Preparing a Standard Solution From Solid or Concentrated Liquid Reagent
Preparing a standard solution means two genuinely different calculations depending on what you're starting from — a solid reagent you weigh out, or a concentrated liquid reagent you dilute — and conflating the two is a common source of error.
From a solid reagent
Straightforward: calculate the mass needed, weigh it out, dissolve in less than your final volume, then bring to the exact final volume in a volumetric flask. Adding solvent to your final volume — rather than adding a fixed volume of solvent to your solute — accounts for the fact that dissolving a solid changes the total solution volume slightly.
From a concentrated liquid reagent
This is where an extra step trips people up. Commercial concentrated acids and bases (like concentrated HCl or H₂SO₄) are sold by weight percentage and density, not molarity — so you first need to calculate the stock's actual molarity before you can figure out how much to dilute.
Once you know the stock's actual molarity, the rest is a standard dilution calculation (V₁ = C₂V₂/C₁) to find how much of the concentrated reagent to measure out.
A worked example
Preparing 1 L of 1 M HCl from concentrated HCl (37% purity, density 1.19 g/mL, molar mass 36.46 g/mol):
Volume needed = (1 M × 1000 mL) / 12.08 M ≈ 82.8 mL
⚠️ Always add concentrated acid to water, never water to acid. Diluting concentrated acid is exothermic, and adding water to concentrated acid can cause dangerous, sudden boiling and splashing. Add the acid slowly to a larger volume of water instead.
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