Question #cec3a

1 Answer
Aug 10, 2017

Answer:

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.