Question

How many milliliters of 0.202MNaOHshould be added to 25.0 mlof 0.0233Msalicylic acid (2-hydroxybenzoic acid) to adjust the pHto 3.50?

Short answer

The required volume of$\mathrm{NaOH}\mathrm{is}2.223\mathrm{mL}$

Step-by-step solution

Henderson-Hasselbalch equation

• The Henderson-Hasselbalch equation is a simplified formula that shows the connection between a solution's pH or pOH, pKa or pKb, and the ratio of concentrations of dissociated chemical species.

Determine the moles of salicylic acid

Calculate the moles of salicylic acid using the formula below: $\mathrm{\eta }\left(\mathrm{salicylic}\mathrm{acid}\right)=\mathrm{c}\times \mathrm{V}$

$\mathrm{\eta }\left(\mathrm{salicylic}\mathrm{acid}\right)=\left(0.023\mathrm{M}\right)\times \left(25\mathrm{mL}\right)$

$\mathrm{\eta }\left(\mathrm{salicylic}\mathrm{acid}\right)=0.5285\mathrm{mmo}1$

Consider the reaction:

localid="1663413505585" $$\begin{gathered} {\mathrm{H}}_2\mathrm{A}+{\mathrm{OH}}^{-}\rightleftharpoons {\mathrm{HA}}^{-}+{\mathrm{H}}_2\mathrm{O} \\ \left[{\mathrm{H}}_2\mathrm{A}\right]=0.5285-\mathrm{x} \\ \left[{\mathrm{HA}}^{-}\right]=\mathrm{x} \end{gathered}$$

Determine the required volume of NaOH

The Henderson-Hasselbach equation should be used next. $$\begin{gathered} \mathrm{pH}=\mathrm{pKa}+\log \left(\left[{\mathrm{HA}}^{-}\right]\right)/\left[{\mathrm{H}}_2\mathrm{A}\right]) \\ 3.50=2.972+\log \left(\frac{x}{0.5285-x}\right) \\ \mathrm{x}=0.4993\mathrm{mmol} \end{gathered}$$

Calculate the required volume of as follows $$\begin{gathered} V\left(\mathrm{NaOH}\right)=\mathrm{n}\times \mathrm{c} \\ V\left(\mathrm{NaOH}\right)=(0.4493\mathrm{mmol})\times (0.202\mathrm{M}) \\ V\left(\mathrm{NaOH}\right)=2.223\mathrm{mL} \end{gathered}$$