# Which of the following corresponds to a final volume of a #12.89 * 10^(-3)# #"M"# solution prepared by the dilution of #"27.9 L"# of a #"433.0-mM"# solution?

##
A) 937.2 L

B) 12.08 L

C) 42.0 L

D) 529 L

E)132 L

A) 937.2 L

B) 12.08 L

C) 42.0 L

D) 529 L

E)132 L

##### 1 Answer

#### Explanation:

The idea here is that when you're diluting a solution, the ratio that exists between the concentration of the stock sample and the concentration of the diluted solution is **equal** to the ratio that exists between the volume of the diluted solution and the volume of the stock solution.

This ratio is called the **dilution factor** and can be calculated by using

#"DF" = V_"diluted"/V_"stock" = c_"stock"/c_"diluted"#

In your case, you know that your diluted solution has

#c_ "diluted" = 12.89 * 10^(-3) color(red)(cancel(color(black)("M"))) * (10^3color(white)(.)"mM")/(1color(red)(cancel(color(black)("M")))) = "12.89 mM"#

and you stock solution has

#c_"stock" = "433.0 mM"#

so you can say that the dilution factor is equal to

#"DF" = (433.0 color(red)(cancel(color(black)("mM"))))/(12.89color(red)(cancel(color(black)("mM")))) = color(blue)(33.59)#

This means that the volume of the diluted solution must be **times** the volume of the stock solution, since

#V_"diluted" = "DF" * V_"stock"#

This means that you have

#V_ "diluted" = color(blue)(33.59) * "27.9 L"#

#V_"diluted" = color(darkgreen)(ul(color(black)("937 L")))#

The answer must be rounded to three **sig figs**, the number of sig figs you have for the volume of the stock solution.

Therefore, you can say that **(a)** is the answer that the problem is looking for here.