How to Convert Milligrams Per Liter to Molarity

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One mole of a substance contains 6.022140857×1023 basic particles of that substance. This is known as Avogadro's number and comes from the number of particles in exactly 12 grams of carbon.

The number of grams of any element that constitute one mole of that element, or its molecular mass, can be found on the periodic table of the elements, usually at the very bottom of each element's square. This number, which has units of mol/g, always relates closely to twice an element's atomic number because each element has an equal number of protons and neutrons and comparatively small mass from other sources. The molecular mass thus increases in a linear manner as one moves to the right and downward in the periodic table.

The molarity of a solution is the number of moles of a dissolved substance per liter of water (or other solvent, but it is usually water). It has units of mol/L, usually designated M. This is useful for chemists to know because it helps predict the behavior of reactions that occur in solutions far more precisely than masses of reactants do. Therefore, you may need to convert mass per unit volume, such as milligrams per liter, to molarity.

For example, suppose you have 5 L of solution containing a concentration of 1,150 mg/L of elemental sodium.

To convert milligrams per liter to molarity:

Step 1: Determine the Mass of Solute Present

Since concentration is mass divided by volume, mass equals volume times concentration:

(5 L)(1,150 mg/L) = 5,750 mg

Step 2: Convert From Milligrams to Grams

Divide by 1,000 to get the number of grams:

5,750 mg ÷ 1,000 = 5.75 g

Step 3: Convert From Grams to Moles

According to the periodic table, the molecular weight of sodium is 22.989.

(5.75 g)(mol/22.989 g) = 0.25 mol

Step 4: Calculate the Molarity

Divide the number of moles by the volume of solution to get molarity:

0.25 mol ÷ 5 L = 0.05 mol/L = 0.05 M

References

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 ScienceBlogs.com 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 www.kemibe.com.

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