Question

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

Answer 1

`"937 L"`

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 `color(blue)(33.59)` 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.