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

Jul 8, 2017

0.5%

#### 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 $\text{25.0 mL}$ to $\text{500 mL}$, which means that the dilution factor is equal to

"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 color(blue)(20 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.