In this example problem, we will balance a reaction for a chemical equation by balancing the atoms of each element on both sides. Our problem reads the combustion of liquid C6H12OH and I2O and water vapor. Write a balanced chemical equation for the reaction. Since this is a combustion reaction, we're combining our C6H12OH liquid with oxygen gas to produce carbon dioxide and water vapor. The elements we need to balance are carbon, hydrogen, and oxygen. We'll start by balancing the elements that only show up in one compound on both sides, which are carbon and hydrogen. We will balance the oxygen last because it shows up in more than one compound on both sides. Initially, we have six carbons on the left and one on the right. So, if we put a 1 as a coefficient in front of C6H12O6 and 6 as a coefficient in front of carbon dioxide, we will have 6 carbons on each side. Next, we can balance hydrogen. We currently have 12 hydrogens on the left (in C6H12O) and in order to get 12 hydrogens on the right, we'll need 6 H2O. Now, we can calculate how many oxygens we currently have on the right. We have 6 carbon dioxides, and each one has two oxygens. We also have 6 H2O molecules, and each H2O molecule has one oxygen. So, we have a total of 18 oxygens on the right. In order to determine the coefficient for O2, we'll know that the sum of oxygen on the left has to be equal to 18. There's one C6H12OH, and it contains one oxygen. Each O2 molecule contains two oxygens, so our coefficient (which we will assign a value of x) times our coefficient has to equal 18. Solving for our coefficient x: x is equal to (18-1)/2, which is 17/2. With this coefficient, we have 18 oxygens on both sides. However, we can't have fractions in our coefficients, so to eliminate the fraction, we'll multiply all of these coefficients by 2, and we'll get the coefficients 2, 17, 12, and 12. We can double-check to make sure we have the same number of elements on both sides, and we'll now have 12 carbons on both sides, 24 hydrogens, and 36 oxygens. So, our balanced chemical equation is: 2 C6H12OH + 17/2 O2 gas produces 12 CO2 gas + 12 H2O gas.