Like I said earlier, I have absolutely no idea of how to go from the statement "equivalence point is defined by the stoichiometry of the reaction" to calculating the equivalence point because the amount of ions produced is governed by dissociation constants.
We have discussed how to calculate pH of any solution in Phosphoric Acid Titration thread that you started less than two weeks ago.
I have looked on the page titrations.info has on calculating the equivalence point for titrations, and they do not contain information enough to solve even for weak acids and bases, much less for polyprotics or mixtures as a general method must do. Here is the page in question: http://www.titrations.info/acid-base-titration-equivalence-point-calculation (there is a solution for weak acids/bases but it is inexact even at that level and so is not the sort of approach I'm looking for).
Page outlines the approach and links to ChemBuddy lectures. It links to the page with simplified methods, but as you stated you know these lectures, finding the page with the full blown approach shouldn't be difficult. Especially after we discussed this approach extensively.
If it is true that the equivalence point is solely to do with reaction stoichiometry, then you should be able to help me calculate it mathematically.
Only if you put an effort. You pretend you understand what I wrote and then you ask exactly the same questions.
My current problem is that Vtitrant is not known at the equivalence point
It is known, as I explained many times.
And let's say I have a mixture of a polyprotic acid that I'm titrating with a polyprotic base. How do I find expression(s) for the equivalence point(s)? (To my knowledge titrations of polyprotics tend to have more than one point of inflection, i.e. more than one equivalence point.)
You are wasting your own time and my time asking the same questions again and again:
http://www.chemicalforums.com/index.php?topic=63076.15
I am ready to help, but from now on I am going to ignore questions that repeat the same problems and misunderstandings we already discussed to death.
Let's start with the basis that I know nothing except how to calculate the pH of a solution using that one equation listed on that page (using the method we outlined together in the Phosphoric Acid titration page). Let's say I don't even know how to get Ca and Cb unless it is given to me, i.e. directly stated in the question. I want to achieve a clear understanding with no flaws of how to calculate it.
However I recognize that you don't want to say the same thing again and again, though I think you are overestimating how much knowledge I already have. So here's my theory as to how to calculate equivalence point. Tell me please if it is right, wrong, or what.
For a single polyprotic acid as the analyte and a single polyprotic base as the titrant, at the equivalence point (according to what you said about them being stoichiometrically equal), Ca1*Va=Cb1*Vb (where the C values are the respective concentrations in the respective solution of acid, i.e. analyte, and base, i.e. titrant). This can be rearranged for V
b to calculate the volume of base you need to add to reach the equivalence point. If a mixture of components is used in the analyte and titrant, we want the sum of all starting concentrations in the analyte multiplied by the volume of the analyte, divided by the sum of all starting concentrations in the titrant, to equal the V
titrant added at the equivalence point.
i.e. V
titrant at equivalence point = Sum of all analytical concentrations of components present in the analyte, in the original analyte solution * Vanalyte / Sum of all analytical concentrations of components present in the titrant, in the original titrant solution
You never explicitly said this to me, so how could you assume I understood this and was simply asking again to annoy you? I would never do that. I'm just trying to come to my own, proper understanding of the matter.
Anyway sorry for the digression. Let me return to seeing if I understand the topic or not.
This V
titrant calculated is the volume of titrant needed to reach the equivalence point. To calculate the [H+] in solution now, keeping in mind that nothing of my knowledge can be assumed, I have to work out the new concentration of each component in the solution at the equivalence point. Returning to the example of a single polyprotic acid and polyprotic base which the pH calculator deals with directly:
Ca2=Ca1*Va/(Va+Vb)
Cb2=Cb1*Vb/(Va+Vb)
where Ca2 is the concentration in the new solution in which there is both some analyte and some titrant, at the equivalence point. Ca1 is the concentration of the acid in the original analyte solution (assuming analyte acid is being titrated by titrant base). Cb is analogous. Correct? I can then simply plug these two values in for Ca and Cb in the equation, along with the original Ka values, and get the polynomial for [H+] I can solve to find [H+] and then pH. Is this right? Sorry that you think I'm wasting your time.