Elements combine in whole number, that we know to be true. Thus, we need to have the smallest whole number ratio of the coefficients used to balance the equation. To balance an equation initially, you may use a fraction, but then you must modify the coefficients to make them whole numbers. Below is an example.
Reaction: C3H6O2 + O2 --> CO2 + H2O
Hint: Wait to balance oxygen last since placing a coefficient in front of elemental oxygen (O2) will not change any other elements.
Initial balancing: C3H6O2 + ?O2 --> 3CO2 + 3H2O
The carbons and hydrogens have been balanced. All that is left are the oxygens. There are a total of 9 oxygens of the product side (right of the arrow). Notice that 2 oxygens exist in the compound on the reactant side. Thus, to balance out the oxygens, an equation can be set up.
2 + x = 9 --> x = 7 --> Seven oxygens are required to balance the reaction, so this dictates that we use a coefficient in front of oxygen (O2) that will produce 7 oxygens. This will cause a coefficient of 3.5 to be used. This is not a whole number, but we can deal with that later.
Almost balanced: C3H6O2 + 3.5O2 --> 3CO2 + 3H2O
Having a fraction as a coefficient is not allowed, thus we must convert 3.5 to a whole number. To accomplish this, we will multiply 3.5 by 2. Just like in algebra, if something is done to one number, we must do the same thing to all of the numbers. Thus, all coefficients will be multiplied by 2. Doing this keeps the equation balanced.
Almost, nearly balanced: 2(C3H6O2 + 3.5O2 --> 3CO2 + 3H2O)
BALANCED!! 2C3H6O2 + 7O2 --> 6CO2 + 6H2O
Make sure that you check all of the elements on each side of the reaction to ensure that is has been balanced correctly.
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