# Limiting Factor: Definition, Principle & Examples

Instructor: LaRita Williams

LaRita holds a master's degree and is currently an adjunct professor of Chemistry.

In this lesson, we will define the term limiting factor with an example and visual representation. We will also learn how to determine the limiting factor of a reaction and discuss its experimental applications.

## Limiting Factor Defined

Do you like to cook? Well, cooking is a lot like chemistry! To cook, we often follow a detailed recipe (experimental procedure) that brings together two or more ingredients (reactants) to make something new (final product).

Let's say you want to make grilled cheese sandwiches, for instance. The recipe you have calls for one slice of cheese and two slices of bread to make one complete sandwich. In the refrigerator you find you have six slices of bread and six slices of cheese. If you tried to make lunch with that ratio of ingredients, you would only be able to make three sandwiches before running out of bread. In this case, bread slices are the limiting factor of your reaction.

A limiting factor, also known as a limiting reactant or limiting reagent, is the reactant that is used up first in a reaction and therefore limits the amount of product that can be formed.

## A Molecular Representation of the Limiting Factor

For a deeper understanding of the limiting factor, we can study a molecular representation of the reaction between oxygen gas (Osub2) and hydrogen gas (Hsub2) to yield water (Hsub2O), shown below in Figure 1. In this particular reaction set up, we see that there are a total of twelve hydrogen atoms and eight oxygen atoms on the reactant's side (left side). In the figure, these hydrogen atoms are depicted as small, grey spheres and the oxygen atoms are the larger, pink spheres.

While it's true that there are fewer oxygen atoms present in the reaction, oxygen is NOT the limiting factor here. Remember, the limiting factor is the reactant that is used up first, not necessarily the reactant present in the smallest amount. To form water (Hsub2O) in this reaction, two hydrogen atoms are consumed for every one oxygen atom. This 2:1 ratio means that all of our hydrogen atoms will be used up in the reaction process and two oxygen atoms will be left over, as shown on the product's side of Figure 1. Thus, hydrogen gas (Hsub2) is the limiting factor of this reaction set up.

## Applications of the Limiting Factor

The limiting factor plays a critical role in chemical experimentation and reaction planning. If we know the amounts of reactants present, we can use simple calculations based on the relative number of moles or molecules to determine which reactant is limiting. Once we identify the limiting factor, we can use the balanced chemical equation to find its molar ratio to the product and predict exactly how much of our product can be formed, the same way we predicted how many sandwiches could be made from six slices of cheese and six slices of bread. The process of using molar ratios to predict the amount of product formed by a reaction is called stoichiometry.

## How To Determine the Limiting Factor of a Reaction

Consider the balanced chemical equation for the reaction between nitrogen gas (Nsub2) and hydrogen gas (Hsub2) to yield ammonia gas (NHsub3):

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