Q40E - Organic Chemistry (Mcmurry)

Question

Thioglycolic acid, HSCH₂CO₂H, a substance used in depilatory agents(hair removers) has pKa = 3.42. What is the percent dissociation ofthioglycolic acid in a buffer solution at pH = 3.0?

Step-by-Step Solution

Answer

The dissociation percentage of thioglycolic acid is -27.55 %.

Step 1: Finding [A - ] by representing HA and A -

Given that pH=3 and pK_a=3.42. On representing and substituting Henderson-Hasselbalch equation,

$$\begin{gathered} \log \frac{\left[\mathrm{HA}\right]}{\left[{\mathrm{A}}^{-}\right]}={\mathrm{pK}}_{\mathrm{a}}-\mathrm{pHorlog}\frac{\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}=\mathrm{pH}-{\mathrm{pK}}_{\mathrm{a}} \\ \log \frac{\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}=3-3.42 \\ \log \frac{\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}=0.42 \\ \frac{\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}=\mathrm{antilog} \mathrm{of}-0.42 \\ \frac{\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}=0.38 \\ \left[{\mathrm{A}}^{-}\right]=0.38\left[\mathrm{HA}\right]---\left(1\right) \end{gathered}$$

Step 2: Finding percent dissociation of thioglycolic acid

There is a presence of both ionized thioglycolic acid at equilibrium and also un-ionized forms.

$$\begin{gathered} \left[\mathrm{HA}\right]+\left[{\mathrm{A}}^{-}\right]=100\%---\left(2\right) \\ \left[\mathrm{HA}\right]+0.38\left[\mathrm{HA}\right]=100\% \\ 1.38\left[\mathrm{HA}\right]=100\% \\ \left[\mathrm{HA}\right]=\frac{100}{1.38} \\ \left[\mathrm{HA}\right]=27.55\% \end{gathered}$$