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Balance Chemical Equations?

(Site updated: November 16, 2010)

Remember, chemistry IS easy! (If you have the right tools to help you learn it.)

The first rule you must understand about balancing equations is...

The Law of Conservation of Mass:

Every single atom which goes into a chemical reaction MUST come out the other side, even if atoms are grouped differently than when they go in. As an example, consider the problem below. Three red, 2 yellow and 5 blue "atoms" go into the chemical reaction. No matter HOW the atoms are arranged or grouped when they come out the other side, every single "atom" that went in MUST come out the other side. In this case, 3 red, 2 yellow and 5 blue "atoms" MUST come out the other side. Count the number of red, yellow and blue "atoms" on each side of this equation. Do you see that the number of "atoms" of each color on both sides of the chemical reaction is the same? That is the first condition you must meet to have a balanced equation.

Graphic showing 3 red atoms, 2 yellow atoms and 5 blue atoms followed by an arrow showing that the atoms are going into a brown box.  The box is labeled 'Chemical Reaction.'  Then there is an arrow coming out the other side.  On that side there are 4 molecules: one made of 1 red atom and 1 yellow atom, one made out of 1 yellow atom and 1 blue atom, and 2 molecules, each made of 1 red atom and 2 blue atoms.  The total number of atoms of each color on each side of the 'Chemical Reaction' box is the same, regardless of how the atoms are arranged.  No atoms are gained.  No atoms are lost.  All are accounted for.

 

The word "conservation" means that nothing gets lost, and nothing gets created out of thin air. The word "mass" refers to the amount of matter. There is no such thing as "losing atoms" in a chemical reaction. Nor can atoms suddenly appear when they weren't there in the first place.


Coefficients and Subscripts:

The next two bits of information you must learn is how to interpret the two kinds of numbers found in chemical equations. The large numbers in red below are called "coefficients," because they "appear with" the formulas and act as multipliers. ("Co" means "with" and "efficient" comes from a Latin word meaning "to accomplish." So you can think of the coefficient and its formula as "accomplishing together" the balancing of a chemical equation. -- I know, a bit obscure.-- Nevertheless...) The small numbers in blue below are called "subscripts," because they are written below the line. ("Script" for "writing" and "sub" for "below.")

Graphic of equation for the synthesis of water.  2 H2 + O2 ' 2 H2O.  The word 'Coefficients' is written above the equation with arrows pointing to the '2' in front of H2 and the '2' in front of H2O.  The word 'Subscripts' is written below the equation with arrows pointing to the small '2' after the H in 2 H2, the small '2' written after the O in O2, and the small '2' written after the H in 2 H2O.


Introducing Color Code Formulas

To make learning the meaning of these numbers as easy as possible, we will postpone using real chemical symbols and real chemical formulas until later. For now we will just use colored circles as our "atoms" and the first letters of their color names as our "chemical symbols." For example:

Color Code Key Chart showing representations of 5 different fake elements based on color, along with their chemical symbols.  Color names are used for simplicity in discussing coefficients and subscripts in chemical equations.  1 red atom = R.  1 yellow atom = Y.  1 blue atom = B.  1 green atom = G.  1 white atom = W.

Using this Color Code Key, we will clarify the meaning of the two numbers used in chemical equations.


Subscripts Tell How Many Atoms of Each Kind

First of all, the subscript tells us how many atoms of each kind exist in any formula. Look at the examples below. The subscript is ALWAYS written AFTER the symbol of the atom to which it refers.

A series of drawings of atoms and groups of atoms in different connectivities and shapes with their color code chemical formula written beneath, so that a person studying the drawings and symbols could comprehend the meaning of the subscript.  Here is a list of the drawings and their accompanying formulas.

1 blue atom         B
2 blue atoms stuck together    B2
3 blue atoms stuck together   B3
1 white atom   W
2 white atoms stuck together    W2
3 white atoms stuck together   W3
2 green atoms stuck together   G2
1 green atom      G
3 yellow atoms connected in a line    Y3
1 red atom     R
4 red atoms connected in a 'U' shape    R4
7 yellow atoms connected in an 'H' shape   Y7

When an atom appears only ONCE in a formula, we do not write the subscript, because it is not needed. If the atom were not there, nothing would be written at all. So the appearance of a symbol in a formula without a subscript tells us that the atom appears there only ONCE.


Combining Two Different "Color" Atoms

What happens when we combine two or more different atoms together? How do we write the formulas then? Study the examples below to see if you can figure it out.

We will write the formula for a molecule made of one atom of blue and one atom of white.

A box combining 1 blue atom and 1 white atom.  What formulas do we get?  There are 6 variations in drawings, yet all have the same formula.  1 blue and 1 white connected horizontally, with the blue atom 'first.'  Formula name is BW or WB.  1 white atom and one blue atom connected horizontally with the white atom 'first.'  Formula name is BW or WB.  1 blue and 1 white atom connected vertically with the blue atom on top.  Formula name is BW or WB.  (Orientation of the molecule doesn't matter.  And in color code formulas as we are using, there is no distinction as to which color symbol is written first in a formula, so either answer, BW or WB, is correct.)

 

In this particular case, since we are only working with colors and not actual element symbols, it does not matter whether we write "B" first or "W" first. Notice also that whichever formula we choose, the formula stays the same, regardless of the molecule's orientation in space.


Now we will write the formula for 1 atom of blue and 2 atoms of white.

A box combining 1 blue and 2 white atoms.  Regardless of how the atoms are drawn or connected, their formula is BW2.  It could also be W2B.  The atoms can be connected in a straight line with the blue atom in the middle or at one end.  The molecule can be bent..  The molecule can be oriented differently in space.  None of this matters in terms of writing its chemical formula.

In most cases when 1 atom of one kind and 2 of another are put together, the single atom will be the central atom of the molecule, as shown in the first four examples in the box above. The last two examples, in which blue is NOT the central atom, were added to show that the formula describing how many atoms there are of each kind is the same, regardless of how the atoms are connected or how they are oriented in space.


Now we will combine 1 atom of blue and 3 atoms of white.

A box combining 1 blue atom and 3 white atoms.  The atoms may be combined in a trigonal shape, with the blue atom in the middle or the atoms may be strung together in a line.  The formula remains BW3 or W3B.

In this case, the atoms will almost always connect with each other as shown in the first example, although the second example is still possible. Again, the important lesson to gain from these examples is that the subscript written after a symbol tells how many atoms of that kind there are in the formula. It does not give any information about HOW the atoms are connected to each other.


Just a side note: There ARE rules for writing chemical formulas, such as which atom symbol is written first, and the formulas CAN show something about connectivity, especially in the case of organic molecules (molecules which exist in living creatures), but our goal here is to understand enough about formulas to balance a chemical equation, so we will ignore the rules of writing sophisticated chemical formulas for now and just concentrate on the principles involved in balancing chemical equations. Later, if you do want information about how to write chemical formulas, there will be a link for you to go to a different web page.

If you like what you're learning so far, consider buying the HOLY MOL-EE! Chemistry Curriculum, being offered at a VERY SPECIAL PRICE right now.

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Here is one more set of examples showing how the subscript gives us information about the number of each kind of atom in a formula. Study the following examples and make sure you understand how the formulas below relate to the pictures of the molecules above them.

this graphic gives 8 examples of different color code molecules connected in different  ways and different shapes.  What remains is that the number of atoms of each color are represented by the subscripts.  Thus:

2 green atoms and 2 white atoms               G2W2
2 red atoms and 3 yellow atoms                  R2Y3
1 blue atom and 3 yellow atoms                  BY3
1 blue atom, 2 white atoms and 1 red atom          BW2R
4 blue atoms and 4 white atoms                            B4W4
2 red atoms, 4 blue atoms and 1 white atom         R2B4W
1 yellow atom, 3 green atoms and 2 white atoms        YG3W2
1 red atom, 2 white atoms and 2 yellow atoms           RW2Y2


Coefficients are Multipliers

Now that you understand how subscripts are used in chemical formulas, we will look at how coefficients are used in chemical equations. Quite simply, a coefficient is a multiplier.

Here are some examples.

Three boxes containing respectively 1, 2 and 3 identical molecules made of 1 blue atom and 2 white atoms.  The first box contains one molecule.  Its formula is BW2.  The second box contains 2 molecules.  Its formula is 2 BW2.  The third box contains 3 molecules.  Its formula is 3 BW2.

The coefficient multiplies, and applies to, the ENTIRE FORMULA written after it, not just the first letter. When you have the balanced equation, you can simply multiply the coefficient by the subscript for each atom represented in the formula to find out how many total atoms you have of each kind. (Remember, when there is only one atom of a kind in the formula there is no subscript written, so we use "1" as the subscript multiplier.)

Analysis of the previous graphic, emphasizing the use of coefficients.  Each of the three representations, BW2, 2 BW2 and 3 BW2 are analyzed for their total atoms and how the coefficient multiplies the number of atoms in each formula to give the total number of atoms in the box.  First box:  BW2   Coefficient of 1 x 1 blue atom in the molecule = 1 total blue atoms in box.  Coefficient of 1 x 2 white atoms in the molecule = 2 total white atoms in box.  Second Box:  2 BW2   Coefficient of 2 x 1 blue atom in each molecule = 2 total blue atoms in box.  Coefficient of 2 x 2 white atoms in each molecule = 4 total atoms of white in box.   Third Box:  3 BW2  Coefficient of 3 x 1 blue atom in each molecule = 3 blue atoms total in box.  Coefficient of 3 x 2 white atoms in each molecule = 6 white atoms total in box.


Do not make this mistake.

Do NOT think that 3 BW3 is the same as B3W6.  Even though the total number of atoms of each color is the same in each box, in the first we have 3 groups of atoms or three molecules, and in the second we have one large molecule.  In real life, these two kinds of molecules would act very differently.  So do NOT make the mistake of writing 3 BW3 as B3W6 or vice versa.

This is just one example of a mistake many students make. The number of atoms of each kind is the same in both cases, but these two molecules are VERY different from each other. Do not EVER make the mistake of writing "3 BW2" as "B3W6" or anything like that.


Balancing Equations.

OK. Now that you have the basics down, let's start actually balancing equations. Just remember that once all the formulas in the initial equation are correct, the ONLY thing you can do to balance an equation is to add groups by changing the coefficients. Once the formulas are correct, you must NOT change the subscripts.

Example 1:

Look at this simple equation. Immediately underneath it are drawings of the molecules these formulas represent. Our task is to find the lowest number of groups of each formula such that all the atoms are accounted for and balanced on both sides of the equation. The "reactants side" of the equation is anything written BEFORE the arrow. The "products side" of the equation is anything written AFTER the arrow.

Color code chemical equation:  __R2 +  __W2 --> __RW2.  Blank lines are placed in front of the formulas in the equation to allow for the writing of coefficients, once the equation is balanced.  The first two terms before the arrow are on the 'Reactants' side.  The term after the arrow ison the 'Products' side.

....Diatomic red molecle + diatomic white molecule -->  molecule made from 1 red and 2 white atoms.  This is a drawing of the unbalanced equation written above.

It can be seen by inspection that there are 2 red atoms on the left and only 1 red atom on the right. Thus, this equation is NOT balanced.

In order to balance the quation, we need at least 1 more red atom on the right side, but we cannot add JUST 1 red atom. Rather, we must add an entire GROUP of atoms which contains our red atom of interest. It's somewhat like buying a box of crayons. In order to get one crayon of a certain color, you must buy the entire box, because they just don't come one crayon at a time.

We have to add at least one red atom to the right side, but in order to do that, we have to add one entire group, so let's do that and see what we get.

__R2 + ___ W2 '  2 RW2.  Below this equation are drawings of the molecules represented so far.  We have 1 red diatomic molecule, 1 diatomic white molecule and 2 molecules of RW2.

Adding the group balances our red atoms, giving us 2 red atoms on each side. However, now the whites are unbalanced. We have 2 white atoms on the left side of the arrow but 4 on the right side. What should we do? Of course, "add a group."

__R2 +  2 W2 '  2 RW2.   Below are drawings of the molecules represented so far.  We have 1 red diatomic molecule, 2 white diatomic molecules and 2 molecules of RW2.

Now if we look at the equation, we see that there are the same number of each kind of atom on both sides of the equation. So this equation is now balanced. All that is left for us to do is write down the coefficients.

Remember, you cannot represent "2 W2" as "W4."

This is a reminder.  2 W2 is NOT equal to W4.  Below this statement are two boxes.  The first has 2 white diatomic molecules.  The second has 1 molecule with 4 white atoms.  There is a 'not equal' sign in between the two boxes.

 

Nor can you represent "2 RW2" as "R2W4."

2 RW2 is NOT equal to R2W4.  Below this statement are two boxes.  The first has 2 molecules, each molecule with 1 red and 2 white atoms.  The second box has only one molecule with 2 red and 4 white atoms, all joined in a letter 'H' shape.

So the balanced equation is:

The balanced equation:   R2 + 2 W2 -->  2 RW2

 

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Example 2:

__B2 + __W2 --> __ BW3.  Underneath B2 is one molecule made from two overlapping blue atoms.  Underneath W2 is one molecule made from two overlapping white atoms.  Underneath BW3 is one molecule made from 1 blue atom with three white atoms attached to it.

Again, we drew the molecules represented by the formulas in the equation. First let's balance the blue atoms. How many blue atoms are there on the left, or "reactants side" of the equation? How many on the right, or "products side"? In order to get one more atom of blue on the right side, what do we need to add? Yes, we need to add an entire group. So let's do that.

__B2 + __W2 ' 2 BW3.  Underneath B2 is one diatomic blue molecule.  Underneath W2 is one diatomic white molecule.  Underneath 2 BW3 are two molecules, each with one central blue atom with three white atoms attached.

See that we have also added the red coefficient, 2, in front of the formula, BW3 , to reflect the addition. This now balances our blue atoms, but the whites are still unbalanced. How many white atoms do we have on the right side of the equation? [Answer: 6] And how do we get 6 atoms of white on the left hand side? Yes, by adding groups. What is the total number of groups we need on the left to balance the 6 whites on the right?

 __B2 + 3 W2 ' 2 BW3.  Underneath B2 is one diatomic blue molecule.  Underneath 3 W2 are three diatomic white molecules.  Underneath 2 BW3 are two molecules, each with one central blue atom with three white atoms attached.

So now we have another correctly balanced equation.

  B2 + 3 W2 --> 2 BW3


Example 3:

 __Y + __R2 --> __ Y2R3.  Underneath Y is one yellow atom.  Underneath R2 is one diatomic red molecule.  Underneath Y2R3 is one group of atoms, which can be either a molecule or a unit salt formula, made from 2 yellow atoms connected with three red atoms.

 

With this equation, first let's look at the yellow atoms. There is 1 yellow on the left, but 2 yellows on the right. What do we do?

 2 Y + __ R2 --> __ Y2R3.  Underneath 2 Y are two single yellow atoms.  Underneath R2 is one diatomic red molecule.  Underneath Y2R3 is one group of atoms with 2 yellow and 3 red atoms connected together.

OK. This balances our yellows, but our reds are still unbalanced. What do we do next?

Construction Caution sign
A word of caution here. Many students at this point make a BIG mistake! They actually take atoms AWAY from Y2R3 and change the formula to Y2R2, as shown below! Don't you do this!

Two boxes demonstrating that it is against the rules of balancing equations to take atoms away from a formula by changing the subscripts in order to balance atoms in an equation.  The examples are  Y2R3 is NOT equal to Y2R2.  Underneath Y2R3 is a group of atoms made from 2 yellow and 3 red atoms connected together.  Under Y2R2 is a group of two yellow and two red atoms connected together, but there are question mark signs pointing to the subscript of '2' behind R in Y2R2.  And there is another question mark pointing to the place where the third red atom is missing from the drawing.

The ONLY thing we can EVER do in balancing equations, once the formulas are correct, is to ADD groups.

So what groups should we add? If we add one group of R2, as shown below, this still doesn't balance the reds.

 2 Y + 2 R2 ' __ Y2R3.  Under 2 Y are two single yellow atoms.  Under 2 R2 are two red diatomic molecules (in other words, two pairs of overlapping atoms to give 4 atoms total but in two different molecules).  Under Y2R3 is one group of  2 yellow and 3 red atoms connected together.  There is also a large purple question mark, begging the question about what we do next to balance this equation.

Can you guess the secret? The secret is to find the least common multiple, (yes, an application of math!) between the original 2 reds on the left side and the 3 reds on the right. What is the least common multiple of 2 and 3? [Answer: 6] How do we get 6 reds on both sides?

 2 Y + 3 R2 '  2 Y2R3.  Under 2 Y are two single yellow atoms.  Under 3 R2 are 3 red diatomic molecules.  Under 2 Y2R3 are two groups of atoms, each group containing 2 yellow atoms and 3 red atoms connected together.

Yes, "3 groups of 2" and "2 groups of 3."

But now the yellows are unbalanced again. What do we do next? Remember, 4 Y does NOT equal Y4.

Reminder boxes.  Two boxes with a 'do not equal' sign in between.  The first box has 4 Y written in it.  Below the 4 Y are 4 separate single yellow atoms.  The second box has the formula Y4.  Below Y4 is one molecule made from 4 yellow atoms connected together.  These two formulas are not equivalent.

We change the coefficient in front of "Y" to 4.

 4 Y + 3 R2 ' 2 Y2R3.  Under 4 Y are 4 separate single yellow atoms.  Under 3 R2 are 3 red diatomic molecules.  Under 2 Y2R3 are two groups of atoms, each one with 2 yellow and 3 red atoms connected together.

So the final balanced equation is:

4 Y + 3 R2 --> 2 Y2R3


One last word: When balancing equations, you ALWAYS want the lowest possible numbers. For example, the above equation may also be written as:

 8 Y + 6 R2 '  4 Y2R3.  12 Y + 9 R2 ' 6 Y2R3.   24 Y + 18 R2 ' 12 Y2R3.  It  is obvious that these equations are multiples of each other.  The balanced equation must always have the lowest coefficients possible and still have a balanced equation.

 

All of these equations are also technically "balanced," but on a test ONLY the lowest numbered choice, i.e., "4Y + 3R2 => 2Y2R3" would be correct. We ALWAYS want the equations with the lowest numbers.


Review:

You should now understand the basics for balancing chemical equations.

1. ALL balanced equations must obey the Law of Conservation of Mass, which means that they must have the same number of atoms of each kind on both sides of the equation.

2. The subscript tells how many atoms of each kind there are in a formula.

3. The coefficient is a multiplier, multiplies every atom in the formula along with its subscript, and is the ONLY number which may be changed in balancing equations.(Once formulas are correct, the ONLY way to add atoms is by adding groups.)

4. P.S. You ALWAYS want the lowest possible numbers.

Have fun! Remember, Chemistry IS easy, if you have the right tools!

(P.S. HOLY MOL-EE! Chemistry is one of the right tools.)

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Page updated November 16, 2010 You may email Lynda directly at chembyrd@yahoo.com