# Question #17770

##### 1 Answer

#### Explanation:

The idea here is that you're **diluting** an initial

As you know, when you're diluting a solution, the ratio that exists between the concentration of the stock solution and that of the diluted solution si **equal** to the ratio that exists between the volume of the diluted solution and that of the stock solution.

This means that you have

#"DF" = V_"diluted"/V_"stock" = c_"stock"/c_"diluted" -># thedilution factor

In your case, the concentration of the solution decreases by a factor of

#"DF" = (50 color(red)(cancel(color(black)("ppm"))))/(20color(red)(cancel(color(black)("ppm")))) = color(blue)(2.5)#

which implies that the volume of the stock solution must be **times smaller** than the volume of the diluted solution.

You will thus have

#V_"stock" = V_"diluted"/color(blue)(2.5)#

which gets you

#V_"stock" = "100 mL"/color(blue)(2.5) = color(darkgreen)(ul(color(black)("40 mL")))#

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