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All good recipes tell the chef how much of each ingredient is required. The process by which we figure out how much of each reactant is required for a chemical process is called balancing the equation.

Let's learn equation balancing by studying the equation for making water from hydrogen and oxygen: H_{2} + O_{2} ⇔ H_{2}O. This equation, as well as any others you may come across, can be balanced by following these steps.

**Step 1**

Before balancing equations, tell yourself never to change any of the chemical formulas of either the reactants or products. If you change the formulas by adding subscripts or altering them in any way, your equation is guaranteed to be wrong!

**Step 2**

Draw a table that shows the number of atoms of each element both before and after the arrow. For the reaction of hydrogen and oxygen to make water, this table would look like this:

Element | Before the Arrow | After the Arrow |
---|---|---|

H | 2 | 2 |

O | 2 | 1 |

**Step 3**

The law of conservation of mass makes it important that the number of atoms of each element doesn't change during the equation. If there were more atoms of an element on one side of the equation than the other, this would imply either the formation or destruction of matter, which the law of conservation of mass for bids.

Change the equation in a way that will make the number of atoms of each element in the "before" and "after" columns match one another. To do this, the formulas of the chemicals involved can't be changed. Instead, we add numbers called "coefficients" in front of the formulas in the equation. These coefficients allow us to multiply the number of atoms of each element in the compound so the columns will match up.

Examining our table, we see that the hydrogen columns already match, so we'll change the equation to make the oxygen columns match. There are two oxygen atoms before the arrow and only one after the arrow, so we'll put a "2" in front of the molecule containing oxygen after the arrow to give us the following:

H_{2} + O_{2} ⇔ 2 H_{2}O

**Step 4**

Redo the table to reflect the change in the equation. If the columns match, the equation is balanced and we're done! If the columns don't match, we need to go back to step 3 and change another number.

In our example, we see that the table has changed in the following way:

Element | Before the Arrow | After the Arrow |
---|---|---|

H | 2 | 4 |

O | 2 | 2 |

The best way to learn how to solve equations is to practice doing them over and over. The tricks in this section help me to solve equations; with practice, you'll discover tricks of your own!

As you can see, the oxygen columns now match perfectly, which is exactly what we were trying to do by adding the "2" in front of H_{2}O. Unfortunately, the hydrogen column, which previously had matched, is now unbalanced. Though this may make it seem as if we've made a mistake, this is a common event when balancing equations.

After an examination of the revised table, it becomes clear that we should add a "2" in front of H_{2} before the arrow so we'll have four hydrogen atoms before the arrow. Our revised equation now looks like this:

- 2 H
_{2}+ O_{2}⇔ 2 H_{2}O

Because we've changed another number, we can redo our table to find that the numbers of hydrogen and oxygen atoms are the same on both sides of the equation:

Element | Before the Arrow | After the Arrow |
---|---|---|

H | 4 | 4 |

O | 2 | 2 |

Problem 1: Balance the following equations:

a) CaCl_{2} + AgNO_{3} ⇔ AgCl + Ca(NO_{3})_{2}

b) (NH_{4})_{2}CO_{3} + FeBr_{3} ⇔ Fe_{2}(CO_{3})_{3} + NH_{4}Br

c) P_{4} + O_{2} ⇔ P_{2}O_{5}

As with recipes, some equations are more difficult than others. Though these may initially be frustrating, below are some tips you can try when the going gets tough:

- If you've been working on an equation for a few minutes and aren't getting any closer to solving it, start over again from scratch. Though this doesn't guarantee success, it will allow you to get a fresh perspective on what you're doing.
- If you still can't solve the problem, start over and put a "2" in front of the most complicated-looking compound in the equation. If you still can't solve the problem, start the equation over by writing a "3" in front of this molecule. Eventually, you'll be able to solve the problem.
- If you can reduce all of the coefficients in an equation by a lowest common denominator, do it! An example of what I mean is shown here.

4 H_{2}+ 2 O_{2}⇔ 4 H_{2}O

If you made the table showing the number of atoms in this equation, it would work out just fine. However, it's more proper to write this in a reduced form by dividing all of the subscripts by two to yield the equation that we solved earlier.

Excerpted from The Complete Idiot's Guide to Chemistry © 2003 by Ian Guch. All rights reserved including the right
of reproduction in whole or in part in any form. Used by
arrangement with **Alpha Books**, a member of Penguin Group
(USA) Inc.

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