Calculating Molarity

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The properties and behavior of many solutions depend not only on the nature of the solute and solvent but also on the concentration of the solute in the solution. Chemists use many different units when expressing concentration; however, one of the most common units is molarity. Molarity (M) is the concentration of a solution expressed as the number of moles of solute per liter of solution:

Molarity (M) =
moles solute
liters solution

For example, a 0.25 M NaOH solution (this is read as 0.25 molar) contains 0.25 moles of sodium hydroxide in every liter of solution. Anytime you see the abbreviation M you should immediately think of it as mol/L.

In order to calculate the molarity of a solution, you need to know the number of moles of solute and the total volume of the solution.

To calculate molarity:

  1. Calculate the number of moles of solute present.
  2. Calculate the number of liters of solution present.
  3. Divide the number of moles of solute by the number of liters of solution.

Instead of calculating the moles of solute and liters of solution present individually, you can also string all the calculations together in one problem:

  1. Divide the amount of solute by the volume of solution (regardless of the initial units given).
  2. Use dimensional analysis to convert the amount of solute to moles of solute.
  3. Use dimensional analysis to convert the volume of solution to liters of solution (if necessary).

The following example will illustrate both methods.

Example: What is the molarity of a solution prepared by dissolving 15.0 g of sodium hydroxide in enough water to make a total of 225 mL of solution?

Method 1:

  • Calculate the number of moles of solute present.
    mol NaOH
    =
    15.0g NaOH
    x
    1 mol NaOH
    40.0 g NaOH
    mol NaOH = 0.375 mol NaOH    

  • Calculate the number of liters of solution present.
    L soln
    =
    225 mL
    x
    1 L
    =
    0.225 L soln
    1000 mL
  • Divide the number of moles of solute by the number of liters of solution.
    M =
    0.375 mol NaOH
    = 1.67 M NaOH
    0.225 L soln

Method 2:

  • Divide the amount of solute by the volume of solution (regardless of the initial units given).
    M =
    15.0 g NaOH
    225 mL soln
  • Use dimensional analysis to convert the amount of solute to moles of solute.
    M =
    15.0 g NaOH
    x
    1 mol NaOH
    225 mL soln
    40.0 g NaOH
  • Use dimensional analysis to convert the volume of solution to liters of solution (if necessary).
    M = 15.0 g NaOH x 1 mol NaOH x
    1000 mL soln
    225 mL soln 40.0 g NaOH
    1 L soln
    M =
    1.67 mol NaOH
    = 1.67 M NaOH
    L soln

As you can see, both methods give exactly the same result. Choose whichever method is most comfortable for you. Just remember that ultimately your units must be mol/L (= M).

Chem 1115

Chem 1215

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Practice Problems

  1. What is the molarity of a solution that contains 1.724 moles of H2SO4 in 2.50 L of solution?
  2. What is the molarity of a solution prepared by dissolving 25.0 g of HCl (g) in enough water to make 150.0 mL of solution?

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