How To Find Molar Concentration

To be able to calculate the concentration of a solution is one of the most basic skills required of a scientist. Without knowing how much of a substance you're working with, you have no control over the reactions you're conducting.

Concentration of a solution is primarily reported in molarity or moles per liter. The abbreviation for molarity is M and the concentration units are mol/L.

The definition of molarity means that you can find the molarity of a solution if you know the total number of moles of the solute and the total volume of the solution. So, in order to calculate the concentration of a solution (in molarity), you need to divide moles of solute by total volume.

Say you have 10 moles of NaCl, and your total volume of solution is 5 L. To find the molarity of this solution, you need to divide the total moles of solute (NaCl) by the total volume:

\(\mathrm{\dfrac{10mol\enspace NaCl}{5L}=2M\enspace NaCl}\)

This means that your 5 L solution which contains 10 moles of NaCl is a 2 M NaCl solution. Here, "M" is said aloud as "molar."

What if you have a solution that contains 10 grams of NaCl in 5 L of solution?

To find the concentration of this new solution you need to convert from grams to moles. This requires the use of the molar mass (given in grams/mole) of the NaCl. The molar mass of a substance is found by adding together the molar mass of the individual components. For NaCl, the two components are sodium and chloride.

To find the molar mass of either of them, you need to look under their symbols on the periodic table. The molar mass of sodium is 22.99 g/mol, and the molar mass of chlorine is 35.45 g/mol. Added together, this gives you the molar mass of NaCl, which is 58.44 g/mol.

Now, you can find the concentration of a 5 L solution that contains 10 grams of NaCl.

Begin by converting grams into moles:

\(\mathrm{ 10g\enspace NaCl\Biggl(\dfrac{1mol\enspace NaCl}{58.44g\enspace NaCl}\Biggr)=0.17mol\enspace NaCl}\)

Next, you need to divide the number of moles by the total volume to find the concentration:

\(\mathrm{\dfrac{0.17mol\enspace NaCl}{5L}=0.034M\enspace NaCl}\)

This means that if you have 10 grams of NaCl in a 5 L solution, you will have a 0.034 M solution of NaCl.

What if you have a solution which contains 1,000 milligrams of NaCl in 5 L of solution?

In this case, you need to first convert from milligrams to grams. There are 1,000 milligrams in 1 gram.

So:

\(\mathrm{1000mg\enspace NaCl\Biggl(\dfrac{1g}{1000mg}\Biggr)=1g\enspace NaCl}\)

Now that you know that 1,000 milligrams corresponds to 1 gram, you can convert grams into moles using the molar mass:

\(\mathrm{ 1g\enspace NaCl\Biggl(\dfrac{1mol\enspace NaCl}{58.44g\enspace NaCl}\Biggr)=0.017mol\enspace NaCl}\)

Finally, you can take the number of moles and divide by the total volume:

\(\mathrm{\dfrac{0.017mol\enspace NaCl}{5L}=0.0034M\enspace NaCl}\)

Thus, 1,000 grams of NaCl in 5 L of total solution is the same as a 0.0034 M solution of NaCl.

The following shows a generalized version of the steps shown above or "concentration formula."

Given moles of solute and liters of solution, molarity is calculated by:

\(\mathrm{\dfrac{mol\enspace solute}{L\enspace solution}=concentration\enspace(M)}\)

Given the amount of solute in grams, the following equation gives concentration:

\(\mathrm{g\enspace solute\Biggl(\dfrac{1mol\enspace solute}{molar\enspace mass\enspace of\enspace solute\enspace g}\Biggr)\Biggl(\dfrac{1}{L\enspace solution}\Biggr)=concentration\enspace(M)}\)

Given the amount of solute in milligrams, the following equation gives concentration:

\(\mathrm{mg\enspace solute\Biggl(\dfrac{1g}{1000mg}\Biggr)\Biggl(\dfrac{1mol\enspace solute}{molar\enspace mass\enspace of\enspace solute\enspace g}\Biggr)\Biggl(\dfrac{1}{L\enspace solution}\Biggr)=concentration\enspace(M)}\)