What the burette actually tells you
A titration is a mole count performed with a tap. You know the titrant's concentration exactly; you measure the volume it takes to reach the end point; the balanced equation converts those moles into moles of the unknown; and the aliquot volume turns that into a concentration.
, read aloud C-a equals n C-b V-b over V-a. is the analyte's concentration, the unknown you came for. is the aliquot — the volume of unknown you pipetted into the flask. is the titrant's concentration, certified on its label, and is the titre, the volume the burette delivered. Subscript a is the analyte throughout and subscript b the titrant; they never swap. And is the mole ratio, moles of analyte per mole of titrant, taken from the balanced equation. It is the one term the glassware cannot give you, and it is the one most often left out — invisible in a 1:1 reaction, and a factor of four adrift on a diprotic acid.
The two volumes only have to match each other, because they divide. Millilitres both sides is fine; one of each is the thousandfold slip.
The water trade mostly avoids the ratio by changing the counting unit instead. Normality: , where is the molarity in mol/L and is the equivalents per mole — how many protons the molecule can give up, or how many charges the ion carries. Sulphuric acid at 0.05 mol/L is 0.1 N. Normality is never smaller than molarity, because a mole supplies one equivalent or several, and never a fraction of one.
The same idea, applied to mass, is the equivalent weight: , grams per equivalent, where is the valence — the charge, or the count of replaceable hydrogens. Work it once for calcium carbonate: 100 g/mol over gives 50 g/eq. That 50 is the most quoted number in water chemistry, and it is why hardness, alkalinity and every ion in the report are converted to “as CaCO₃” — one common currency, so that a calcium and a magnesium and a bicarbonate can be added together and mean something.