# Question 17770

Jun 6, 2017

$\text{40 mL}$

#### Explanation:

The idea here is that you're diluting an initial $\text{50 ppm}$ solution to a final volume of $\text{100 mL}$ and a final concentration of $\text{20 ppm}$.

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

$\text{DF" = V_"diluted"/V_"stock" = c_"stock"/c_"diluted} \to$ the dilution 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 $\textcolor{b l u e}{2.5}$ times smaller than the volume of the diluted solution.

You will thus have

${V}_{\text{stock" = V_"diluted}} / \textcolor{b l u e}{2.5}$

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.