How to Calculate the Normality of NaOH

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Normality is a unit of concentration in acid-base chemistry that is usually expressed in equivalents per liter. An equivalent is the number of equivalent weights (not the mass) of a substance. Equivalent weight, in turn, is the molar mass of a substance divided by the number of hydrogen (H+) or hydroxide (OH-) ions with which one molecule of the substance reacts in solution.

For example, calcium carbonate, which has the formula CaCO3, has a molar mass of 100.1 g. You can determine this from any periodic table of the elements. Ca has a molar mass of 40.1, C a molar mass of 12, and O a molar mass of 16, making the total molar mass of calcium carbonate equal to 40.1 + 12 + 3(16) = 100.1. Because a calcium ion has a positive charge of 2, and exists as Ca2+, each molecule of CaCO3 can potentially react with two OH- ions. Thus the equivalent weight of CaCO3 is 100.1 ÷ 2 = 50.05 g/Eq.

The upshot of this is that a 1 L solution containing, for example, 200.2 g of CaCO3 (i.e., 2 mol) would have a molarity of 2 M, but would have a normality of 2 N, because the equivalent weight of CaCO3 is only half its molecular mass, meaning that 1 mol = 2 Eq.

This principle applies to other compounds as well, for example, sodium hydroxide (NaOH). To calculate the normality of a solution of NaOH:

Step 1: Determine the Number of Moles of NaOH in the Sample

Assume for this problem that you have 0.5 L of a 2.5 M solution of NaOH. This means you have 1.25 mol of NaOH total.

Step 2: Look  Up the Molar Mass of NaOH

From the periodic table, the molar mass of Na = 23.0, that of ) = 16.0, and that of H = 1.0. 23 + 16 + 1 = 40 g.

Step 3: Determine the Number of Equivalents

You have 1.25 mol of a substance with a molar mass of 40.0 g.

(1.25 mol)(40 g/mol) = 50 g

Since the valence of NaOH is 1, for this compound, 1 mol = 1 eq. This means that for NaOH solutions, normality and molarity are the same, unlike the case with CaCO3.

Thus the normality of your NaOH solution = 2.5 N.


About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at

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