Originally Posted by
juliaxo
Because whatever is on the products side has to be equal to what is on the reactants side. So, your original equation was SO2 + O2 -> SO3, and you have 1 sulfur and 4 oxygen on the reactant side, but 1 sulfur and 3 oxygen on the products side. So by adding the coefficients and making it 2SO2 + O2 -> 2SO3, you now have 2 sulfur and 6 oxygen on the reactants side and the products side, so the equation is balanced.
If I had numbers like S 3 and 4 I just multiply by whatever will make both the same number. It takes a while to get used to all of it, but my teacher would give us really complicated combustion reactions to balance where your ending coefficients of the balanced equations are numbers like 17 and 51 and they take like 20 minutes to balance, it really is just guessing and checking half the time.