One definition, three questions
is a definition, not a discovery — and definitions are the most useful relations you own, because they can be read in any direction without asking permission. is the molar concentration in mol/L, the amount of solute in moles, and the volume of the finished solution in litres.
That last word is worth a paragraph. is not the water you added; it is the volume of everything in the vessel once the solute is in and dissolved. On a plant tank filled to a mark the distinction rarely bites, and in a volumetric flask it is the entire discipline of the technique: dissolve first, then make up to the mark.
Three questions, one relation. Find the strength: . Find the moles in a tank you already have: , and the litres cancel. Find the volume a duty needs: , and read its shape — double the stock strength and the draw halves. That single line is why concentrated product is worth paying freight on.
When a batch starts from dry solid, two relations run in series and the order is not negotiable: first, to turn the weighing into moles, then to spread those moles through the tank. Skipping the first step is how a tank ends up labelled in kilograms per litre, which is a real unit and not the one the method calls for.
And keep the sanity check close: on a plant, working concentrations are mostly between 0.01 and a few mol/L. An answer of 300 mol/L is not a strong solution — it is a decimal point that got out.