Chapter 12.23

[504420311]

So I understand on how to calculate the initial pH, and the volume at the stoichiometric point, but I'm still confused on how to calculate the final pH of the solution if we are not given what the final volume is.

[Christopher Phung 3G]

If you're not doing a titration or a dilution, there isn't really an "initial" or "final" pH. The pH is a number describing the concentration of hydronium ions in solution at equilibrium.
If you are doing a titration or dilution, then both the initial volume and final volumes must be known in order to calculate the pH before titration/dilution and after titration/dilution.

[504420311]

This problem is a titration and they ask you to find the initial, final, and pH at stoichiometric point. And also the volume at the stoichiometric point. I was able to do all of this except the final pH, because they only give you the initial sample volume and Molarity and the the titration Molarity. Is there another equation I can use to find final pH?

[Christopher Phung 3G]

The initial pH of the titration is the pH of the sample.
If the problem you're working on is 12.23, then the quick and dirty way of finding the pH at the stoichiometric point is to recognize that both the sample and titrant are strong acids and bases, which means the stoichiometric point is at 7 pH.
The final pH of the titration is the pH of the titrant.
Technically, the "final" volume of a titration is at infinity, when the sample is 100% titrant.

[Christopher Phung 3G]

So to solve the final pH for 12.23, we need to find the pH of 0.005 M HCl. HCl dissociates completely, so for every liter of 0.005 M HCl, we have 0.005 moles of H⁺. That is, we have 0.005 M H⁺. The pH of 0.005 M H⁺ is 2.3.

[Caitlin3H]

The quick and dirty way of finding the pH at the stoichiometric point is to recognize that both the sample and titrant are strong acids and bases, which means the stoichiometric point is at 7 pH.
The final pH of the titration is the pH of the titrant.
Technically, the "final" volume of a titration is at infinity, when the sample is 100% titrant.

Hey! I'm also confused by the same question, but what you said doesn't make sense. According to the answer guide the final pH was 2.54 while the pH at the stoichiometric point was 7.00.

[CatherineLe_1J]

What Christopher wrote does make sense because with strong acid-strong base titrations the stoichiometric point is at pH 7 (Course Reader p. 149).

Also about the final pH, the textbook explains on p. 483 (Section 12.4) that "Titrations typically end at this point [when the indicator changes color]. However, if we were to continue the titration, we would find that the pH falls slowly toward the value of the acid itself as the dilution due to the original analyte solution becomes less and less important. "

Therefore final pH is close to the pH of 0.005 M HCl = -log(0.005) = 2.3. I'm not sure how the manual got the exact 2.54 value, but it does make sense. Hope this helps!

[CatherineLe_1J]

Actually I just figured it out but it was knowing that the total volume of HCl added was 30mL from the manual.
From there you find the excess concentration of H₃O⁺: 0.0001 mol/.035 L = 2.9 x 10^-3 M.
Then pH = -log(2.9 x 10^-3) = 2.54.

[Sohaib Kazmi 4H]

The problem with the question is it didn't give any final mL values for added HCl. The manual referenced the 30mL, which obviously isn't where we'd get the absolute minimum pH possible, but the question itself did not. I think it's a problem with the question itself.

That being said, it would be a simple calculation to determine the final pH if we did have the 30mL in the beginning. Then it's a matter of plugging the points in and graphing accordingly.