Can acid concentration be determined from Ka values in a titration? [duplicate]








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[I need to find the Ka of a weak acid in titration with a strong base](/questions/28545/i-need-to-find-the-ka-of-a-weak-acid-in-titration-with-a-strong-base)

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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.)




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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