Your Name:
Other Members:



Date:

Chemical equations express possibly the most important chemical law ever discovered. Antoine Lavosier, considered by many to be the father of modern chemistry, expressed this law as follows:

“We may lay it down as an incontestible axiom, that, in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment; the quality and quantity of the elements remain precisely the same; and nothing takes place beyond changes and modifications in the combination of these elements.”

That is, matter is neither created nor destroyed. The amount and type of chemical elements remain the same before and after a chemical reaction; they are simply rearranged into different chemical compounds.

Chemical compounds are combinations of elements which cannot be separated by physical means (by freezing, boiling, or sorting). They exist as a result of chemical bonds between atoms of different elements. A chemical compound is defined by the ratio of each type of atom involved in the compound. Here are some examples:

AlCl₃ is a compound of aluminum and chlorine. In each molecule of this compound there is always just one Al atom and exactly 3 Cl atoms.

K₂SO₄: two atoms of potassium, one atom of sulfur and four atoms of oxygen

Fe(OH)₃: one atom of iron, three atoms of oxygen, and three atoms of hydrogen.

The little numbers below and to the right of the atomic symbols (K) and groups of atoms (OH) in these compounds are called subscripts. The subscripts tell you how many of each kind of atom are in the compound. When balancing chemical equations you may never change the subscripts. Changing subscripts changes the compound. For example, H₂O is harmless but H₂O₂ is a strong oxidizer and is used as bleach and to kill bacteria.

In chemical reactions, which are represented by chemical equations, it is often the case that more than one molecule of a compound is required to react with the others. This is shown by a coefficient as follows:

2H₂O - there are (2 × 2) atoms of hydrogen (total = 4) and (2 × 1) atoms of oxygen (total = 2).

2NH₄NO₃ - there are (2 × 1) + (2 × 1) atoms of nitrogen (total = 4), there are (2 × 4) atoms of hydrogen (total = 8), and (2 × 3) atoms of oxygen (total = 6).

2Mg(OH)₂ - there are (2 × 1) atoms of magnesium (total = 2), there are (2 × 1 × 2) atoms of oxygen (a total of 4), and (2 × 1 × 2) atoms of hydrogen (total = 4).

Coefficients in front of chemical formulas are multipliers. A coefficient of 2 means that every atom is multiplied by two. If an atom or group of atoms has a subscript, then the subscript is multiplied by two as well.

---

To help you to be sure you understand these ideas, try a few problems. Each problem gives you a chemical formula either with or without a coefficient. Write the number of each type of atom in a chart.

1. 3N₂O₅

   N	6
   O	15

2. NaC₂H₃O₂
3. 5Al₂O₃

4. 2Mg(OH)₂
5. 2Al₂(SO₄)₃
6. 4CuCO₃

 

How to Balance a Chemical Equation

Now that we have the background necessary, let’s move on to balancing chemical equations. The following is one method for taking on this challenging task.

1. Count the atoms of each kind on the reactant (left) side and product (right) side.
2. Find the least common multiple (LCM) for each type of atom.
   

   For example, in the unbalanced equation O₂ --> O₃ the LCM is six. That means that there should be 6 oxygen atoms on each side of the equation. The equation is balanced by changing coefficients until this is so:
   3O₂ --> 2O₃

3. Sometimes, adding a coefficient to one formula to balance one kind of atom will throw the other atoms out of balance. Just keep track and go back to fix it.

   For example, in the unbalanced equation KClO₃ --> KCl + O₂ the K and Cl are balanced with one of each on both sides of the equation. The oxygen has an LCM of 6 so you add coefficients: 2KClO₃ --> KCl + 3O₂. This makes it so that K and Cl don’t balance anymore. But by noticing that the LCM for both elements is now 2 you can add a coefficient to KCl on the products side to get the equation to balance: 2KClO₃ --> 2KCl + 3O₂

   The key here is to make a series of changes, each of which gets you closer to a balanced chemical equation.
4. Sometimes atoms of one element appear more than once on one side of an equation. Balance those last. Find the elements which appear in the fewest numbers of molecules and balance them first. Continue in sequence until you balance the element which appears in the most molecules last.
5. Since hydrogen is likely to appear in many molecules in an equation, save balancing it until you have balanced other elements first.
6. Balance molecules of O₂ or molecules that contain oxygen after you have balanced hydrogen.
7. Never change subscripts: don’t be tempted to change NaCl to Na₂Cl since that does not exist. Do not change H₂O to H₂O₂ since they are not the same chemical.
8. Do not put a coefficient in the middle of a formula. It just doesn’t work! (Do not write something like H₂2O).
9. A chemical equation is properly balanced only when the final set of coefficients are all whole numbers with no common factors other than one. For example, this equation is balanced:
   4H₂ + 2O₂ ---> 4H₂O
   but all the coefficients have a common factor of two. The best way to write this equation is:
   2H₂ + O₂ ---> 2H₂O

Here is an example of how to approach the problem of balancing a chemical equation: Fe + O₂ ---> Fe₂O₃
In the unbalanced equation, there is only one Fe on the left and two on the right. Putting a two in front of the Fe on the left brings the irons into balance.
2Fe + O₂ ---> Fe₂O₃
Now the oxygen needs to be balanced. This is a common problem, here is how to solve it:

1. The oxygen on the left comes in units of two, the oxygen on the right in units of three. The LCM is 6
2. Put a coefficient of 3 in front of the oxygen on the reactant side. Put a coefficient of 2 in front of the Fe₂O₃ on the product side.

2Fe + 3O₂ ---> 2Fe₂O₃
The Fe was balanced, but has become unbalanced because of the changes made to balance oxygen. Changing the two to a four in front of Fe on the left solves this.
4Fe + 3O₂ ---> 2Fe₂O₃

 

Problems

Balance the following chemical equations. Please write neatly and clearly indicate the final answer for each problem. I advise you to use a pencil and erase the coefficients that you change, leaving only the correct solution for each equation.

 

More Problems