Process & Water Chemistry · Molarity, asked every way
One definition, three questions
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One definition, three questions

C=nVC = \dfrac{n}{V} 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. CC is the molar concentration in mol/L, nn the amount of solute in moles, and VV the volume of the finished solution in litres.

That last word is worth a paragraph. VV 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: C=nVC = \dfrac{n}{V}. Find the moles in a tank you already have: n=CVn = C V, and the litres cancel. Find the volume a duty needs: V=nCV = \dfrac{n}{C}, 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: n=mMn = \dfrac{m}{M} first, to turn the weighing into moles, then C=nVC = \dfrac{n}{V} 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.