When working with chemical solutions in the lab, there is usually a concentration associated with them. The concentration of a solution is often given in **molarity** (moles of solution per liter solution). Sometimes, however, it can be given by milligrams or grams of solute per liter solution (mg/L or g/L). To go from mg/L to moles/L you will need to convert mg to moles. How do you do that?

Well, you make use of the molar mass of the solute! This allows you to convert from grams of a substance to moles of a substance.

## Converting From Milligrams to Grams

Say you have 1,567 milligrams of NaCl in 1 L of solution. How would you calculate the molarity? Well, first you need to convert the solute (NaCl) from milligrams to grams. And then you can go from grams to moles.

There are 1,000 milligrams in every gram. This gives a **conversion factor** to change the quantity of 1,567 milligrams into grams:

By making sure that the units cancel, you can be sure that you are using the conversion factor correctly. Thus, you can see that 1,567 milligrams of NaCl is the same as 1.567 grams of NaCl.

Why convert from milligrams to grams? Because the molar mass of the solute gives you the mass of a substance per mole of that substance.

## Converting From Grams to Moles

To convert from grams to moles you need to use the molar mass. The molar mass of a substance is calculated by adding together the molar mass of the components involved. For example, for NaCl, you would need the molar mass of sodium and the molar mass of chloride. You can find these using the periodic table.

The molar mass of sodium is 22.99 grams/mole or g/mol, and the molar mass of chloride is 35.45 g/mol. Added together, this makes the molar mass of NaCl 58.44 g/mol. Using this conversion factor, you can convert from grams of NaCl to moles of NaCl:

In 1.567 grams of NaCl, there are 0.027 moles of NaCl. Now that you know there are 0.027 moles of NaCl, you can divide by the total volume (1 L) to find the molarity:

The concentration of a 1 liter solution containing 1,567 milligrams is thus 0.027M.

Take a look at the following examples that convert g/L to molarity in one step and convert mg/mL to molarity in one step.

## Convert From mg/mL to Molarity

What is the molarity of a 15 mg/mL solution of magnesium chloride?

First, mg/mL is the same as g/L. This makes it a little easier because you don't need to convert between milligrams and grams or milliliters and liters. With the concentration in g/L you can then convert grams to moles (the molar mass of MgCl_{2}) and you'll have the molarity. Take a look:

What if you have a protein solution and the concentration is given to you in mg/mL? Say you have a solution of proteinase K that is 25 mg/mL. How would you find the molarity of this solution?

You can make use of the molecular weight of the protein. Proteinase K is 29,800 kDa, which is about the same as 29,800 g/mol. This give you another conversion factor. Here's how you would find the concentration of the solution:

This means that a 25 mg/mL solution of proteinase K is the same as a 8.4 x 10^{-4} M solution of proteinase K. Saying 25 mg/mL is much easier than 8.4 x 10^{-4} M, so sometimes talking about concentrations in milligrams per milliliter can be easier.

References

Tips

- Use an online conversion calculator to double-check your answers.

About the Author

Riti Gupta holds a Honors Bachelors degree in Biochemistry from the University of Oregon and a PhD in biology from Johns Hopkins University. She has an interest in astrobiology and manned spaceflight. She has over 10 years of biology research experience in academia. She currently teaches classes in biochemistry, biology, biophysics, astrobiology, as well as high school AP Biology and Chemistry test prep.