Stoichiometry

Stoichiometry is the quantitative description of the relationships between substances consumed and formed in a chemical reaction. It uses chemical formulas and balanced equations to connect amounts of reactants with amounts of products. In chemistry, stoichiometric calculations determine how much material a reaction requires, which reactant limits production, and the maximum quantity of product obtainable under specified assumptions. These relationships describe material proportions rather than the speed or mechanism of a reaction. (goldbook.iupac.org)

Balanced equations and conservation

A chemical equation identifies reactants and products, while its coefficients specify their relative quantities. Balancing requires equal numbers of atoms of every chemical element on both sides. Equations involving charged species must also conserve total electric charge. Balancing changes coefficients, not formula subscripts: changing a subscript changes the identity of the substance. (openstax.org)

For example, complete combustion of methane is represented by

One methane molecule reacts with two oxygen molecules to produce one molecule of carbon dioxide and two molecules of water. The equation conserves one carbon atom, four hydrogen atoms, and four oxygen atoms. Its coefficients express a ratio of $1:2:1:2$, not a ratio of masses. Multiplying every coefficient by the same factor leaves the reaction proportions unchanged. (openstax.org)

A balanced equation is a material-accounting statement. It does not establish that the reaction occurs under particular conditions or that the written transformation happens in a single molecular event. (goldbook.iupac.org)

Amount of substance and mass calculations

Stoichiometric ratios are usually applied through amount of substance, symbol $n$, measured in the mole. This is a base unit of the International System of Units. One mole contains exactly $6.02214076\times10^{23}$ specified elementary entities, corresponding to the fixed value of the Avogadro constant. The entities must be identified, such as atoms, molecules, or ions. (bipm.org)

A sample’s mass $m$ is converted to amount using its molar mass $M$:

For a reaction $aA+bB\rightarrow cC+dD$, the amount of $C$ associated with consumption of $A$ is

Thus, a typical mass calculation converts the known mass to moles, applies the coefficient ratio, and converts the resulting moles to the desired mass. Directly applying coefficient ratios to masses generally gives an incorrect result because different substances have different molar masses. (openstax.org)

As a calculated illustration, complete combustion of $1.00$ mol of methane requires $2.00$ mol of oxygen and produces $1.00$ mol of carbon dioxide and $2.00$ mol of water. Using approximate molar masses, these quantities correspond to $16.0$ g, $64.0$ g, $44.0$ g, and $36.0$ g respectively; total reactant and product masses agree within rounding. (openstax.org)

Limiting reactants and reaction yield

When reactants are supplied in nonstoichiometric proportions, the limiting reactant determines the theoretical maximum amount of product. Other reactants remain in excess if the limiting reactant is completely consumed by the specified reaction. Identification requires comparing available molar amounts with the equation’s coefficients, rather than simply choosing the smallest mass or mole quantity. (openstax.org)

For example, consider the same methane reaction with $1.00$ mol of methane and $1.50$ mol of oxygen. Oxygen is limiting: it permits consumption of only $0.750$ mol of methane. Assuming complete reaction along the stated pathway, the products are $0.750$ mol of carbon dioxide and $1.50$ mol of water, with $0.250$ mol of methane remaining. These values follow directly from the balanced equation. (openstax.org)

The theoretical yield is the maximum product quantity predicted from the limiting reactant. Actual yield is the quantity obtained experimentally. Their comparison gives

Incomplete reaction, competing transformations, and losses during isolation can reduce actual yield. Stoichiometry supplies the theoretical benchmark, not a guarantee of experimental recovery. (openstax.org)

Solutions and quantitative analysis

For a solution of molar concentration $c$ and volume $V$, the amount of dissolved substance is $n=cV$, with consistent units. This connects measured solution volumes to reaction ratios and forms a basis of analytical chemistry calculations. The relevant volume is the total solution volume, not merely the volume of solvent added. (openstax.org)

For reactants $A$ and $B$ with coefficients $a$ and $b$, their stoichiometric equivalence condition is

Equal reacting mole quantities therefore apply only when the coefficients are equal; a $1:2$ reaction requires twice as many moles of the second reactant. (openstax.org)

Extent of reaction and limitations

The extent of reaction, $\xi$, expresses reaction progress as a single amount-valued quantity. For a closed system undergoing one specified reaction,

where the signed stoichiometric number $\nu_i$ is negative for reactants and positive for products. This follows from $dn_i=\nu_i\,d\xi$ and depends on the normalization of the written equation. (goldbook.iupac.org)

Stoichiometry must be distinguished from chemical kinetics and reaction mechanism. Coefficients constrain relative consumption and production, but generally do not determine the exponents in an experimentally established rate law. Moreover, a single overall equation may be insufficient when side products form or intermediates accumulate: the observed relationship between substance amounts can change during the reaction. (openstax.org)