Balancing Chemical Equations

This week’s blog is for high schoolers (or anyone else taking a chemistry class)!  If you are in a chemistry class, or have ever taken a chemistry class, you know it’s important to understand how to balance a chemical equation.  A chemical equation is how we can describe the reaction between two atoms or molecules in a concise way (for more information on chemical reactions, click here).  On the left side of a chemical equation are the reactants, or the substances we start with before the reaction.  On the right side of the equation are the products, the substances that are created in the reaction.  For instance, the reaction between hydrogen and oxygen to create water would be written like this:

We would read this equation as “hydrogen reacts with oxygen to produce water”.  You will also notice in this equation that there is a number two in front of the hydrogen, and a number two in front of the water (H2O).  These numbers are called coefficients, and they are there to show us that for this reaction to take place, two molecules of H2 must react with one molecule of O2 to form two molecules of water. 

You may ask, “Why should we need these coefficients?  Why not just write it out as simply as possible?”   Well, if we write out what really happens in the reaction, our equation would look like this:

Yes, this is very simple, but there is a problem with it.  Hydrogen and oxygen (as well as nitrogen and halogens like chlorine and fluorine) don’t appear as single atoms in nature, they appear as molecules with two atoms each. 

In order to understand what is really happening during the reaction, we must write our reactants as they really appear.  This means writing their formulas as H2 and O2 (because one molecule has two atoms of hydrogen or two atoms of oxygen).  Now if we try to write our chemical formula using these correct molecular formulas, we end up with this:

But now we have another problem...now the equation does not balance. 

What we mean by this is that the number and type of atoms from the reactants on the left side of the equation do not match the products on the right side.  We know that in the real world this cannot be the case, because the law of conservation of mass states that atoms are neither created nor destroyed in any chemical reaction. 

Take a look at our last equation again.  On the left there are two hydrogen atoms and on the right there are two oxygen atoms.  On the right there are two hydrogen atoms (this is good), but only one oxygen atom.  This implies that one of the oxygen atoms just disappeared, and we know this cannot be!  This means the equation is unbalanced.  To fix this, we need to add our coefficients.  Let’s start out by bringing back the missing oxygen atom.  We do this by putting the coefficient 2 in front of water.  This means now there are two molecules of water, each of which has one oxygen atom, for a total of two oxygen atoms.

But now on the right side there are four hydrogen atoms:  each molecule of water has two hydrogen atoms, and there are two molecules, for a total of four hydrogen atoms.  We can fix this by putting the coefficient 2 in front of the hydrogen on the left side, giving us a total of four hydrogen atoms on the left side also.

Now our equation is balanced! 

Let’s try another synthesis reaction—the reaction between nitrogen and hydrogen to form ammonia:

Let’s start by balancing the nitrogen.  There are two nitrogen atoms on the left, and one on the right.  We can make these balance by adding the coefficient 2 in front of the ammonia on the right side:

Now the hydrogen must be balanced; there are two hydrogen atoms on the left, and six on the right.  We can make this balance by adding the coefficient 3 in front of the hydrogen on the left side:

This equation is now balanced!

Now let’s try another, more challenging reaction, such as the displacement reaction between aluminum and hydrochloric acid (remember, a displacement reaction happens when atoms of one element displace the atoms of another element in a molecule).  In this reaction, aluminum displaces hydrogen as the bonding partner with chloride:

Clearly this equation is not balanced.  There is one aluminum atom on each side, so this is OK so far.  There is only one hydrogen atom on the left but there are two on the right, and there is only one chloride atom on the left and there are three on the right.  We need to find a way to balance the hydrogen and chloride atoms. 

First, let’s look at the chloride atoms, since this is the largest imbalance between the two sides.  To fix this imbalance, we would need to put a coefficient 3 in front of the hydrochloric acid:

Now, look at the hydrogen atoms.  There are now three on the left and two on the right.  To make this balance we need to find the least common multiple of two and three, which is 6.  This means we need 6 hydrogen atoms on either side of the equation.  This is how our coefficients will look:

Our aluminum is still OK, but now we need to look at the chloride again.  We have six atoms of chloride on the left side, and three on the right.  We can fix this by adding the coefficient 2 in front of the aluminum chloride molecule:

Now our hydrogen atoms balance, and our chloride atoms balance, but our aluminum atoms don’t!  Finally, these also need to balance, so we need two on the left side; we simply add the coefficient 2 in front of the aluminum atoms on the left:

Now all atoms in the equation balance.  This equation required a little more jostling back-and-forth, but don’t let that worry you!  Just keep going back and forth until all the atoms balance, starting with the atoms that are the most imbalanced, and working toward the ones that are the least imbalanced.  This is a little like hitting a baseball, or riding a bike—it takes a little practice to get really good at it!

Let’s try one more, the combustion of propane in oxygen from the air:

Because the oxygen appears in both of the products of the reaction, I’m going to leave oxygen for last.  The greatest imbalance is for hydrogen, with eight atoms on the left, and two on the right.  To make the hydrogen balance, we need to insert the coefficient 4 in front of the water:

Next let’s look at the carbon atoms.  There are three on the left and one on the right, so we need to add the coefficient three in front of the carbon dioxide:

The hydrogen and carbon atoms now balance, what about oxygen?  There are ten oxygen atoms on the right side, so we must add the coefficient 5 in front of the oxygen.

Now all atoms balance on both sides of the equation.

NOTE:  The most important step of balancing a chemical equation is simply making sure that your reactants and products are written correctly.  If they are not, the equation will never balance and you will spend many fruitless hours struggling.  If you are having a lot of trouble getting a reaction to balance, this is usually a good place to start looking for answers! 

TRY THESE!!

Fill in the blanks with the proper coefficients. 

1)      _Al + _O2 = _Al2O3

2)      _Na + _H2O = _NaOH + _H2

3)      _C2H4 + _O2 = _CO2 +_H2

4)      _Si2H6 + _O2 = _SiO2 + _H2O

5)      _CH3OH + _O2  = _CO2 + _H2O

ONLY WHEN YOU ARE DONE....go ahead and scroll down!


 















Answers:

1)      4, 3, 2

2)      2, 2, 2, 1

3)      1, 2, 2, 2

4)      2, 7, 4, 6

5)      2, 3, 2, 4