What is a Stoichiometric Coefficient?

Have you ever looked at a chemical equation and noticed the numbers preceding the chemical symbols? These numbers are essential for understanding the stoichiometry of a reaction.

In this article, you'll learn:

• What stoichiometry in chemistry is;
• What a stoichiometric coefficient is; and
• An example of a stoichiometric reaction.

Ready to understand how and where the stoichiometric coefficient plays a vital role in chemistry? Keep reading or head over to our chemical equation balancer!

In chemistry, stoichiometry, from the ancient Greek στοιχεῖον (stoikheîon, "element") and μέτρον (metron, "measure"), is a method used to analyze the quantities of reactants and products involved in a chemical reaction. It also describes the quantitative ratios of elements in chemical formulas. In other words, answering what stoichiometry is in chemistry means understanding how chemical equations relate quantities of substances to one another.

During a chemical reaction, changes occur in the substances present: some substances are consumed, known as "reactants", while other substances are formed, referred to as "products". On a microscopic scale, a chemical reaction is a change in the bonds between atoms, caused by the movement of electrons: some bonds are broken, others are formed, but the atoms themselves are conserved. This is known as the law of conservation of mass, which is expressed by two principles:

• The conservation of the number of atoms of each chemical element; and
• The conservation of overall charge.

The stoichiometric relationships between the quantities of reactants consumed and products formed follow directly from the principles of conservation of mass. They are determined from the balanced chemical equation of the reaction.

What is a chemical reaction equation?

Before diving into what a stoichiometric coefficient is, you need to understand what a stoichiometric equation (or, balanced chemical reaction equation) is. In short, it's an expression specifying the chemical formulas of the reactants, those of the products, and the proportions in which the reactants and products are involved:

where:

• ${\displaystyle \mathrm {R} _{1},\mathrm {R} _{2}}, ...$ — Chemical formulas of the different reactants;
• ${\displaystyle r_{1},r_{2}}, ...$ — Number of entities (molecules or moles, for example) of the reactants involved in the reaction;
• ${\displaystyle \mathrm {P} _{1},\mathrm {P} _{2}}, ...$ — Chemical formulas of the different products; and
• ${\displaystyle p_{1},p_{2}}, ...$ — Number of entities of the products resulting from the reaction.

When the reaction can occur in both directions, and in particular when the reactants and products are in equilibrium, the arrow ${\displaystyle \rightarrow }$ is replaced by the double arrow ${\displaystyle \rightleftharpoons }$:

What is a stoichiometric coefficient?

When writing the balanced equation for a chemical reaction, it must adhere to the principles of mass conservation. To comply with these rules, a number called a stoichiometric coefficient must be placed in front of the chemical formula of each chemical species, indicating the proportions between the species involved and those formed. These are therefore dimensionless numbers that should not be confused with a quantity of matter. The reaction equation is independent of the amount of matter. Still, it allows the quantities of matter after the reaction to be calculated if the actual amounts involved at the start are known.

Example: The formation of water is a classic example of a stoichiometric reaction, where reactants combine in exact proportions defined by their stoichiometric coefficients.

The stoichiometric coefficient for $\mathrm{H_2}$ (hydrogen gas) is 2, for $\mathrm{O_2}$ (oxygen gas) is 1 (since no number is explicitly written, it is assumed to be one) and the stoichiometric coefficient for $\mathrm{H_2O}$ (water) is 2.

These coefficients tell us that 2 moles of $\mathrm{H_2}$ react with 1 mole of $\mathrm{O_2}$ to produce 2 moles of $\mathrm{H_2O}$.

As you can see from the example above, each stoichiometric coefficient defines the fixed numerical relationship between reactants and products in a stoichiometric reaction.

Need help balancing?

Balancing complex chemical equations can sometimes be tricky! If you're struggling to find the correct stoichiometric coefficients for your stoichiometric equation, you can check our article entitled "How do you balance chemical equations?"

When methane ($\mathrm{CH_4}$) burns, it reacts with oxygen ($\mathrm{O_2}$) in the air; during this reaction, carbon dioxide ($\mathrm{CO_2}$) and water ($\mathrm{H_2O}$) are formed.

The starting point for the reaction equation will therefore be:

However, this equation is incorrect because it does not comply with the principle of conservation of mass. For example, for the element hydrogen ($\text{H}$), there are 4 hydrogen atoms in the reactants and only 2 in the products. We therefore balance this chemical reaction by introducing a stoichiometric coefficient in front of the chemical formulas of each species. Thus, if we write:

It complies with the conservation rule for the elements carbon ($\text{C}$) and hydrogen ($\text{H}$) but not for oxygen ($\text{O}$); we therefore correct it to:

The final equation represents the correct stoichiometric formula of the methane combustion reaction. It reflects the fact that the chemical reaction balance is as follows: one mole of methane reacts with two moles of oxygen to form one mole of carbon dioxide and two moles of water.

The stoichiometric coefficient is a fundamental concept in chemistry. Understanding what a stoichiometric coefficient is allows you to interpret any stoichiometric equation, analyze a stoichiometric reaction, and determine the correct stoichiometric formula for a chemical reaction.