# Basic Stoichiometry Equations with Explanations

Today we are talking about stoichiometry, which is a fancy word that means “relationships.” But not any kind of relationships! Stoichiometry refers specifically to relationships that exist between different chemical species in a balanced chemical equation.

In case that definition was confusing to the majority of readers, let’s take a step back and explain some key concepts.

In general, when we study chemistry, one of the main parts of this study is the study of chemical reactions, which is when one or more chemical species, under certain conditions, turn into new chemical species. The chemical species that we start with are called the REACTANTS, and the ones that we end with are called the PRODUCTS. The conditions that we use to transform reactants into products are generally referred to as REACTION CONDITIONS.

I can describe chemical reactions in a number of different ways, but one of the most compact ways is to use a chemical equation. In a chemical equation, we generally write the reactants on the left side of the equation, and the products on the right side. We use an arrow to signify that we are converting from reactants to products, and write the reaction conditions over the arrow.

Let’s consider the following example of how we can make ammonia gas (with a chemical formula of NH3) from the reaction of hydrogen gas and nitrogen gas.

In this chemical equation, the reactants (shown in red) are hydrogen gas and nitrogen gas; the product (shown in blue) is ammonia gas; and the reaction conditions (show above the arrow in black) are high temperature and pressure (450oC and 200 atm).

Because of the law of conservation of mass, which says that mass cannot be created or destroyed, we know that the number and types of atoms on the reactant side of the equation have to be equal to the number and types of atoms on the product side of the equation. Or in other words, what goes in (on the reactant side) must come out (on the product side).

In order to make sure that we are obeying the law of conservation of mass, we often add numbers in front of the chemical species (reactants and products) to make sure that the numbers and types of atoms on each side of equation are equal. This is why, in the equation above, you see a number 3 in front of the chemical symbol for hydrogen (H2), and a 2 in front of the chemical symbol for ammonia (NH3). There is no number in front of the chemical symbol for nitrogen (N2), which means that there is an implied number 1. With these numbers, we are able to ensure that the number and types of atoms (hydrogen and nitrogen atoms) are the same on both sides of the equation, which means that we have a balanced chemical equation.

What do these numbers actually mean? They are telling us the stoichiometry of this reaction, or in other words, the relationship between the amount of each chemical species that is involved in this chemical equation.

Once we have a balanced chemical equation (and only when we have a balanced chemical equation), if we know how much of one chemical species is involved in the reaction, we can figure out how much of any of the other chemical species is involved as well.

What do we mean when we say “how much”?

This term can have a variety of meanings, but in stoichiometry, we are referring specifically the number of moles of each reactant or product (or the number of molecules). For example, in the reaction above, we react three moles of hydrogen gas (indicated by the number 3 in front of the H2) with one mole of nitrogen gas (indicated by the implied number 1 in front of N2), and obtain two moles of ammonia gas (indicated by the number 2 in front of the NH3).

We can also use any multiple of these amounts, as long as the same ratio between the chemical species applies. What does this mean? This equation also indicates that six moles of hydrogen gas can react with two moles of nitrogen gas to produce four moles of ammonia gas (multiplying each of the coefficients by two), because the stoichiometry of this reaction (i.e., the relationship between the amounts of each species) is the same as for the original balanced chemical equation.

If you are wondering what are moles, be aware that this term does not refer to the mammals that are called moles! Instead, this term, which was developed by a scientist named Amedeo Avogadro, refers to a very large number. How large? 6.02 x 1023, which is very large indeed! It is a number with special meaning in chemistry in a variety of contexts. In the context of stoichiometry, we use the coefficients of the balanced chemical equation to tell us how many moles of molecules are reacting.

How can we use stoichiometry in real life? Well, we can use it to solve a whole variety of chemistry problems. In particular, as long as we are given a balanced chemical equation and quantitative information about one of the chemical species involved in a reaction, we can figure out quantitative information for any of the other species.

### Let’s look at some examples:

##### Example 1:

Let’s look at the equation to make water, whose chemical formula is H2O. The balanced chemical equation is shown below.

How many moles of H2O would I produce if I reacted 4 moles of H2 with excess O2?

Solution:

Here we are told that there is enough oxygen, or O2, to fully react with the H2, so we are only concerned with the stoichiometry between H2 and H2O. We see from the balanced chemical equation that two moles of H2 react to form two moles of H2O, which means that we have a 1:1 relationship between their molar amounts. If we react four moles of H2 with excess O2, then we will obtain four moles of H2O as the product.

##### Example 2:

Let’s consider the reaction of sodium hydroxide, NaOH, with hydrochloric acid, HCl. These two species react to form salt (NaCl) and water, in a reaction that is termed “neutralization.” The balanced chemical equation for this reaction is shown below:

How many grams of HCl would be needed to fully react with 2.0 grams of NaOH?

Solution:

This question is trickier, because it gives us information in terms of grams, and is asking for a solution in terms of grams as well. We know that the stoichiometry information is only about moles though, so what do we do? Well, we can use the following approach:

1. Convert the grams of NaOH into moles of NaOH.
2. Use stoichiometry to figure out how many moles of HCl are needed to react with that many moles of NaOH.
3. Convert the moles of HCl into grams of HCl to obtain the final answer.

Let’s show how this approach works with the actual numbers of the problem:

1. Convert the grams of NaOH into moles of NaOH.
1. 0 grams of NaOH can be converted into moles using the molar mass of NaOH (40.0 grams/mole), which means that 2.0 grams is equal to 0.050 moles (2.0/40.0).
2. Use stoichiometry to figure out how many moles of HCl are needed to react with that many moles of NaOH.
1. Because the stoichiometry of the reaction shows a 1:1 ratio between NaOH and HCl, 0.050 moles of NaOH will need 0.050 moles of HCl to react fully.
3. Convert the moles of HCl into grams of HCl to obtain the final answer.
1. 050 moles of HCl can be converted into grams of HCl using its molar mass (36.5 g/mol) to give 1.8 grams of HCl (0.050*36.5).

In general, let’s say that in a stoichiometry problem, we are given information about chemical species A and we want to find out information about chemical species B. To do so (in a general fashion), we need to first convert the information given to us into the number of moles of chemical species A, then use stoichiometry to find the mole-to-mole ratio between chemical species A and chemical species B, and then convert the moles of chemical species B into whatever measure of chemical species is being asked for (mass, volume, molecules, etc.).

Once we get comfortable with this general approach, then stoichiometry problems can be lots of fun! Happy calculating, readers!

Author: Mindy Levine

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