So far, stoichiometry problems may have given you a mass of one reactant and asked for the mass of a product. In real labs, though, reactants are often liquids — solutions of known concentration — and you measure out a volume rather than weighing a mass. Solution stoichiometry is just regular stoichiometry with one extra first step: converting concentration and volume into moles using before you touch the mole ratio. Why is that step unavoidable? A balanced equation is a recipe written in PARTICLES: means one silver ion reacts with one chloride ion. Millilitres of solution tell you nothing about particles until you know how crowded the solute is — 10 mL of a 2.0 mol/L solution holds more solute than 100 mL of a 0.10 mol/L solution. Concentration is exactly the conversion factor that turns a volume of solution into a number of moles.
The solution-stoichiometry roadmap
The overall logic mirrors any stoichiometry problem, just with a different starting conversion. Always travel through moles: you can never apply a mole ratio to millilitres, grams or mol/L directly. The net ionic equation is often the most useful equation here, because it shows exactly which ions combine and in what ratio.
- Write and balance the chemical equation.
- Convert the given concentration and volume of the known substance into moles: .
- Use the mole ratio from the balanced equation to convert to moles of the substance you want.
- Convert those moles into whatever final unit the question asks for (mass, volume, or concentration).
Working backwards: finding an unknown concentration
The roadmap runs in either direction. Often the unknown is the concentration of a solution — how much chloride is in a well-water sample, or how concentrated a bottle of cleaning solution is. You react a measured volume of the unknown with a reagent, measure how much reacted (a mass of dried precipitate, or a volume of a solution of known concentration), convert THAT to moles, use the mole ratio to get the moles of the unknown, and finally divide by the volume of the unknown sample: . Weighing a precipitate to find an amount is called gravimetric analysis; measuring a reacting volume is the basis of titration, which you will meet at the end of this unit.
| You are given | First conversion | You are asked for | Last conversion |
|---|---|---|---|
| c and V of reactant A | n = cV | mass of product | m = nM |
| c and V of reactant A | n = cV | volume of solution B | V = n / c |
| mass of precipitate | n = m / M | concentration of reactant A | c = n / V |
| c and V of both reactants | n = cV for each | mass of product | find the limiting reagent, then m = nM |
Limiting reagent with two solutions
When two solutions react together, you can't assume both are fully used up — just like with masses, one reactant may run out first (the limiting reagent) while some of the other remains unreacted (the excess reagent). The method is the same as any limiting reagent problem: calculate the moles of product each reactant COULD produce if it reacted completely, and whichever gives the smaller amount identifies the limiting reagent (and the actual amount of product formed). An equivalent check: divide each reactant's moles by its coefficient in the balanced equation; the smaller result is the limiting reagent. For example, in \text{Pb{(NO}_3)}_2 + 2\text{KI}, mixing 0.00600 mol of each gives quotients of for lead(II) nitrate and for potassium iodide, so KI is limiting — even though the two solutions had identical volumes and concentrations. Equal moles do NOT mean equal reacting power when the coefficients differ.
Solution stoichiometry is how chemistry becomes practical dosing. A water treatment plant calculates how much alum solution to add per litre of raw water from the mole ratio of the precipitation reaction; a hospital lab finds the chloride concentration in blood serum from the volume of silver nitrate solution that reacts with it; and an environmental lab can report lead in drinking water by precipitating it and weighing the solid. In every case, adding too little leaves the target ion behind, and adding too much wastes reagent and leaves a new ion in the water — which is why the exact stoichiometric amount matters.