Lessons · Percent yield

Percent yield: how much of the theoretical maximum did we actually get?

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

In a gravimetric analysis, 25.0 mL of 0.100 M ZnCl₂(aq) is mixed with 20.0 mL of 0.150 M Na₂CO₃(aq); the zinc carbonate precipitate is filtered, dried, and weighed. 0.276 g of ZnCO₃ is recovered. What mass should form in theory, which reactant limits it, and what percent yield does the recovered solid represent?

Mass of

\mathrm{ZnCO_{3}}

precipitate

0.313 g

Limiting reagent

ZnCl₂

Left in solution

Na₂CO₃ 0.5 mmol

Percent yield theoretical is the ledger's maximum extent — the actual falls short

0.313 gtheoretical (max from the ledger)

→

0.276 gactually recovered

88.0%actual ÷ theoretical × 100

A real yield falls short of the theoretical maximum — side reactions, incomplete precipitation, losses on filtering — and can never exceed 100%: that would create matter from nothing.

Molecular equation — what you combine

\mathrm{ZnCl_{2}}\,\text{(aq)} + \mathrm{Na_{2}CO_{3}}\,\text{(aq)} \rightarrow \mathrm{ZnCO_{3}}\,\text{(s)} + 2\,\mathrm{NaCl}\,\text{(aq)}

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

\mathrm{Zn}^{2+} + 2\,\mathrm{Cl}^{-} + 2\,\mathrm{Na}^{+} + \mathrm{CO_{3}}^{2-} \rightarrow \mathrm{ZnCO_{3}} + 2\,\mathrm{Na}^{+} + 2\,\mathrm{Cl}^{-}

Net ionic — spectators cancelled, the reaction that actually happens

\mathrm{Zn}^{2+} + \mathrm{CO_{3}}^{2-} \rightarrow \mathrm{ZnCO_{3}}

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 ZnCO₃ is treated as insoluble by rule insol-carbonate: “Carbonates are insoluble, except those of group 1 cations and ammonium.” (openstax-chemistry-2e).

✗ Common misconception: “The limiting reagent is whichever reactant has the smaller volume.”

The smaller-volume solution (Na₂CO₃(aq), 20.0 mL) is actually in excess. Moles decide it, not volume: ZnCl₂ reaches 0 in the ledger and limits the reaction — watch the final (mol) column.

Modeling assumptions — author-asserted, disclosed not discharged

model ZnCl₂ and Na₂CO₃ are strong electrolytes and dissociate completely in water.
rule ZnCO₃ is treated as insoluble and precipitates completely (the theoretical yield).
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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