# Question 2b71d

Jul 6, 2017

$\text{5 mL}$

#### Explanation:

The idea here is that when you're diluting a solution, its concentration decreases and its volume increases by the same factor called the dilution factor.

$\text{DF" = "concentration stock"/"concentration diluted" = V_"diluted"/V_"stock}$

In your case, you know that the concentration of the solution must decrease by a factor of

"DF" = (1000 color(red)(cancel(color(black)("ppm"))))/(50color(red)(cancel(color(black)("ppm")))) = color(blue)(20)

This means that the volume of the stock solution, i.e. of the concentrated solution, must be color(blue)(20 times smaller than the volume of the diluted solution.

You will thus have

${V}_{\text{stock" = V_"diluted}} / \textcolor{b l u e}{20}$

which, in your case, is equal to

V_"stock" = "100 mL"/color(blue)(20) = color(darkgreen)(ul(color(black)("5 mL")))

The answer is rounded to one significant figure.

So, in order to prepare your target solution, use $\text{5 mL}$ of $\text{1000-ppm}$ stock solution and add enough water to get its volume to $\text{100 mL}$.

Jul 6, 2017

100mL, if that is the smallest volume accurate measurement available.

#### Explanation:

The volumes and concentrations are ratios.
?mL_(Conc) * 1000"ppm" = 100mL_(Dil) * 50"ppm"

?mL_(Conc) = (100mL_(Dil) * 50"ppm")/1000
?mL_(Conc) = 5mL

Thus, you would need to put exactly 5mL of the 1000ppm stock solution into a solution diluted to 50mL final volume.

If all you have is a 100mL volumetric pipet, you would need to scale that up to use the minimum 100mL volume. Then, starting with 100mL of stock solution we can use the calculation to see how much final solution we will need.

$100 m {L}_{C o n c} \cdot 1000 \text{ppm" = ?mL_(Dil) * 50"ppm}$

 ?mL_(Dil) = (100mL_(Conc) * 1000"ppm")/50
 ?mL_(Dil) = 2000mL#

So, taking 100mL of the stock solution with the pipet and putting it in a 2L+ size flask or beaker, you would then pipet diluent (water?) until the final solution is 2000mL – add 1900mL of diluent with 19 additional loads and discharges of the pipet.

THEN you can use the pipet to take exactly 100mL of your final 50ppm solution.