Stoichiometry

Stoichiometry is the branch of chemistry concerned with the quantitative relationships between reactants and products in chemical reactions. It is founded on the law of conservation of mass, which states that matter can neither be created nor destroyed, thereby requiring that the total mass of the reactants equals the total mass of the products. As a result, chemical equations must be written using whole-number ratios, known as stoichiometric coefficients, which reflect the proportional quantities of substances that participate in a reaction.
Stoichiometry enables chemists to determine how much product is formed from given quantities of reactants, or conversely, how much of one reactant is required when the amounts of other reactants or products are known. These quantitative relationships underpin much of practical chemistry, including analytical chemistry, industrial synthesis, environmental chemistry, and gas-phase studies.

Balancing the combustion of methane

A common example used to demonstrate basic stoichiometric principles is the combustion of methane. The unbalanced reaction can be written as:
CH₄ + O₂ → CO₂ + H₂O
In its unbalanced form, the equation displays a mismatch in atom counts: four hydrogen atoms occur on the reactant side but only two appear in the product, and two oxygen atoms occur in the reactants but three appear in the products. To balance the hydrogen, the coefficient of water is increased to 2, and to balance the oxygen, the coefficient of oxygen gas is increased to 2. The balanced equation is:
CH₄ + 2O₂ → CO₂ + 2H₂O
Thus, one molecule of methane reacts with two molecules of oxygen to yield one molecule of carbon dioxide and two molecules of water. This is an example of complete combustion, in which the carbon-containing fuel reacts fully with oxygen to form carbon dioxide and water without producing carbon monoxide or soot.
The coefficients in the balanced equation represent molar ratios, meaning that one mole of methane consumes two moles of oxygen and produces one mole of carbon dioxide and two moles of water. These ratios form the basis of reaction stoichiometry.

Reaction stoichiometry

Reaction stoichiometry describes the quantitative relationships among substances as they undergo chemical transformation. Using mole ratios derived from a balanced equation, chemists can calculate the extent of reaction and determine the precise amounts of reactants consumed and products formed.
In the methane combustion reaction:

• 1 mol CH₄ reacts with
• 2 mol O₂ to produce
• 1 mol CO₂ and
• 2 mol H₂O.

Because the mole is directly related to the relative atomic masses of the constituent elements, stoichiometric relationships can be converted into mass relationships using molar mass values. This application of mass–mole conversion is known as composition stoichiometry.
Stoichiometry also plays a key role in determining reaction yields, limiting reagents, and theoretical production in laboratory and industrial processes. For reactions involving gases, stoichiometric analysis may also employ the ideal gas law to relate volumes, pressures, and temperatures, an area described as gas stoichiometry.

Principles underlying stoichiometry

Stoichiometry rests on several foundational chemical laws:

• Law of conservation of mass: the mass of the reactants equals the mass of the products.
• Law of definite proportions: compounds contain elements in fixed mass ratios.
• Law of multiple proportions: when two elements form multiple compounds, the mass ratios of one element relative to a fixed mass of the other appear in small whole numbers.
• Law of reciprocal proportions: the mass proportions in which two elements combine with a third element reflect their own combining ratio.

These laws highlight the integer ratios by which atoms combine and react. Because chemical reactions consist of discrete interactions at the atomic scale, the overall reaction stoichiometry must correspond to whole numbers of reacting species.
Reactants consumed during the overall reaction are referred to as stoichiometric reactants, in contrast with catalytic substances, which participate in elementary steps yet are regenerated and not consumed overall.

Etymology and historical development

The term stoichiometry was first introduced in 1792 by Jeremias Benjamin Richter in his foundational work on the measurement of mass relationships in chemical reactions. He used the term to describe the science of quantifying the proportions in which chemical elements react. The word derives from the Ancient Greek terms meaning “element” and “measure”, reflecting its quantitative nature. Early chemists used stoichiometry to determine the composition of substances at a time when the concept of elements was still evolving; for example, compounds such as aluminium oxide were once considered elemental because they could not be further decomposed by available methods.
Stoichiometry has since become indispensable in modern chemistry, forming a bridge between atomic theory and macroscopic chemical measurements.

Moles, molar mass, and mass-to-mole conversions

A central tool in stoichiometry is the mole, defined as containing exactly one Avogadro number of entities. Each element has a characteristic atomic mass, often an average value that accounts for naturally occurring isotopes. Compounds therefore possess definite molar masses derived from the sum of the atomic masses of their constituent atoms.
Converting between grams and moles is routine in stoichiometric calculations. A typical example is determining the amount of a substance contained in a given mass. For sodium chloride:
200 g NaCl ÷ 58.44 g mol⁻¹ = 3.42 × 10⁻¹ mol
Such conversions enable quantitative analysis in both laboratory and industrial settings.

Molar proportions and balanced equations

Balanced equations express the fixed molar proportions in which reactants combine and products form. For example, in hydrogen–oxygen reactions forming water, the balanced equation:
2H₂ + O₂ → 2H₂O
shows a 2:1:2 ratio among the gaseous reactants and liquid product, allowing calculation of any one quantity given the others.
In more complex reactions such as the combustion of methanol, the molar ratio permits conversion between reactants and products. For instance, the production of water from a known amount of methanol follows directly from the relevant coefficients.
Stoichiometric compounds themselves display fixed whole-number molar proportions, such as the 2:1 hydrogen-to-oxygen ratio in water.

Determining product quantities

Stoichiometry provides a systematic method for calculating product yields. Consider the displacement reaction in which copper metal reacts with silver nitrate solution to produce silver:

1. Write and balance the equation.
2. Convert the mass of copper to moles.
3. Use the mole ratio to find moles of silver produced.
4. Convert moles of silver to mass.

Through these steps, stoichiometry quantitatively links initial reactant amounts to final product masses, provided that the reaction proceeds to completion and reagents are present in appropriate proportions.