Chemistry · General chemistry I · Concept

Stoichiometry and theoretical yield

Stoichiometry predicts how much product a reaction can form. Convert each given mass to moles, use the mole ratio from the balanced equation, then convert back to grams; when two reactants are given, the one that runs out first sets the theoretical yield.

Start with the reaction, then use the quantities

Stoichiometry connects amounts of reactants and products through a balanced chemical equation. Before calculating a yield, establish which reaction you are modeling and check that atoms are conserved. For pure calcium carbonate reacting with aqueous hydrochloric acid, we use the reaction below.

{CaCO}_{3} (s) + 2 HCl (aq) \to {CaCl}_{2} (aq) + H_{2} O (l) + {CO}_{2} (g)

Check atoms in the balanced reaction
Element	Reactant side	Product side
Ca	1	1
C	1	1
O	3	3
H	2	2
Cl	2	2

Read the coefficients as mole ratios

The coefficient 2 before HCl means that one mole of CaCO₃ requires two moles of HCl. The understood coefficient 1 before CO₂ means one mole of CaCO₃ can produce one mole of CO₂. These are ratios of amounts in moles, not ratios of masses in grams.

\frac{2 mol HCl}{1 mol {CaCO}_{3}}, \frac{1 mol {CO}_{2}}{1 mol {CaCO}_{3}}

Why must we balance before calculating?

Changing a coefficient changes how many formula units take part. Changing a subscript changes the substance itself. Balance with coefficients while keeping CaCO₃, HCl, CaCl₂, H₂O and CO₂ chemically unchanged. The coefficients then provide the conversion ratios.

Use molar mass to move between grams and moles

A balanced equation relates mole amounts, so an amount given in grams is divided by its molar mass first. CaCO₃ has one calcium, one carbon and three oxygens. Moles, molar mass and Avogadro’s number covers these conversions in full.

M ({CaCO}_{3}) = 40.08 + 12.01 + 3 (16.00) = 100.09 g/mol

Find which reactant runs out first

When two reactant amounts are given, the one that runs out first limits the product. Divide each amount in moles by its coefficient: the smallest value belongs to the limiting reactant. Limiting reactant and percent yield works a full example.

reaction extent = min (\frac{n ({CaCO}_{3})}{1}, \frac{n (HCl)}{2})

Convert the allowed product amount into the requested unit

Once the limiting amount is known, use the product coefficient to find moles of product. Multiply by the product’s molar mass to obtain grams. Carry units through the factors so you can see each connection.

m ({CO}_{2}) = n ({CO}_{2}) M ({CO}_{2})

Explain what theoretical yield means

Theoretical yield is the maximum predicted by the stated reaction and available reactants. It assumes complete conversion with no competing reaction. Actual recovered product may be lower because of incomplete reaction or collection losses. A chalk sample can also contain substances other than CaCO₃; this example explicitly assumes pure calcium carbonate.

What if actual yield is measured?

Percent yield compares a measured actual yield with the theoretical yield for the same product; Limiting reactant and percent yield works an example. Do not substitute a theoretical prediction for an experimental measurement.

percent yield = \frac{actual yield}{theoretical yield} \times 100 %

Common mistakes

Using gram ratios directly from reaction coefficients.
Assuming a reactant is in excess without checking its amount.
Reporting theoretical yield as if it were an experimental result.

Key terms

Limiting reactant: The reactant that runs out first. It sets the most product the reaction can make; the other reactants are left over, in excess.
Theoretical yield: The most product a reaction can make, calculated from the limiting reactant, assuming the reaction goes to completion with no losses or side reactions.
Molar mass: The mass of one mole of a substance, in g/mol. It converts between grams and moles: moles = mass ÷ molar mass.
Mole ratio: A ratio of moles of two substances taken from the coefficients of a balanced equation, such as 2 mol H₂ : 1 mol O₂. It converts moles of one substance into moles of another.

Work through an example

Model 5.00 g of pure CaCO₃ with 0.200 mol HCl. What is the theoretical mass of CO₂?

Theoretical yield of CO₂ from CaCO₃ and HCl →

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