# Question #7fc93

##### 1 Answer

#### 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.

#color(blue)(ul(color(black)("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 **part** solute for every **parts** of solution.

This is equivalent to a concentration of

#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** **parts** of solution.

The diluted solution must be

#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

#"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