Question

Question #cec3a

Answer 1

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.

`"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.

`"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 `"1 mL"`. You dilute the concentrated solution by adding `"9 mL"` of water, which makes the total volume of the diluted solution equal to `"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

`"DF"_ "8 dilutions" = c_"initial"/c_"final"`

This means that the final concentration of the solution will be

`c_"final" = c_"initial"/10^8`

In your case, this is equivalent to

`c_"final" = "0.1 M"/10^8 = 10^(-9)` `"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 `"pH"` of this solution is equal to `7` at room temperature.

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