Molarity Example Problem

Converting Mass to Moles

Sugar cubes are pre-measured blocks of sucrose. You can calculate the molarity of a solution made from dissolving sugar in water.
Sugar cubes are pre-measured blocks of sucrose. You can calculate the molarity of a solution made from dissolving sugar in water. André Saß / EyeEm / Getty Images

Molarity is a unit in chemistry that quantifies the concentration of a solution by measuring moles of solute per liter of solution. The concept of molarity can be tough to grasp, but with enough practice, you'll be converting mass to moles in no time. Use this example molarity calculation of a sugar solution to practice. The sugar (the solute) is dissolved in water (the solvent).

Calculating Molarity Example Problem

In this problem, a four gram sugar cube (sucrose: C12H22O11) is dissolved in a 350-milliliter cup of hot water. Find the molarity of the sugar solution.

Start with the equation for molarity: M (molarity) = m/V

Then, use the equation and follow these steps to calculate molarity.

Step 1: Determine Moles of Solute

The first step in calculating molarity is to determine the number of moles in four grams of solute (sucrose) by finding the atomic mass of each atom in the solution. This can be done using the periodic table. The chemical formula for sucrose is C12H22O11: 12 carbon, 22 hydrogen, and 11 oxygen. You will need to multiply the atomic mass of each atom by the number of atoms of that element in a solution.

For sucrose, multiply the mass of hydrogen (which is about 1) by the number of hydrogen atoms (22) in sucrose. You may need to use more significant figures for the atomic masses for your calculations, but for this example, only 1 significant figure was given for the mass of sugar, so one significant figure for atomic mass is used.

Once you have the product of each atom, add together the values to get the total grams per mole of sucrose. See the calculation below.

C12H22O11 = (12)(12) + (1)(22) + (16)(11)
C12H22O11 = 144 + 22+ 176
C12H22O11 = 342 g/mol

To get the number of moles in a specific mass of solution, divide the mass in grams by the number of grams per mole in the sample. See below.

4 g/(342 g/mol) = 0.0117 mol

Step 2: Determine the Volume of Solution in Liters

In the end, you need the volume of both the solution and the solvent, not one or the other. Often, however, the amount of solute dissolved in a solution doesn't change the volume of the solution enough to affect your final answer, so you can simply use the volume of solvent. Exceptions to this are often made clear in a problem's instructions.

For this example, just convert milliliters of water to liters.

350 ml x (1L/1000 ml) = 0.350 L

Step 3: Determine the Molarity of the Solution

The third and final step is to plug the values you have obtained in steps one and two into the molarity equation. Plug 0.0117 mol in for m and 0.350 in for V.

M = m/V
M = 0.0117 mol/0.350 L
M = 0.033 mol/L

Answer

The molarity of the sugar solution is 0.033 mol/L.

Tips for Success

Be sure to use the same number of significant figures, which you should have obtained from the period table, throughout your calculation. Not doing so can give you an incorrect or imprecise answer. When in doubt, use the number of significant figures provided to you in the problem in the mass of solute.

Keep in mind that not every solution is comprised of only one substance. For solutions made by mixing two or more liquids, finding the correct volume of solution is particularly important. You can't always just add together the volumes of each to get the final volume. If you mix alcohol and water, for example, the final volume will be less than the sum of the volumes of alcohol and water. The concept of miscibility comes into play here and in examples like it.