Lessons · Precipitation

Which reactant runs out when the coefficients aren't 1-to-1?

Machine-checked — balanced, charge-conserved, extent-verified by ChemKernel Solubility rule-sourced (openstax-chemistry-2e) 3 modeling assumptions (disclosed)

30.0 mL of 0.100 M CaCl₂(aq) is mixed with 25.0 mL of 0.100 M Na₃PO₄(aq). A white precipitate of calcium phosphate forms. What mass of Ca₃(PO₄)₂ forms, which reactant limits the reaction, and which ions are left in solution? Watch the coefficients: the balanced reaction consumes calcium and phosphate in a 3-to-2 ratio, so more moles does not mean more room to react.

Mass of

\mathrm{Ca_{3}(PO_{4})_{2}}

precipitate

0.310 g

Limiting reagent

CaCl₂

Left in solution

Na₃PO₄ 0.5 mmol

Molecular equation — what you combine

3\,\mathrm{CaCl_{2}}\,\text{(aq)} + 2\,\mathrm{Na_{3}PO_{4}}\,\text{(aq)} \rightarrow \mathrm{Ca_{3}(PO_{4})_{2}}\,\text{(s)} + 6\,\mathrm{NaCl}\,\text{(aq)}

Complete ionic — every strong electrolyte shown as free ions strong-electrolyte model

3\,\mathrm{Ca}^{2+} + 6\,\mathrm{Cl}^{-} + 6\,\mathrm{Na}^{+} + 2\,\mathrm{PO_{4}}^{3-} \rightarrow \mathrm{Ca_{3}(PO_{4})_{2}} + 6\,\mathrm{Na}^{+} + 6\,\mathrm{Cl}^{-}

Net ionic — spectators cancelled, the reaction that actually happens

3\,\mathrm{Ca}^{2+} + 2\,\mathrm{PO_{4}}^{3-} \rightarrow \mathrm{Ca_{3}(PO_{4})_{2}}

Spectator ions (unchanged, still dissolved): Cl⁻ Na⁺

Verification Every claim below was proven at build time — not asserted.

✓ Atoms balance across the equation [conservation matrix]
✓ Charge balances (net ionic re-verified) [charge row]
✓ Units cancel through the dimensional chain [units engine]
✓ No amount goes negative — extent is physical [nonnegative-extent guard]

rule-sourced Ca₃(PO₄)₂ is treated as insoluble by rule insol-phosphate: “Phosphates are insoluble, except those of group 1 cations and ammonium.” (openstax-chemistry-2e).

✗ Common misconception: “The limiting reagent is whichever reactant you have fewer moles of.”

Divide each reactant's amount by its coefficient — that capacity is what runs out. CaCl₂: 3 mmol ÷ 3 = 1 mmol of reaction; Na₃PO₄: 2.5 mmol ÷ 2 = 1.25 mmol. CaCl₂ is smaller, so it limits — even though it starts with more moles (3 vs 2.5 mmol). Raw moles mislead when the coefficients differ; watch the final (mol) column.

Modeling assumptions — author-asserted, disclosed not discharged

model CaCl₂ and Na₃PO₄ are strong electrolytes and dissociate completely in water.
rule Ca₃(PO₄)₂ is treated as insoluble and precipitates completely.
model Solution volumes are additive.

Concepts in this lesson

Linked into the Chemical Atlas where an entry exists; the rest fill in as the Atlas grows.

Practice this

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