# Question 7fc93

Feb 8, 2017

$\text{12 mL}$

#### Explanation:

Your starting point here will be to calculate the dilution factor, which represents the ratio that exists between the concentration of the stock solution and the concentration of the diluted solution.

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{DF" = c_"stock"/c_"diluted}}}}$

In other words, the dilution factor tells you how concentrated the stock solution was compared with the diluted solution.

You can also express the dilution factor as the ratio between the volume of the diluted solution and the volume of the concentrated solution

color(blue)(ul(color(black)("DF" = V_"diluted"/V_"stock")))" " " "color(orange)("(*)")

Now, your stock solution has a concentration of $1 : 250$, which basically means that you get $1$ part solute for every $250$ parts of solution.

This is equivalent to a concentration of 0.40%, since you get

100 color(red)(cancel(color(black)("parts solution"))) * "1 part solute"/(250 color(red)(cancel(color(black)("parts solution")))) = "0.40 parts solute"

for every $100$ parts of solution.

The diluted solution must be $1 : 5000$, which is equivalent to 0.020%, since

100 color(red)(cancel(color(black)("parts solution"))) * "1 part solute"/(5000 color(red)(cancel(color(black)("parts solution")))) = "0.020 parts solute"

This means that the dilution factor must be

"DF" = (0.40 color(red)(cancel(color(black)(%))))/(0.020color(red)(cancel(color(black)(%)))) = color(blue)(20)

Since you know that the diluted solution has a volume of $\text{240 mL}$, you can use equation $\textcolor{\mathmr{and} a n \ge}{\text{(*)}}$ to find the volume of the stock solution

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

Plug in your values to find

V_"stock" = "240 mL"/color(blue)(20) = color(darkgreen)(ul(color(black)("12 mL")))#

The answer is rounded to two sig figs.

So, to make this $1 : 5000$ diluted solution, you start with $\text{12 mL}$ of $1 : 250$ solution and you add enough water to get its volume to $\text{240 mL}$.