6: Solubility Product
- Page ID
- 516591
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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
- The 1:6 Stoichiometry Rule: In this iodometric titration, the mole ratio between the analyte (\(\mathrm{IO_3^-}\)) and titrant (\(\mathrm{S_2O_3^{2-}}\)) is 1 to 6:
- Reaction 1: \(1\text{ mol }\mathrm{IO_3^-}\) reacts with excess \(\mathrm{I^-}\) in acid to produce \(3\text{ mol }\mathrm{I_2}\).
- Reaction 2: \(3\text{ mol }\mathrm{I_2}\) reacts with \(6\text{ mol }\mathrm{S_2O_3^{2-}}\) titrant.
- Calculation Rule: \(\text{Moles of }\mathrm{IO_3^-} = \frac{1}{6} \times \text{Moles of }\mathrm{S_2O_3^{2-}}\). If you omit this factor of 6, your calculated \(K_{\mathrm{sp}}\) will be erroneous by a factor of 216 (\(6^3\))!
- \(K_{\mathrm{sp}}\) from Molar Solubility (\(s\)): If the molar solubility of \(\mathrm{Ca(IO_3)_2}\) is \(s\), then \([\mathrm{Ca^{2+}}] = s\) and \([\mathrm{IO_3^-}] = 2s\). The solubility product constant becomes: \[ K_{\mathrm{sp}} = [\mathrm{Ca^{2+}}][\mathrm{IO_3^-}]^2 = (s)(2s)^2 = 4s^3 \]
2. Required Technical Skills
- Gravity Filtration: The saturated equilibrium solution must be filtered through dry filter paper into a clean, dry receiving beaker. Residual water drops will dilute the saturated solution, causing falsely low solubility and \(K_{\mathrm{sp}}\) values.
- Starch Indicator Endpoint: Starch forms a dark blue-black complex with triiodide (\(\mathrm{I_3^-}\)). The endpoint is signaled by the sharp disappearance of the blue-black color, yielding a colorless solution.
3. Critical Safety
- Strong Acid & Elemental Iodine: Acidification with \(3\text{ M }\mathrm{HCl}\) generates molecular iodine (\(\mathrm{I_2}\)), which can stain and irritate skin. Wear chemical splash goggles and protective gloves at all times.
- To prepare a saturated aqueous solution of calcium iodate, \(\mathrm{Ca(IO_3)_2}\).
- To experimentally determine the concentration of iodate ions (\(\mathrm{IO_3^-}\)) in a saturated solution using an iodometric redox titration with standardized sodium thiosulfate (\(\mathrm{Na_2S_2O_3}\)).
- To calculate the molar solubility (\(s\)) and solubility product constant (\(K_{\mathrm{sp}}\)) of calcium iodate and compare the experimental result with literature values.
INTRODUCTION
The solubility of a substance defines the maximum amount of solute that dissolves in a given quantity of solvent at a specific temperature to establish dynamic equilibrium, yielding a saturated solution. For slightly soluble ionic salts, this dissolution equilibrium is quantitatively expressed by the solubility product constant (\(K_{\mathrm{sp}}\)).
For calcium iodate, \(\mathrm{Ca(IO_3)_2}\), the heterogeneous dissolution equilibrium in water is represented by:
\[ \mathrm{Ca(IO_3)_2(s)} \rightleftharpoons \mathrm{Ca^{2+}(aq)} + 2\,\mathrm{IO_3^-(aq)} \]
The corresponding solubility product expression is given by:
\[ K_{\mathrm{sp}} = [\mathrm{Ca^{2+}}][\mathrm{IO_3^-}]^2 \]
where \([\mathrm{Ca^{2+}}]\) and \([\mathrm{IO_3^-}]\) represent the molar equilibrium concentrations of the dissociated ions in a saturated solution.
To determine \(K_{\mathrm{sp}}\) experimentally, the equilibrium concentration of iodate ions is measured using a two-step iodometric redox titration. An aliquot of saturated \(\mathrm{Ca(IO_3)_2}\) filtrate is treated with excess potassium iodide (\(\mathrm{KI}\)) and acidified with hydrochloric acid (\(\mathrm{HCl}\)). The iodate ions oxidize iodide to molecular iodine (\(\mathrm{I_2}\)):
\[ \mathrm{IO_3^-(aq)} + 5\,\mathrm{I^-(aq)} + 6\,\mathrm{H^+(aq)} \rightarrow 3\,\mathrm{I_2(aq)} + 3\,\mathrm{H_2O(l)} \]
The liberated iodine (\(\mathrm{I_2}\)) is immediately titrated with a standardized solution of sodium thiosulfate (\(\mathrm{Na_2S_2O_3}\)), reducing iodine back to iodide while thiosulfate is oxidized to tetrathionate (\(\mathrm{S_4O_6^{2-}}\)):
\[ \mathrm{I_2(aq)} + 2\,\mathrm{S_2O_3^{2-}(aq)} \rightarrow 2\,\mathrm{I^-(aq)} + \mathrm{S_4O_6^{2-}(aq)} \]
Starch indicator is added near the endpoint to form a deep blue-black complex with remaining iodine. The titration is complete when the blue-black color permanently disappears.
Tracing electron transfer through both reactions establishes the overall stoichiometry:
- Step 1: \(1\text{ mole}\) of \(\mathrm{IO_3^-}\) generates \(3\text{ moles}\) of \(\mathrm{I_2}\).
- Step 2: Each mole of \(\mathrm{I_2}\) consumes \(2\text{ moles}\) of \(\mathrm{S_2O_3^{2-}}\).
- Net Relationship: It requires 6 moles of thiosulfate to react with the iodine produced by 1 mole of iodate: \[ \text{Moles of }\mathrm{IO_3^-} = \frac{1}{6} \times \text{Moles of }\mathrm{S_2O_3^{2-}} \]
Solubility Product Expression:
\[ K_{\mathrm{sp}} = [\mathrm{Ca^{2+}}][\mathrm{IO_3^-}]^2 \]
Titration Stoichiometry (1:6 Ratio):
\[ \text{Moles of }\mathrm{IO_3^-} = \frac{\text{Moles of }\mathrm{S_2O_3^{2-}}}{6} = \frac{M_{\mathrm{S_2O_3^{2-}}} \times V_{\mathrm{S_2O_3^{2-}}}}{6} \]
Calculating \(K_{\mathrm{sp}}\) from Molar Solubility (\(s\)):
\[ s = [\mathrm{Ca^{2+}}] = \frac{1}{2}[\mathrm{IO_3^-}] \]
\[ K_{\mathrm{sp}} = (s)(2s)^2 = 4s^3 \]
- 6.1: Solubility Product - Experiment
- This page details safety precautions for handling hydrochloric acid, emphasizes its corrosive nature, and includes a materials list for an experiment with calcium nitrate and potassium iodate. It outlines a two-part experimental procedure: preparing a saturated calcium iodate solution and analyzing it through titration with sodium thiosulfate. Additionally, it underscores the importance of proper chemical disposal to ensure safety and adherence to laboratory standards.
- 6.2: Solubility Product - Pre-lab
- This page outlines the importance of potassium iodide and hydrochloric acid in titration, highlighting starch as an indicator through its color change at the endpoint. It describes an experimental scenario involving the filtering of a saturated solution and its impact on the concentration of \(\ce{IO3^-}\), questioning how this would affect the calculated \(K_{sp}\). It encourages readers to consider the implications of water contamination on experimental outcomes.
- 6.3: Solubility Product - Data and Report
- This page details a laboratory exercise on titration to assess the concentrations and solubility of calcium iodate. It provides data recording tables for sodium thiosulfate solution volumes and calculated moles of iodate and calcium ions. Key concepts covered include confirming thiosulfate-iodate mole ratio, differentiating precision from accuracy using percent difference, and comparing calculated solubility with standard values, along with discussing potential errors in solubility measurements.