3: Acid Dissociation Constant
- Page ID
- 516588
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- To titrate an unknown weak acid using a pH probe.
- To use the titration curve to determine the \(\mathrm{p}K_{\mathrm{a}}\) (and therefore the \(K_{\mathrm{a}}\)) of the acid and identify candidate weak acids.
- To determine the molar concentration of the unknown weak acid solution from the titration equivalence point.
INTRODUCTION
This lab experiment focuses on titrating an unknown weak acid using a pH probe. The primary goal is to determine the acid dissociation constant (\(K_{\mathrm{a}}\)) of the unknown weak acid.
The procedure involves titrating the acid with a standardized 0.10 M \(\mathrm{NaOH}\) titrant solution while continuously monitoring pH with a pH sensor under magnetic stirring.
Data collection begins by recording the initial pH of a known volume of unknown weak acid diluted with deionized water. The \(\mathrm{NaOH}\) titrant is added slowly while monitoring pH until the solution pH exceeds 11.
The \(K_{\mathrm{a}}\) value is determined using the Henderson-Hasselbalch equation. Specifically, at the half-equivalence point of the titration, the pH equals the \(\mathrm{p}K_{\mathrm{a}}\) of the weak acid. From the \(\mathrm{p}K_{\mathrm{a}}\), the \(K_{\mathrm{a}}\) can be calculated directly. The titration curve is also analyzed to determine the exact concentration of the unknown acid from the volume of titrant required to reach the equivalence point.
Calculating the \(K_{\mathrm{a}}\)
For a monoprotic weak acid, \(\mathrm{HA}\), the Henderson-Hasselbalch equation is:
\[ \text{pH} = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\mathrm{A^-}]}{[\mathrm{HA}]} \right) \]
where \([\mathrm{HA}]\) and \([\mathrm{A^-}]\) represent the equilibrium molar concentrations of the weak acid and its conjugate base, respectively.
At the half-equivalence point, \(V_{1/2} = \frac{1}{2} V_{\text{eq}}\):
\[ [\mathrm{HA}] = [\mathrm{A^-}], \quad \text{so} \quad \frac{[\mathrm{A^-}]}{[\mathrm{HA}]} = 1, \quad \text{and} \quad \log(1) = 0 \]
Therefore, at the half-equivalence point:
\[ \text{pH} = \mathrm{p}K_{\mathrm{a}} \]
The \(K_{\mathrm{a}}\) value is then calculated from the definition of \(\mathrm{p}K_{\mathrm{a}}\):
\[ \mathrm{p}K_{\mathrm{a}} = -\log K_{\mathrm{a}} \quad \longrightarrow \quad K_{\mathrm{a}} = 10^{-\mathrm{p}K_{\mathrm{a}}} \]
You will determine the equivalence point (\(V_{\text{eq}}\)) visually from the inflection point of your titration curve.
- Steepness Matters: The sharper the steep rise in pH, the more precisely you can identify \(V_{\text{eq}}\).
- Data Density: Adding large increments of base (e.g., 1.0 mL) near the equivalence point will jump over the inflection point. You must add small dropwise increments near the equivalence point to locate the exact center of the steep region.
Henderson-Hasselbalch Equation:
\[ \text{pH} = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\mathrm{A^-}]}{[\mathrm{HA}]} \right) \]
Definition of \(\mathrm{p}K_{\mathrm{a}}\):
\[ \mathrm{p}K_{\mathrm{a}} = -\log K_{\mathrm{a}} \quad \text{or} \quad K_{\mathrm{a}} = 10^{-\mathrm{p}K_{\mathrm{a}}} \]
- 3.1: Acid Dissociation Constant - Experiment
- This page details the safety precautions and materials required for titrating a monoprotic weak acid with NaOH. It includes a three-part experimental procedure: setting up the titration, gradually adding NaOH while recording pH changes, and repeating with a second sample. The page stresses the importance of safe chemical waste disposal and proper handling of caustic substances.
- 3.2: Acid Dissociation Constant - Pre-lab
- This page discusses the titration of a monoprotic acid, detailing the acid dissociation reaction and its constant (Ka). It highlights the importance of the half-equivalence point where acid and conjugate base concentrations are equal. A practical titration example with a weak acid and \(\ce{NaOH}\) is provided, stressing the importance of careful volume additions near the equivalence point for accurate endpoint determination, supported by hypothetical titration curves.
- 3.3: Acid Dissociation Constant - Data and Report
- This page details a titration lab activity focused on recording and analyzing data. Students learn to create titration curves, identify key points, estimate pH and acid dissociation constants (Ka), and assess the precision of their techniques through percent difference. They also identify an unknown acid by comparing their experimental Ka to literature values and calculating percent error, enhancing their data analysis and critical thinking skills in chemistry.