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### Topic: End-Point and Indicators  (Read 10287 times)

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#### Borek

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##### Re: End-Point and Indicators
« Reply #15 on: November 06, 2012, 03:34:53 AM »
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.

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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.

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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.

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My current problem is that Vtitrant is not known at the equivalence point

It is known, as I explained many times.

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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.
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##### Re: End-Point and Indicators
« Reply #16 on: November 06, 2012, 01:37:35 PM »
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.

Quote
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.

Quote
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.

Quote
My current problem is that Vtitrant is not known at the equivalence point

It is known, as I explained many times.

Quote
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 Vb 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 Vtitrant added at the equivalence point.

i.e. Vtitrant 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 Vtitrant 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.

#### Borek

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##### Re: End-Point and Indicators
« Reply #17 on: November 07, 2012, 05:42:53 PM »
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 Vb to calculate the volume of base you need to add to reach the equivalence point.

Correct so far.

Quote
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 Vtitrant added at the equivalence point.

This gets a little bit tricky, as if you have a mixture of components, you may have several equivalence points. Not all of them have to be visible on the titration curve.

Quote
This Vtitrant 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)

Taking care of dilution, see http://www.titrations.info/titration-curve-calculation

Note that calculation of pH at equivalence point is just a part of the calculation of the titration curve. Titration curve can be calculated from the first principles (that we discussed earlier) or using much more convenient, simplified methods (that can give only approximate results in some cases).

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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?

Yes, that's the general method.
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##### Re: End-Point and Indicators
« Reply #18 on: November 08, 2012, 12:30:21 PM »
Quote
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 Vtitrant added at the equivalence point.

This gets a little bit tricky, as if you have a mixture of components, you may have several equivalence points. Not all of them have to be visible on the titration curve.

I think I've understood most of the rest so I would like to explore this in a bit more detail. Don't think I'm ignoring the rest of your post; it's just that I think I understand the rest already (for example we've already been through calculating the titration curve, simply using the main equation of the pH calculator for various different values of Vb, so need not discuss this any further unless another difficulty crops up).

The problem is, if the equivalence point is defined as per my interpretation of "stoichiometric equivalence" (which you didn't correct above), surely there will only be one equivalence point as there will only be one solution when you do:

Vtitrant at equivalence point = Sum of all analytical concentrations of components present in the analyte, using concentrations of each component in the original analyte solution * Vanalyte / Sum of all analytical concentrations of components present in the titrant, using concentrations of each component in the original titrant solution

There should only be one solution to that which would suggest that there is only one equivalence point, but like you said titration curves of mixtures or polyprotics tend to have more than one equivalence point don't they? So perhaps a more extensive definition of equivalence point would help us include these as well.

#### Borek

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##### Re: End-Point and Indicators
« Reply #19 on: November 08, 2012, 02:19:58 PM »
The problem is, if the equivalence point is defined as per my interpretation of "stoichiometric equivalence" (which you didn't correct above), surely there will only be one equivalence point

Yes, it is a  matter of mixtures and polyprotics. See the attached curve for phosphoric acid - there are two inflection points, first at the moment when the first proton is neutralized, second at the moment second proton is neutralized; in water solutions third equivalence point is not visible. We can say each inflection point fits the definition of the equivalence point, it is just a matter of the reaction that we think about.
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