Introduction to percentage solutions

Percentage weight by volume (w/v) solutions

Percentage volume by volume (v/v) solutions

Percentage weight by weight (w/w) solutions

Summary

**Introduction**

For some reason percentage solutions cause students problems. I have no idea why this should be the case, and once you have completed this course percentage solutions should no longer cause you any problems.

**What are percentage solutions?**

A percentage solution is an amount or volume of something per 100 ml or 100 g of a solution. It is as simple as that.

**Why are they used?**

Percentage solutions are just a convenient and easy way to record solution concentrations. One advantage of percentage solutions is that you don't need to know anything about the compound in terms of molecular weight as all you need is the percentage of the solution.

**Why are their three types of percentage solutions?**

This is slightly difficult to explain, particularly before we have tackled the calculation of percentage solutions in the subsequent lectures.

However, there are three types of percentage solution:

**Percentage weight by volume (w/v**)**Percentage volume by volume (v/v**)**Percentage weight by weight (w/w**)

So, why?

Well, there are three types of percentage solution to take in to account the problems associated with measuring out material. All three can be used for describing the concentration of a solution, and using the wrong type at the wrong time can result in solutions of an incorrect final concentration.

In the different types, w/v, v/v, and w/w, the first letter represents the solute (the thing being dissolved or diluted, and the second letter represents the solvent (e.g. water) into which the solute is being mixed or dissolved.

When measuring out a powder, e.g. sodium chloride, you would use weight as the material is a solid and measuring out a consistent volume of sodium chloride would be very difficult as the volume would be dependent on crystal size and how those crystals settle. So, for a solid we tend to use weight, and so would use w/v (weight by volume) or w/w (weight by weight), where the solid is represented by the first w (weight).

When measuring out a liquid you could use weight (w) or volume (v) to describe the amount of liquid being used. However, it should be noted that weight (w) or volume (v) cannot be used interchangeably (i.e. if it says v/v you can't switch to w/v) in such situations as you will end up with the wrong concentrations.

For example, let's say you have to make a 5% solution of glycerol (we will get in to the calculations more in the later lectures, but stick with me as we work through this). If you make this as
**w/v**, **v/v** or **w/w** you can end up with different final concentrations.

The molecular weight of glycerol is: 92.09 g/mol

And the density (how much 1 ml weighs) of glycerol is: 1.261 g/ml

If you were to make 100 ml of a 5% (w\v) solution (see a later lecture for an explanation of the calculation) you would take 5 g of glycerol and make up to 100 ml with water. This would be equivalent to 50 g in 1 litre, so it would be 50/92.09, or 0.543 M solution (molarity calculations are also explained in another lecture).

If you were to make 100 ml of a 5% (v/v) solution (see a later lecture for an explanation of the calculation) you would take 5 ml of glycerol and make up to 100 ml with water.

As the density of glycerol is 1.261 g/ml, then 5 ml would be 6.305 g per 100 ml, or 63.05 g per litre. This would be a 63.05/92.09, or 0.685 M solution, which is clearly different from the concentration of the 5% (w/v) solution (0.543 M) calculated above.

Finally, a 5% (w/w) solution. In this case it is mass of the compound divided by the mass of the compound plus the mass of liquid (this is explained in more detail in a later lecture), so in the case of glycerol a 5% (w/w) solution in water would be 5 g of glycerol mixed with 95 ml of water (as 1 ml of water weighs 1 g). As we know the density of glycerol is 1.261 g/ml, the 5 g would be 5/1.261, or 3.965 ml. This means the final volume would be 95 + 3.965, which is 98.965 ml. This 98.965 ml contains 5 g of glycerol, so this would be 50.523 g per litre. As the molecular weight of glycerol is 92.09 g/mol, then the concentration would be 0.549 M.

As can be seen, for a 5% glycerol solution we have 3 possible final concentrations:

- 5% w/v = 0.543 M
- 5% v/v = 0.685 M
- 5% w/w = 0.549 M.

Hence, as you can see when working with percentage solutions it is very important to state whether it is weight by volume (w/v), volume by volume (v/v), or weight by weight (w/w).

**Summary**

An understanding of percentage solutions and how they are calculated is critical in the biosciences and chemistry as the concentration of solutions is often quoted in percentage terms.

**Missing something? A mistake?**

Have I missed something in this lecture? Is there something you would like to be included? Have I made a mistake?

If the answer is yes to any of the above questions then please email me at drnickmorris@gmail.com and tell me what you would like included and why, or what the mistake is and where it can be found. Thanks.

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