The chemical equation represents a chemical reaction. For example, we can represent the combustion of methane gas using the equation shown. Methane gas reacts with oxygen gas to produce carbon dioxide gas and water vapor. The reactants are shown on the left, the products are shown on the right, and they're separated by an arrow. The state of each reactant or product can be represented in parentheses with a "g" for gas, "l" for liquid, "s" for solid, or "aq" for an aqueous solution where water is the solvent. According to the law of conservation of mass, we cannot create or destroy mass in a chemical reaction, so we need the same number of atoms of each element on each side of our chemical equation. We can only balance a chemical equation using coefficients; we cannot change the subscripts within a compound. If the coefficient is 1, it's not written explicitly. So in the combustion of methane gas, one molecule of methane combines with two molecules of oxygen gas to produce one molecule of carbon dioxide gas and two molecules of water vapor. With these coefficients, we have one atom of carbon on each side, four atoms of hydrogen, and four atoms of oxygen. To balance a chemical equation, we first write the unbalanced equation without coefficients, just indicating which substances are reactants and products. Then we begin balancing the equation starting with elements that show in only one substance on each side of the equation. If there's more than one element that is in only one substance on each side of the equation, we can start with the element in the most complicated compound first. We'll balance atoms that occur as free elements last. For example, the oxygen molecule in the combustion of methane was a free element. If we have fractions in our coefficients, we can multiply all coefficients by the same factor to eliminate the fractions and get whole numbers. And finally, we can check to make sure that all of our elements are balanced with the same number of atoms on each side. Let's practice by balancing this combustion reaction. We need to balance carbon, hydrogen, nitrogen, and oxygen. Since oxygen shows up as a free element, we'll balance oxygen last. The other three elements show up in only one compound on each side of the equation, so we can balance them first. Let's start with carbon. We can get four carbon atoms on each side of our equation by using coefficients of one and four. Next, we can balance hydrogen. We have six atoms of hydrogen on the left, so we can add a coefficient of three in front of H2O to get six atoms of hydrogen on the right. To balance nitrogen, we currently have two atoms of nitrogen on the left, and we can get two atoms on the right by adding a coefficient of two in front of nitrogen dioxide. Lastly, we'll balance oxygen. On the right, we have four carbon dioxide molecules with two oxygen atoms each, plus three water vapor molecules with one oxygen atom each, and two nitrogen dioxide molecules with two oxygen atoms each. This gives us a total of 15 oxygen atoms on the right. On the left, we have two oxygen atoms in C4H6N2O2 and we want to calculate the coefficient for the oxygen molecule. We'll represent that coefficient as "x". So on the left, we have two plus two "x" oxygen atoms because each oxygen molecule has two oxygen atoms. We can set these to be equal to each other and solve for "x". Subtracting two from each side, we get 2x equals 13. And dividing both sides by two, we get x equals 13/2; x is our coefficient for the oxygen molecule. We don't want fractions in our coefficients, so we can multiply all coefficients by two to get all whole numbers. Our new coefficients are 2, 13, 8, 6, and 4. In our last step, we can double-check that we have the same number of atoms of each element on both sides of the equation. We have 8 carbon atoms, 12 hydrogen atoms, 4 nitrogen atoms, and 30 oxygen atoms. This chemical equation is now balanced.