Determine Concentration and Molarity

Determine a Concentration From A Known Mass of Solute

If you know how much solute you have, you can calculate molarity.
If you know how much solute you have, you can calculate molarity. Chris Ryan / Getty Images

Molarity is one of the most common and important units of concentration used in chemistry. This concentration problem illustrates how to find molarity of a solution if you know how much solute and solvent are present.

Concentration and Molarity Example Problem

Determine the molarity of a solution made by dissolving 20.0 g of NaOH in sufficient water to yield a 482 cm3 solution.

How to Solve the Problem

Molarity is an expression of the moles of solute (NaOH) per liter of solution (water).

To work this problem, you need to be able to calculate the number of moles of sodium hydroxide (NaOH) and be able to convert cubic centimeters of a solution into liters. You can refer to the Worked Unit Conversions if you need more help.

Step 1 Calculate the number of moles of NaOH that are in 20.0 grams.

Look up the atomic masses for the elements in NaOH from the Periodic Table. The atomic masses are found to be:

Na is 23.0
H is 1.0
O is 16.0

Plugging these values:

1 mol NaOH weighs 23.0 g + 16.0 g + 1.0 g = 40.0 g

So the number of moles in 20.0 g is:

moles NaOH = 20.0 g × 1 mol/40.0 g = 0.500 mol

Step 2 Determine the volume of solution in liters.

1 liter is 1000 cm3, so the volume of solution is: liters solution = 482 cm3 × 1 liter/1000 cm3 = 0.482 liter

Step 3 Determine the molarity of the solution.

Simply divide the number of moles by the volume of solution to get the molarity:

molarity = 0.500 mol / 0.482 liter
molarity = 1.04 mol/liter = 1.04 M

Answer

The molarity of a solution made by dissolving 20.0 g of NaOH to make a 482 cm3 solution is 1.04 M

Tips for Solving Concentration Problems

  • In this example, the solute (sodium hydroxide) and solvent (water) were identified. You may not always be told which chemical is the solute and which is the solvent. Often the solute is a solid, while the solvent is a liquid. It's also possible to make up solutions of gases and solids or of liquid solutes in liquid solvents. In general, the solute is the chemical (or chemicals) present in smaller amounts. The solvent makes up most of the solution. 
  • Molarity is concerned with the total volume of the solution, not the volume of the solvent. You can approximate molarity by dividing moles of solute by volume of solvent that is added, but this isn't correct and can lead to significant error when a large amount of solute is present.
  • Significant figures can also come into play when reporting concentration in molarity. There will be a degree of uncertainty in the mass measurement of the solute. An analytical balance will yield a more precise measurement than weighing on a kitchen scale, for example. The glassware used to measure the volume of solvent also matters. A volumetric flask or graduated cylinder will yield a more precise value than a beaker, for example. There's also error in reading the volume, relating to the meniscus of the liquid. The number of significant digits in your molarity is only as many as that in your least precise measurement.