**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 cm^{3} solution.

**Solution**

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 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 cm^{3}, so the volume of solution is:
liters solution = 482 cm^{3} × 1 liter/1000 cm^{3} = 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 cm^{3} solution is 1.04 M