# Question cec3a

Aug 10, 2017

Here's what I got.

#### Explanation:

The idea here is that you're performing a serial dilution, so you should be aware of the fact that the overall dilution factor will be equal to the product of the dilution factors of each individual dilution.

${\text{DF"_"overall" = "DF"_1 xx "DF"_2 xx ... xx "DF}}_{n}$

As you know, the dilution factor can be calculated by dividing the volume of the diluted solution by the volume of the concentrated solution.

$\text{DF" = V_"diluted"/V_"concentrated}$

In your case, you're performing $8$ identical dilutions that have

"DF" = ((1 + 9)color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("mL")))) = 10

That is the case because, for each dilution, the volume of the concentrated solution is equal to $\text{1 mL}$. You dilute the concentrated solution by adding $\text{9 mL}$ of water, which makes the total volume of the diluted solution equal to $\text{10 mL}$.

So, you can say that after $8$ dilutions, the overall dilution factor will be

"DF"_"8 dilutions" = overbrace(10 xx 10 xx... xx 10)^(color(blue)("8 times")) = 10^8#

Now, the dilution factor also tells you the ratio that exists between the concentration of the concentrated solution and the concentration of the diluted solution.

For the overall dilution, you have

$\text{DF"_ "8 dilutions" = c_"initial"/c_"final}$

This means that the final concentration of the solution will be

${c}_{\text{final" = c_"initial}} / {10}^{8}$

In your case, this is equivalent to

${c}_{\text{final" = "0.1 M}} / {10}^{8} = {10}^{- 9}$ $\text{M}$

Now, for all intended purposes and based on the number of significant figures that you have for your values, you can go ahead and say that the $\text{pH}$ of this solution is equal to $7$ at room temperature.

It's worth mentioning that the actual $\text{pH}$ of this solution--I won't do the calculation here--is approximately equal to $6.998$ at room temperature.