Question

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

Answer 1

`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 `"25.0 mL"` to `"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.