Reagent make-up and dilution

Reagents arrive strong and are used weak. Concentrated sulfuric acid is stored near its sale strength and diluted to a leach-feed strength; caustic comes as a concentrated solution and is let down to a dosing strength. Make-up is the routine of taking a stored strength to a working strength, and it is one of the most common calculations on a plant — done right when the units are respected, wrong when they are not.

The C₁V₁ = C₂V₂ relation

The governing relation is conservation of solute: what you dilute does not change how much reagent is present, only how much water it sits in. In concentration-and-volume terms that is C₁V₁ = C₂V₂ — the solute in the strong feed equals the solute in the diluted product. Solve it for the feed volume and you have the make-up recipe: V₁ = C₂V₂ ÷ C₁. The same balance works whether the concentrations are in g/L, molarity, or any consistent pair, provided both sides use the same unit. Where engineers slip is mixing a wt% feed with a g/L target without crossing through density first — the relation is exact, but only when C₁ and C₂ are in the same currency.

On a real circuit the arithmetic is usually done in g/L, because that is what the plant meters, and the bridge from the stored wt% to a feed g/L is the density of the concentrated reagent — the same density bridge from the concentration and density topics. So a make-up calculation is two steps: convert the stored strength to g/L using its density, then apply C₁V₁ = C₂V₂ to find the feed volume for the batch or rate you want. The worked thread below runs exactly that, from committed sulfuric-acid density nodes.

The heat of dilution

One factual boundary belongs on this page and stops there. Diluting concentrated sulfuric acid is strongly exothermic — mixing the acid into water releases a large amount of heat, enough to raise the temperature sharply and, if done wrong, to boil and spit. That heat of dilution is a real hazard boundary, and it sets why the order of addition and the dilution rate are controlled on a plant. This page states that the heat exists and is governed; it does not give a dilution procedure, and any actual make-up follows the site’s engineered method and controls, not a teaching page.

The calculator below solves C₁V₁ = C₂V₂ for any one unknown and gives the volume of diluent to add; the sulfuric-acid hub supplies the density that turns a stored wt% into the g/L the relation needs.