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

Reading Chemical Equations

Chemical equations are symbolic representations of how chemicals interact with each other—how they react. The basis of the chemical equation is the chemical notation for molecules of the elements and compounds.

The periodic table serves as the basis for how compounds. Each element is represented by a chemical symbol. For instance, hydrogen is represented by the symbol H, sodium by Na, chlorine by Cl, and aluminum by the symbol Al.

Every symbol for every element begins with a capital letter. If there is more than one letter in the symbol, the following letters will be lower-case. This is very, very important!  CO₃ is not the same as Co₃.

When a single molecule of a given compound contains more than one atom of a particular element, it is sub-scripted or followed by a number telling how many. When there are more than one molecules present, the molecule is preceded by the number of molecules (called the coefficient).

With that in mind, the following should be understandable: 3H₂O

In the above, there are 3 molecules of the compound H₂O which includes two hydrogen atoms and one water atom.

Working with invisible molecules might not make the simplicity of the system obvious. In order to build familiarity with the notation system, consider how it might be used by a restaurant that serves breakfasts.

Suppose, on the menu, there were a few set items:

• A "side of bacon" is 2 strips of bacon.
• A "lite breakfast" is 2 eggs and one piece of toast.
• A "good morning" is 2 strips of bacon and 2 pancakes.
• A "hungry jack" is 2 eggs, 4 strips of bacon, and one piece of toast.

If the manager decided to use symbols for the pieces of food, the following would be one way to do that:

• Ba = bacon
• E = egg
• T = toast
• Pc = pancakes

Using these symbols and modeling after chemical notation, the waiter would, for each item on the menu, write:

• Ba₂ = side of bacon
• E₂T = lite breakfast
• Ba₂Pc₂= good morning
• E₂Ba₄T= hungry jack
• 3T = 3 orders of toast

This symbolic notation is exactly like that used for chemical compounds. If you can understand how the coefficients and subscripts work, then you can look at a chemical equation and pick out the different numbers present for each atom!

To use the restaurant model a bit further, consider how compounds could be combined.

Suppose the cook had prepared some food and plated it in anticipation of a regular customer. Say he made a few sides of bacon and a couple of lite breakfasts. Now, suppose that the town doctor rushes in and asks for one hungry jack to go!

While the cook started cooking more food, the waitress could grab one of the lite breakfasts and two sides of bacon, plate them up as one hungry jack, and send the doctor on his way (presumably to do something urgent.) Using the notation for chemical equations, that would look like this:

E₂T + 2Ba₂ -> E₂Ba₄T

In a balanced equation, the number of atoms on each side must always be the same. So in the above, on the left side of the arrow (which is generally read as "yields" — and is sometimes represented with an equal sign) there are 2 eggs, 1 piece of toast and 2 sets of 2 strips of bacon (4 bacons). On the right side, there is also 2 eggs, one piece of toast, and 4 strips of bacon.

Consider this "re-plating" of food:

2Ba₂Pc₂ + E₂T = E₂Ba₄T + 2Pc₂

  +       

=

  +  

This time, the left side has 4 bacons, 4 pancakes, 2 eggs, and one piece of toast. The right side has to end up with exactly that combination, but since the bacon was plated with the eggs and toast, the pancakes all ended up left over on two plates. The components of the breakfasts are switched around and re-organized so that the new plates are composed of the same things, but in different order.

The principle is the same for chemical compounds. Using the principles above, the following notation of a reaction should make sense:

2Al + 6HCl = 2AlCl₃ + 3H₂

On the left are 2 aluminums, 6 hydrogens, and 6 chlorines. Thus, on the right those atoms are re-organized into 2 molecules of aluminum chloride and 3 molecules of hydrogen. (Since the aluminum chloride molecule has 3 chlorines, and there are 2 molecules, that accounts for the 6 chlorines on the left. Similarly, each hydrogen molecule has 2 hydrogens, so there are 3 molecules of hydrogen.)

Just as in the example of the breakfasts, chemical equations must end up with the same number of parts (atoms) as they begin with.

Examples

In NaHCO₃ there are 1 Na, 1 H, 1 C and 3 O.

In 2H₂O there are 4 H and 2 O

In 4NaCl there are 4 Na and 4 Cl

In 3H₂SO₄ there are 6 H, 3 S, and 12 O

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Summary Remarks

• Each element is represented by a chemical symbol that begins with a capital letter, and if there is more than one letter in the symbol, the following letters will be lower-case.
• When a single molecule of a given compound contains more than one atom of a particular element, it is sub-scripted or followed by a number telling how many.
• When there are more than one molecules present, the molecule is preceded by the number of molecules (called the coefficient).
• In a balanced equation, the number of atoms on each side must always be the same.
• The equations tell how many of each molecule combines and what the resulting compounds are.