More About Coefficients in Chemical Equations

In any given chemical reaction, the equation that describes it is made up of numbers and symbols that represent the molecules that are combining. Any molecule is represented by the atomic symbols and subscripts telling how many of each type of atom make up a single molecule.

When the equation is balanced, coefficients are added to the molecules of the reactants and to the molecules of the products until the number of atoms of each type are equal on each side of the reaction. Thus, if a reaction begins with 4 atoms of "X" and 3 of "Y", it must end up with the same number of each atom.

To balance an equation, coefficients are added in front of the molecules. The coefficient tells how many of which molecule is needed in order to come up with the right number of atoms on each side. The coefficient is a multiplier for the numbers of each atom in each molecule of the equation.

As has been explained previously (for example), 3 C6H12O6 means 3 molecules of C6H12O6, which results in 18 C, 36 H, and 18 O atoms.

However, the coefficients also give more information. They serve additionally as a ratio of molecules that will react with each other. The coefficients can be seen as the how many of any numeric units are needed to properly react.

Using water as an example, the equation is this:

2H2 + O2 --> 2H2O

At the simplest level, this means 2 molecules of H2 reacted with 1 molecule of O2 results in 2 molecules of H2O.

HOWEVER, it ALSO means that any number of molecules can be combined, so long as the ration of 2:1 --> is preserved. Thus:

2 molecules of H2 reacted with 1 molecule of O2 results in 2 molecules of H2O

2 dozen molecules of H2 reacted with 1 dozen molecules of O2 results in 2 dozen molecules of H2O

2 score molecules of H2 reacted with 1 score molecules of O2 results in 2 score molecules of H2O

2 bazillion molecules of H2 reacted with 1 bazillion molecules of O2 results in 2 bazillion molecules of H2O

And for the most relevant example…

2 moles of H2 reacted with 1 mole of O2 results in 2 moles of H2O

It is when we relate the coefficients to moles that we tap a great deal of power! While we cannot count moles, we can use the atomic mass of the atoms to find the right amounts of elements or compounds to use in reactions.

For the reaction of sodium (Na) and Chlorine (Cl) we can use the balanced equation to determine the masses of the two elements that would be needed in a reaction. Here is the reaction:

2 Na + Cl2 → 2 NaCl

According the the formula above, we need molecules of Na and Cl2 in a ration of 2:1. Thus, if we have 2 moles of Na and 1 mole of Cl2 we will have the right ratio for a complete reaction with no left-overs.

From the atomic masses, we know that one mole of NA weighs 22.989 grams. Thus, we begin with 45.979 grams of sodium, we will have the right amount.

Because chlorine is always Cl2, one mole of it will weigh 70.90 grams. Finding the mass of a gas is not as easy as finding the mass of a solid, but it can be done, so starting with 70.90 grams of chlorine is the right amount as well.

It is the coefficients of the balanced equation that guide us to these masses. Understanding that coefficients give us the correct ratio of molecules allows us to use the relationship between atomic mass and numbers of moles to come up with the correct amounts of reactants for any reaction.

Balancing Chemical Equations and Reactions

General Chemistry Index

"Chemical reactions must be balanced." What does that mean?

The number of atoms that begin the reaction must end up somewhere. If there are ten atoms at the beginning, when the reaction is done, there will still be ten atoms. However, how the atoms are combined into compounds changes!

The action of balancing chemical equations primarily sets out to find the ratios of compounds that result in there being the same number of atoms in the product as there were in the reactants. This is the most fundamental concept that must be understood. It is so important, it bears being repeated and emphasized.

At the most basic level, balancing chemical equations is the process of finding coefficients which result in the number of atoms in the reactants being equal to the number of atoms in the product.

If there are 8 atoms total in all of the molecules of the reactants, then there MUST be 8 atoms total in all of the molecules of the products.

It does not matter how many different compounds are involved. It does not matter how many molecules of any of the compounds are involved. The driving factor in balancing equations is that the number of atoms on each side of the reaction are equal—and the mass is the same on both sides.

Read that last sentence ten times!

Conservation of Matter

The reason that the number of atoms must be the same stems from the Law of Conservation of Matter. In basic terms, the Law of Conservation states that matter cannot be created or destroyed. It really, if thought about, is logical. If you have 15 atoms of something, no matter how you combine or arrange them, you end up with 15 of something.

This law drives chemistry and chemical reactions. This is why that the number of atoms cannot change. 

One way to look at this principle as it applies to chemical reactions is to compare the mass of the reactants to the mass of the products. Because the number of atoms CANNOT change, and because each atom has a certain mass, there should be no difference between the mass of the products and the mass of the reactants.

METHOD

The process of balancing an equation begins by writing out all of the reactants and the products, putting them on opposite sides of either an equal sign or an arrow. Water and aluminum chloride will be used as examples.

Suppose it is desirable to combine oxygen and hydrogen to make water. The formula for those two elements are O2 and H2, meaning that each molecule of oxygen has 2 oxygen atoms and each molecule of hydrogen has two hydrogen atoms. The formula for water is H2O, meaning there are two hydrogen atoms and one oxygen atom in each molecule.

EXAMPLE AS INSTRUCTION

So the reaction looks like this, to begin with:

H2 + O2 = H2O

However, this equation is NOT in balance. On the left side (reactant side), there are two hydrogen and two oxygen, but on the right side (product side), there is only ONE oxygen. To correct this, the following can be done:

H2 + O2 = 2H2O

Adding the coefficient of 2 in front of the water molecule results in there being two oxygens present, so the number of oxygens balance. HOWEVER, adding the coefficient means that there are, now, 4 hydrogen present. Another adjustment needs to take place. 

The equation can be brought into balance if 4 hydrogens can be on the left side of the equation. This can happen by adding yet another coefficient:

2H2 + O2 = 2H2O

At last, everything balances—on the left are 4 hydrogen and 2 oxygen, and on the right are the same numbers of the same atoms.

LET'S DO THAT AGAIN!

Look at the unbalanced formula for making aluminum chloride:

Al + HCl = AlCl3 + H2

To balance this, several coefficients are needed. That HCL has one of each hydrogen and chlorine on the left, but there are 3 and 2 of them on the right, results in some "tricky" math. 

Trying a coefficient of 2 on the left results in:

Al + 2HCl = ?AlCl3 + H2

That brought the hydrogen into balance, but the chlorine still did not work out. Where 3 chlorines are needed, only two were available. The balanced equation requires this:

2Al + 6HCl = 2AlCl3 + 3H2

Thus, there are on BOTH sides of the equal sign: 2 Al, 6 H, and 6 Cl.

Summary Thoughts:

To balance a chemical equation:

• Begin with the atomic symbols for each element or compound involved.
• Place the reactants on the left of the yield symbol (or equal sign) and the products on the right.
• Change the coefficients as needed until—VITAL CONCEPT—there are the same number of each atom on both sides of the equal sign.

• The coefficients must be lowest common factor and it must be a whole number. Thus, if you have 2, 4, 2 then you need to reduce that to 1,2,1.

• You CANNOT change subscripts. You can ONLY change coefficients
• You CANNOT change subscripts. You can ONLY change coefficients
• You CANNOT change subscripts. You can ONLY change coefficients
• You CANNOT change subscripts. You can ONLY change coefficients
• You CANNOT change subscripts. You can ONLY change coefficients

MORE INFO

In the following video, a pseudo-hands-on method for balancing equations is presented. It shows how to "draw out" the reaction and make sure it is balanced.

https://youtu.be/9BlQmfE9cfQ