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What is % v/v, % w/w and % w/v?

% v/v
  • The volume concentration is expressed as % v/v, which stands for volume per volume. This is used when both chemicals in a solution are liquid.
  • For example, 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.
% w/w
  • The weight concentration of a solution is expressed as % w/w. This stands for weight per weight. In this case, the volume of each chemical is disregarded and only the weight is used. So, if the total mass of a 100g solution is made up of 30g hydrochloric acid in 70g of water, then we would express this as hydrochloric acid 30% w/w.

% w/v
  • Mass concentration of a solution is expressed as % w/v for weight per volume. It can alternatively be abbreviated to m/v for mass per volume. This is used when a solid chemical is dissolved in a liquid.
  • If 1g of potassium iodide is used to make up a total volume of 100ml, then a 1% w/v solution of potassium iodide has been made.

Calculating Percentages
Each percentage type can be calculated by making small changes to the same method. For example, to find the % w/v of a solution the calculation is:

(Mass of Solute (g) / Volume of Solution (ml)) x 100

Therefore, to figure out the % w/v of a 100ml solution that is made up of 65g sulphuric acid, we would divide 65g by 100ml and then multiply the answer by 100. This tells us that there is a sulphuric acid solution of 65% w/v.


Example:
What is the % w/v of a solution that has 7.5 g 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.

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