# What is the new concentration of a #10%# solution if we dilute a sample from #"25.0 mL"# to #"500 mL"# ?

##### 1 Answer

#### Explanation:

The idea here is that when you're performing a **dilution**, the concentration of the solution **decreases** by the *same factor* (known as the **dilution factor**) as the volume **increases**.

#"volume" uarr "by a factor"color(white)(.)color(blue)("DF") implies "concentration" darr "by the same factor"color(white)(.)color(blue)("DF")#

In your case, the volume of the solution increases from

#"DF" = (500 color(red)(cancel(color(black)("mL"))))/(25.0color(red)(cancel(color(black)("mL")))) = color(blue)(20)#

Now remember, the **same dilution factor** is applied to the concentration of the solution, i.e. the concentration of the diluted solution must be **times lower** than the concentration of the stock solution.

This means that the concentration of the diluted solution will be

#"% diluted" = (10%)/color(blue)(20) = color(darkgreen)(ul(color(black)(0.5%)))#

The answer is rounded to one **significant figure**.