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Say I have a sample of vinegar and I want to find the concentration of ethanoic acid in it. So I perform a titration using a $\mathrm{pH}$ meter, and using that data I can draw a $\mathrm{pH}$ curve and find quantities such as the initial $\mathrm{pH}$, the half-equivalence point, the equivalence point, and the $\mathrm{pH}$ at the equivalence point.

I feel like my teacher hasn't explained this very clearly, but given the $K_{\mathrm a}$ value for ethanoic acid and the data collected from the titration, is it possible to determine the initial concentration? If so, how do I proceed?

(I'm aware of the simple stoichiometric method, just curious whether this approach will work.)

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The Henderson-Hasselbalch equation will help:

$$\mathrm{pH} = \mathrm{p}K_{\mathrm a} + \log {[\ce{A-}]\over [\ce{HA}]}$$

Once the $\mathrm{p}K_{\mathrm a}$ is known, the equation will tell you the ratio of acetate to acetic acid (ethanoic acid). The ratio changes at various $\mathrm{pH}$ values.

The $\mathrm{p}K_{\mathrm a}$ is 4.76, so for a $\mathrm{pH}$ below 3.75 the dominant species in solution will be acetic acid; at pH 5.76, the dominant species in solution is the acetate ion. If you want to make a solution at a particular $\mathrm{pH}$ value, use the equation to give you the ratio of acetate to acetic acid needed.

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Yes. Your question is basically how to determine $K_\mathrm a$ from $\mathrm{pH}$ of a salt of the acid. Since ethanoic acid is a weak acid, its salt will hydrolyze to give an alkaline solution. You can calculate the $K_\mathrm a$ given that the concentration and the $\mathrm{pH}$. The equation for hydrolysis of sodium ethanoic is

$\ce{CH3COO- +H2O <=> CH3COOH + OH-}$.

$\ce{CH3COO-}$ is the conjugate base of $\ce{CH3COOH}$, therefore its $\mathrm pK_\mathrm b$ equals to $14 - \mathrm pK_\mathrm a$. You can then establish a equation for $K_\mathrm b$ using the concentration of the reactants and products.

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  • $\begingroup$ How does this find the concentration of the acid? $\endgroup$ – jerepierre Aug 14 '15 at 13:04
  • $\begingroup$ @jerepierre [OH-] could be found from the pH value at the equivalence point and so does [CH3COOH]. Thus [CH3COO-] can be found using the equation for Kb. $\endgroup$ – ℵ_ϵ Aug 14 '15 at 14:21
  • $\begingroup$ I'm not sure I'm trying to determine the Ka. If I'm not mistaken, the Ka can be found from the titration curve at the half-equivalence point, right? My question is how the concentration of ethanoic acid in vinegar can be found given the Ka and other corresponding quantities that can be found on a titration curve. $\endgroup$ – Razorlance Aug 16 '15 at 10:39

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