# Question 689e9

Sep 6, 2015

The dilution factor is equal to $8$.

#### Explanation:

The dilution factor is simply the ratio between the final volume and the initial volume of the solution.

$\textcolor{b l u e}{\text{DF" = V_"final"/V_"initial}}$

You start with 3 mL of stock solution, which you mix with 3 mL of water in tube $A$. For this dilution you get

${V}_{\text{final" = "3 mL" + "3 mL" = "6 mL}}$

The dilution factor will be

DF_1 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2

Now you take a 3-mL sample from the solution in tube $A$, and mix it with 3 mL of water in tube $B$.

The final volume will once again be $\text{6 mL}$, which means that you get the same dilution factor for this second dilution

DF_2 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2

Finally, you do the same thing for tube $C$. After you take a 3-mL sample from tube $B$ and mix it with 3 mL of water in tube $C$, you will get the same dilution factor again

DF_3 = V_"final"/V_"initial" = (6color(red)(cancel(color(black)("mL"))))/(3color(red)(cancel(color(black)("mL")))) = 2#

This means that you've essentially performed a serial dilution, for which multiple dilution steps have thesame dilution factor.

To get the overall dilution factor, you multiply the dilution factors you have for each successive step

$D {F}_{\text{total}} = D {F}_{1} \times D {F}_{2} \times D {F}_{3}$

$D {F}_{\text{total}} = 2 \times 2 \times 2 = \textcolor{g r e e n}{8}$

This means that you've performed a $1 : 8$ dilution of the original stock solution.