In chemistry and pharmacology, percentages (% v/v, % v/w, % w/w, and % w/v) are used to express the concentration of a solute (usually a substance dissolved in a solvent) in a solution. The different types of percentages represent the ratio of volume or weight of the solute to the volume or weight of the solution or solvent. Let's break down each type:
% v/v (percent volume/volume):
This percentage represents the volume of the solute (liquid) in a given volume of the solution (liquid). It is calculated as follows:
% v/v = (Volume of solute / Volume of solution) x 100
Example 1, if you mix 20 mL of alcohol with 80 mL of water, the % v/v of alcohol in the resulting solution is:
% v/v = (20 mL / 100 mL) x 100 = 20%
Example 2, when 50ml of sulphuric acid is diluted with 50ml of water, there will
be 50ml of sulphuric acid in a total volume of 100ml. Therefore, we would express
the concentration of this solution as sulphuric acid 50% v/v.
% v/w (percent volume/weight):
This percentage represents the volume of the solute (liquid) in a given weight of the solution (solid or liquid). It is calculated as follows:
% v/w = (Volume of solute / Weight of solution) x 100
For example, if you dissolve 30 mL of liquid medicine in 120 grams of syrup, the % v/w of the medicine in the syrup is:
% v/w = (30 mL / 120 g) x 100 = 25%
% w/v (percent weight/volume):
This percentage represents the weight of the solute (solid) in a given volume of the solution (liquid). It is calculated as follows:
% w/v = (Weight of solute / Volume of solution) x 100
For example, if you dissolve 10 grams of sugar in 200 mL of water, the % w/v of sugar in the solution is:
% w/v = (10 g / 200 mL) x 100 = 5%
It's important to pay attention to the units of measurement (volume or weight) used in the given data to correctly interpret and calculate the different types of percentages.
% w/w (percent weight/weight):
This percentage represents the weight of the solute (solid) in a given weight of the solution (solid or liquid). It is calculated as follows:
% w/w = (Weight of solute / Weight of solution) x 100
For example, if you mix 15 grams of salt with 85 grams of sugar, the % w/w of salt in the mixture is:
% w/w = (15 g / 100 g) x 100 = 15%
Example:
What is % w/v of a solution that has 7.5g of sodium chloride diluted to 100 mL
with deionized water?
By definition, a percent w/v solution is the measure of weight per 100 mL.
7.5 g/100 mL = 7.5%
You can calculate this value as well:
X% = 7.5 g NaCl/100 mL of solution
X/100 = 7.5/100
Cross multiplying,
100 X = 750
X = 7.5% w/v
When working out the % v/v of a solution, the same method is used except for the volume of the solute (ml) divided by the volume of the solution (ml). For example, a 1000ml solution that contains 450ml methanol has a methanol concentration of 45% v/v (450 / 1000 x 100).
The method for calculating % w/w uses the same steps instead it is weight divided by weight.