Deriving Formula for Concentration of Hydronium at Equivalence Point?

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Discussion Overview

The discussion revolves around deriving a formula for the concentration of hydronium ions at the equivalence point of a titration involving a strong base (sodium hydroxide) and a weak acid (acetic acid). The context is a homework problem related to a lab report, focusing on the theoretical aspects of acid-base chemistry.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant seeks to derive a formula for hydronium concentration at the equivalence point, referencing the equality of moles of acetic acid and sodium hydroxide.
  • Another participant challenges the initial understanding by stating that at the equivalence point, the solution consists of a salt of the weak acid, implying it behaves as a conjugate base.
  • A participant suggests using the relationship between the acid dissociation constant (Ka), base dissociation constant (Kb), and the ion product of water (Kw) to derive the formula.
  • There are attempts to use approximated formulas for hydroxide concentration in the context of weak bases and acids.
  • One participant expresses uncertainty about manipulating the equations to isolate [H3O+].
  • A later reply provides a formula for Kb in terms of hydroxide concentration and concentration of the weak acid, suggesting a method to proceed with the derivation.
  • Another participant expresses gratitude for the assistance and notes a newfound ability to use LaTeX for posting formulas.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the approach to derive the formula, with differing views on the implications of the equivalence point and the appropriate mathematical manipulations. The discussion remains unresolved regarding the exact steps to derive the desired expression.

Contextual Notes

There are limitations in the assumptions made about the concentrations of species at the equivalence point, and the dependency on the definitions of the constants involved (Ka, Kb, Kw) is not fully explored. Some mathematical steps remain unresolved.

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Homework Statement


This is a part of the lab report for a practical I did last week. I need to derive the following formula for the concentration of hydronium at the equivilance point of a strong base weak acid titration (acetic acid with sodium hydroxide).

Homework Equations


M=V/c

Formula for acid constant.


The Attempt at a Solution


My attempt at a solution is attached (the last portion of the attached image, after the text). Not sure how to move on from this, to get to the expression with the radical sign and Kw (product of the acid and base constants).

[PLAIN]https://files.itslearning.com/data/his/46492/1.png

Thanks in advance.
 
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No idea what you are doing here. At the equivalence point you just have a solution of a salt of a weak acid - that's equivalent to the solution of a conjugate base...
 
I am asked to derive the formula at the top of the picture, for the concentration of hydronium. Thought that the equivalence point was the point where number of moles of CH3COOH was equal to the number of moles og NaOH, so I tried to derive the formula from that equiality. :)

Could I write:

expression for Ka*expression for Kb=Kw, and derive the formula from this?

Thanks.
 
Thank you.


Tried to use the approximated formula now, and here is what I got. Think I got it right so far, but how should I proceed to solve it in terms of [H3O+]? Tried to multiply both sides with [H3O+]/[OH-], but I don't think that's right.

[PLAIN]https://files.itslearning.com/data/his/46492/2.jpg
 
Last edited by a moderator:
You can assume [HA] is so low Cb has not changed. Scroll down to the bottom of the page I linked to.

You can use LaTeX to post formulas:

[noparse]K_b = \frac {[OH]^2} {C_b-[HA]}[/noparse]

gives

K_b = \frac {[OH]^2} {C_b-[HA]}
 
Thank you very much. Solved it now. :)

Didn't know that this forum supported TEX/LaTEX, much more convenient than my copy/paste method i guess.
 

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