1. Percent By Mass Percent by mass, %m/m can be calculated as:
Defined as how many parts exist in every 100 parts of the whole; In other words, the mass of the solute divided by the mass of the solution (mass of solute plus mass of solvent), multiplied by 100.
Percent by mass, %m/m can be calculated as:
Example: Determine the percent composition by mass of a 100 g salt solution which contains 20 g salt.
Solution: 20 g NaCl / 100 g solution x 100 = 20% NaCl solution

2. Percent By Volume
If both the solute and solvent are both liquids, we need to use a different way to define the concentration percentage.
Volume percent or volume/volume percent most often is used when preparing solutions of liquids.
Another example: 70% v/v rubbing alcohol may be prepared by taking 700 ml of isopropyl alcohol and adding sufficient water to obtain 1000 ml of solution (which will not be 300 ml).

3. Mole Fraction
Yet another way to use the famous Mole, Mole Fraction takes into account the number of moles of a particular compound compared to the number of total moles in solution.
Ex.: 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)

4. Mole Fraction Example:
Solution: 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 = = 6 mol xwater = 5 mol / 6 mol = x glycerol = 1 mol / 6 mol = It's a good idea to check your math by making sure the mole fractions add up to 1: xwater + xglycerol = = 1.000

5. Molality
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.
Ex.: What is the molality of a solution of 10 g NaOH in 500 g water?

6. Solution
10 g NaOH / (40 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

7. Normality
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.
Ex.: 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.