Equivalent Weight from Molar Mass and Valence

Reactions in water happen equivalent-for-equivalent, not gram-for-gram: one charge neutralizes one charge, one H⁺ neutralizes one OH⁻. The equivalent weight is simply the mass of a species that carries one mole of that reacting capacity — molar mass divided by valence. Calcium carbonate, M = 100.087 with a divalent cation, has EW = 50.04 g/eq, which is why 50.04 turns up in every "as CaCO₃" conversion in this trade. Sulphuric acid, M = 98.08 with two replaceable protons, has EW = 49.04 g/eq, so a pound of pure H₂SO₄ neutralizes almost exactly a pound of alkalinity expressed as CaCO₃ — the near-1:1 coincidence that lets operators do acid-feed arithmetic in their heads.

The valence you divide by is the one that applies to the reaction in question, and that is where people go wrong. Sodium carbonate reacting as a base uses z = 2 (EW 53.0), but if you are counting sodium ions it behaves as z = 2 for a different reason. Bicarbonate is z = 1 (EW 61.0) in the alkalinity titration but the carbonate it came from is z = 2 (EW 30.0). Write down which reaction you mean before you pick z, and the rest of the water chemistry falls into line.