4: Titration of a Diprotic Acid
- Page ID
- 516589
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. Prerequisite Math & Theory
- Polyprotic Stoichiometry: A diprotic acid (\(\mathrm{H_2A}\)) releases two protons sequentially in separate dissociation steps:
- First Equivalence Point (\(V_{\text{eq1}}\)): All \(\mathrm{H_2A}\) is converted to \(\mathrm{HA^-}\).
- Second Equivalence Point (\(V_{\text{eq2}}\)): All \(\mathrm{HA^-}\) is converted to \(\mathrm{A^{2-}}\).
- The Rule: It takes the same stoichiometric amount of base to remove the second proton as it does the first. Therefore, \(V_{\text{eq2}} \approx 2 \times V_{\text{eq1}}\).
- Finding \(\mathrm{p}K_{\mathrm{a}}\) Values:
- \(\mathrm{p}K_{\mathrm{a1}}\) is the pH at \(0.5 \times V_{\text{eq1}}\).
- \(\mathrm{p}K_{\mathrm{a2}}\) is the pH at \(V_{\text{eq1}} + 0.5 \times (V_{\text{eq2}} - V_{\text{eq1}})\), which simplifies to \(1.5 \times V_{\text{eq1}}\).
2. Required Technical Skills
- pH Probe Calibration: Calibrating a pH sensor using standard buffer solutions.
- Titration Data Collection: Recording precise incremental volume and pH readings using manual entry or an automated drop counter.
- Finding Inflection Points: Because the first inflection "step" on a diprotic curve can be subtle, locating the maximum slope (\(\frac{\Delta \text{pH}}{\Delta V}\)) yields the most accurate equivalence volume.
3. Critical Safety
- Chemical Handling: Sodium hydroxide and unknown acid solutions are corrosive. Wear chemical splash goggles at all times in the laboratory.
- To titrate an unknown diprotic weak acid using a pH probe.
- To use the titration curve to determine \(\mathrm{p}K_{\mathrm{a1}}\) and \(\mathrm{p}K_{\mathrm{a2}}\) (and calculate \(K_{\mathrm{a1}}\) and \(K_{\mathrm{a2}}\)) to identify a candidate weak acid.
- To calculate the molar concentration of the unknown diprotic acid solution from the titration equivalence volumes.
INTRODUCTION
This laboratory experiment investigates the potentiometric titration of an unknown diprotic weak acid, represented as \(\mathrm{H_2A}\). Unlike monoprotic weak acids, a diprotic acid contains two acidic protons that dissociate in a stepwise manner, each defined by its own acid dissociation equilibrium and constant (\(K_{\mathrm{a1}}\) and \(K_{\mathrm{a2}}\)). The primary objective is to evaluate these stepwise dissociations and determine the quantitative constants defining the acid's chemical behavior.
A potentiometric titration is performed by continuously monitoring solution pH as a standardized strong base, 0.10 M \(\mathrm{NaOH}\), is added incrementally from a buret.
The collected titrant volume and pH data are plotted to produce a diprotic titration curve featuring two distinct inflection regions. From this curve, the first (\(V_{\text{eq1}}\)) and second (\(V_{\text{eq2}}\)) equivalence points are identified, corresponding to the complete neutralization of the first and second protons, respectively. The \(\mathrm{p}K_{\mathrm{a1}}\) and \(\mathrm{p}K_{\mathrm{a2}}\) values are estimated directly from the pH at the corresponding half-equivalence points. From these values, \(K_{\mathrm{a1}}\) and \(K_{\mathrm{a2}}\) are calculated. Finally, the molarity of the unknown acid is calculated from the equivalence points, and a candidate identity is proposed by comparing experimental \(\mathrm{p}K_{\mathrm{a}}\) values to a reference table of literature constants.
Diprotic acids feature two equivalence points. Because the stoichiometry is 1:1 for each proton removal step, a built-in mathematical relationship exists:
- The total volume of titrant required to reach the second equivalence point (\(V_{\text{eq2}}\)) must be approximately twice the volume required to reach the first equivalence point (\(V_{\text{eq1}}\)).
- Data Check: If your experimental \(V_{\text{eq2}}\) is not approximately \(2 \times V_{\text{eq1}}\), re-examine your titration curve to ensure an endpoint was not misidentified.
Henderson-Hasselbalch Equation:
\[ \text{pH} = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \]
Definition of \(\mathrm{p}K_{\mathrm{a}}\):
\[ \mathrm{p}K_{\mathrm{a}} = -\log K_{\mathrm{a}} \quad \text{or} \quad K_{\mathrm{a}} = 10^{-\mathrm{p}K_{\mathrm{a}}} \]
- 4.1: Titration of a Diprotic Acid - Experiment
- This page provides safety guidelines for handling caustic solutions, particularly during a titration experiment involving an unknown diprotic weak acid and sodium hydroxide. It details necessary equipment and chemicals, outlines a three-part procedure for setting up and conducting the titration, and emphasizes accurate data recording of pH changes and buret readings.
- 4.2: Titration of a Diprotic Acid - Pre-lab
- This page covers the titration of a diprotic acid (H2A) with NaOH, detailing two dissociation reactions and their corresponding constants (Ka1 and Ka2). It emphasizes the concentrations at half-equivalence points and involves calculations for NaOH volumes to reach the first and second equivalence points. Additionally, it requires a sketch of the expected titration curve with volume markers.
- 4.3: Titration of a Diprotic Acid - Data and Report
- This page details a titration lab where students determine an unknown acid's concentration by analyzing titration curves. They collect data from two titrations, create graphs, and identify features like equivalence points. Key calculations include estimating pKa values and comparing results for internal consistency through percent differences. The ultimate goal is to identify the unknown acid based on its pKa values.