# How can I change percent concentration?

Dec 25, 2014

Let's address the question for both percent concentration by mass and for percent concentration by volume.

Percent concentration by mass is defined as the mass of solute divided by the total mass of the solution and multiplied by 100%. So,

c% = m_(solute)/(m_(solution)) * 100%, where

${m}_{s o l u t i o n} = {m}_{s o l v e n t} + {m}_{s o l u t e}$

There are two ways to change a solution's concentration by mass

• Adding more solute - making the solution more concentrated;
• Adding more solvent - making the solution more dilute;

Let's take an example to better illustrate this concept. Say we dissolve 10.0g of a substance in 100.0g of water. Our concentration by mass will be

c% = (10.0g)/(10.0g + 100.0g) * 100% = 9.09%

Now let's try doubling the mass of the solute; the new concentration will be

c% = (2 * 10.0g)/(2*10.0g + 100.0g) * 100% = 16.7%

However, if we keep the mass of the solute at 10.0g and doubled the mass of the solvent (in this case, water), the concentration will be

c% = (10.0g)/(10.0g + 2*100.0g) * 100% = 4.76%

The same is true for percent concentration by volume, which is defined as the volume of the solute divided by the total volume of the solution and multiplied by 100%.

c_(volume)% = V_(solute)/(V_(solute) + V_(solvent)) * 100%

It's easy to see that manipulating either the volume of the solute or the volume of the solvent (or both) would change the solution's percent concentration by volume.