Chemical dilutions are not always straightforward. Common methods of dilution include molarity and percentage by weight or percentage by volume dilutions. Normality is not a direct measurement of the amount of a compound in a solution, but an indirect one that measures the amount of hydrogen ions that will occur when a chemical is diluted. It is related to molarity, so in order to calculate normality, the chemist also has to know the molarity of the chemical. Normality is a useful tool for figuring out how much of an acid or a base to dilute.
Find out how many grams a mole of nitric acid is. Nitric acid's chemical formula is HNO3, which means it has one hydrogen, one nitrogen and three oxygen atoms in its structure. Each of these atoms weighs a particular amount, and if you add them all together you can calculate how much mass one molecule of HNO3 has. One mole of a substance is its molecular weight as grams. One mole of nitric acid is 63.0128 grams. This means that if you dissolve 63.0128g of nitric acid into one litre of water, the resultant solution is at a molarity concentration of one, also referred to as 1M.
Count how many hydrogens are in the nitric acid. The hydrogens turn into electrically charged ions in solution and it is this electric charge that normality measures. HNO3 has only one hydrogen that can turn into an ion.
Relate the molarity of the solution to the normality. A 1M solution of an acid or base is not necessarily equivalent to a solution of one normal, or 1N. Chemists use the concept of "equivalents" in this calculation. An equivalent refers to the amount of hydrogen ions relative to the molarity. In the case of nitric acid, the equivalent is one hydrogen to 1M. (If the acid had two hydrogens, then the equivalent would be two.)
Use the now known normality of one mole of nitric acid to calculate a 6N solution. A 1N solution contains one mole, or 63.0128g of nitric acid. To make up a solution that has six times more normality (or 6N,) you have to put six times more nitric acid into the solution. An equation to help you calculate this is: Normality (N) = Molarity (M) x Equivalent. For nitric acid this translates to: 6N = ?M x 1. So you need six moles of substance per litre to make up a 6N solution.
Multiply 63.0128g by six to get the amount of nitric acid you need to dissolve in one litre to make up a 6N solution. This turns out to be 378.0768g.