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Calculate the change in pH of a buffer made by combining $\pu{500 ml}$ of $\pu{0.1 M}$ $\ce{CH_3CH_2COOH}$ and $\pu{500 ml}$ of $\ce{CH_3CH_2COONa}$, when $0.04$ moles of $\ce{NaOH}$ is added to the solution. Assume the addition of sodium hydroxide has no effect on volume.
($\pu{\mathit{K_a} = 1.3 \times 10^{-4}}$)

My solution:

$$\pu{0.10 M \times ~ 500 ml = 0.05 mol} \ \ce{CH3CH2COOH}$$ $$\pu{0.12 M \times ~ 500 ml = 0.06 mol} \ \ce{CH3CH2COO-}$$

$$\pu{pH = p\mathit{K_a} + \log \left(\frac{0.06}{0.05}\right) = 3.965}$$

Using the equation again where the salt is $\pu{0.1M}$ and the acid is $\pu{0.01M}$ due to the addition of $\ce{NaOH}$ yields a wrong result equal to $1$.

I honestly find the wrong answer to be logical, however I can't think of a way to find the right one.

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The reaction is $\ce{NaOH + CH3CH2COOH -> Na+ + H2O + CH3CH2COO-},$ so adding $\pu{0.04}$ moles $\ce{NaOH}$ will result in the solution having $\pu{0.06 +0.04 = 0.1 mol CH_{3}CH_{2}COO^-}$ and $0.05 - 0.04 = 0.01\, \pu{mol} \, \ce{CH3CH2COOH}.$ Then, you can use the Henderson-Hesselbach equation to find the final pH is equal to $-\log(1.3*10^{-4})+\log\left(\frac{0.1}{0.01}\right) \approx 4.886.$

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  • $\begingroup$ Huh?!? You start out with 0.05 moles of acetate anion and make 0.04 more. That is 0.09 moles total. $\endgroup$ – MaxW May 30 '17 at 20:12
  • $\begingroup$ @MaxW I believe the question has a typo because in the OP's attempted solution, he states that the acetate anion has a concentration of 0.12 M. $\endgroup$ – Teoc May 30 '17 at 20:14

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