# How to Calculate Concentration of a Chemical Solution

The concentration of a chemical solution refers to the amount of solute that is dissolved in a solvent. Although it’s common to think of a solute as a solid that is added to a solvent (e.g., adding table salt to water), the solute could exist in another phase. If the solute and the solvent are in the same phase, then the solvent is the substance presence in the largest percentage. For example, if we add a small amount of ethanol to water, then the ethanol is the solute and the water is the solvent. If we add a smaller amount of water to a larger amount of ethanol, then the water would be the solute.

### Units of Concentration

Once the solute and solvent have been identified, you can determine the concentration of the solution. There are several ways to express concentration. The most common units are percent composition by mass, mole fraction, molarity, molality, or normality.

#### Percent Composition by Mass (%)

This is the mass of the solute divided by the mass of the solution (mass of solute plus mass of solvent), multiplied by 100.

Example:
Determine the percent composition by mass of a 100 g salt solution which contains 20 g salt.

20 g NaCl / 100 g solution x 100 = 20% NaCl solution

#### Mole Fraction (X)

Mole fraction is the number of moles of a compound divided by the total number of moles of all chemical species in the solution. The sum of all mole fractions in a solution must equal 1.

Example:
What are the mole fractions of the components of the solution formed when 92 g glycerol is mixed with 90 g water? (molecular weight water = 18; molecular weight of glycerol = 92)

90 g water = 90 g x 1 mol / 18 g = 5 mol water
92 g glycerol = 92 g x 1 mol / 92 g = 1 mol glycerol
total mol = 5 + 1 = 6 mol
xwater = 5 mol / 6 mol = 0.833
x glycerol = 1 mol / 6 mol = 0.167

It’s a good idea to check your math by making sure the mole fractions add up to 1:
xwater + xglycerol = .833 + 0.167 = 1.000

#### Molarity (M)

Molarity is probably the most commonly used unit of concentration. It is the number of moles of solute per liter of solution (not volume of solvent).

Example:
What is the molarity of a solution made when water is added to 11 g CaCl2 to make 100 mL of solution?

11 g CaCl2 / (110 g CaCl2 / mol CaCl2) = 0.10 mol CaCl2
100 mL x 1 L / 1000 mL = 0.10 L
molarity = 0.10 mol / 0.10 L
molarity = 1.0 M

#### Molality (m)

Molality is the number of moles of solute per kilogram of solvent. Because the density of water at 25 °C is about 1 kilogram per liter, molality is approximately equal to molarity for dilute aqueous solutions at this temperature. This is a useful approximation, but remember that it is only an approximation and doesn’t apply when the solution is at a different temperature, isn’t dilute, or uses a solvent other than water.

Example:
What is the molality of a solution of 10 g NaOH in 500 g water?

10 g NaOH / (4 g NaOH / 1 mol NaOH) = 0.25 mol NaOH
500 g water x 1 kg / 1000 g = 0.50 kg water
molality = 0.25 mol / 0.50 kg
molality = 0.05 M / kg
molality = 0.50 m

#### Normality (N)

Normality is equal to the gram equivalent weight of a solute per liter of solution. A gram equivalent weight or equivalent is a measure of the reactive capacity of a given molecule. Normality is the only concentration unit that is reaction dependent.

Example:
1 M sulfuric acid (H2SO4) is 2 N for acid-base reactions because each mole of sulfuric acid provides 2 moles of H+ ions. On the other hand, 1 M sulfuric acid is 1 N for sulfate precipitation, since 1 mole of sulfuric acid provides 1 mole of sulfate ions.

### Making Dilutions

You dilute a solution whenever you add solvent to a solution. Adding solvent results in a solution of lower concentration. You can calculate the concentration of a solution following a dilution by applying this equation:

MiVi = MfVf

where M is molarity, V is volume, and the subscripts i and f refer to the initial and final values.

Example:
How many millilieters of 5.5 M NaOH are needed to prepare 300 mL of 1.2 M NaOH?

Solution:
5.5 M x V1 = 1.2 M x 0.3 L
V1 = 1.2 M x 0.3 L / 5.5 M
V1 = 0.065 L
V1 = 65 mL

So, to prepare the 1.2 M NaOH solution, you pour 65 mL of 5.5 M NaOH into your container and add water to get 300 mL final volume.