mass: m = n × M = C × V × M. If it comes from a stock solution, the same number of moles is taken as a smaller volume of a more concentrated solution.
On dilution the moles do not change: the stock and the final solution contain the same amount of solute, which is why C1V1 = C2V2. Keeping the solute amount as the anchor makes both routes the same calculation in different directions and gives a natural check on the units.
Preparing from a solid: worked example
To prepare 250 mL of 0.100 M NaCl, first find the moles needed: n = 0.100 mol/L × 0.250 L = 0.0250 mol. Sodium chloride has a molar mass of 22.99 + 35.45 = 58.44 g/mol, so the mass is 0.0250 × 58.44 = 1.461 g.
Weigh 1.461 g of NaCl, transfer it to a 250 mL volumetric flask, add about half the solvent and swirl to dissolve, then make up to the mark with solvent and mix. The phrase 250 mL of solution means the final volume after the solute is dissolved, not 250 mL of solvent, and the difference matters for the concentration.
Preparing from a stock: worked example
To make 250 mL of 0.100 M from a 1.00 M stock, use C1V1 = C2V2: V1 = C2V2 / C1 = (0.100 × 0.250) / 1.00 = 0.0250 L, or 25.0 mL of stock. The diluent volume is V2 − V1 = 250 − 25.0 = 225 mL, and the dilution factor is C1/C2 = 10, meaning one part stock to nine parts diluent.
Measure 25.0 mL of stock, add it to a 250 mL volumetric flask, then bring the total to the mark with diluent and mix. The order matters for concentrated acids and bases: the usual safety rule is to add the concentrated acid to water, never water to concentrated acid, and the specific lab protocol always takes precedence.
Units, glassware and significant figures
Concentrations may be given in M (mol/L) or mM (mmol/L), and volumes in L or mL. Convert everything to moles and liters before applying a formula, then convert the answer to the unit that the protocol uses. Mixing 0.100 M with 250 mL without converting the volume is a common mistake that makes the answer 1000 times too large or small.
The precision of the calculation should match the glassware. A 1.461 g mass on a balance that reads 0.001 g and a 250 mL volumetric flask support three or four significant figures; a graduated cylinder does not. Record the temperature if the solution is prepared at an unusual temperature, because the volume of the flask is calibrated at a stated temperature.
A quick unit check helps: 1 mM is 0.001 M, so 100 mM equals 0.100 M, and 250 mL is 0.250 L. Converting both concentration and volume to M and L before substituting avoids most unit mistakes, and the final answer can be converted back to milliliters for the protocol.
Lab caveats that change the answer
The arithmetic assumes pure solute and ideal volumes. If the solid has a stated assay, divide the calculated mass by the purity fraction; if the solute is a hydrate, its formula molar mass already includes the water. Volume contraction or expansion on mixing can change the final volume slightly, and the volumetric flask is only accurate at its calibration temperature.
None of this replaces the lab protocol. Always label the solution with its concentration and identity, follow the safety data sheets and local rules for the chemicals involved, and use the preparation steps appropriate to the glassware available.