6: Solubility Product
- Page ID
- 516591
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- To prepare a saturated solution of calcium iodate.
- To determine the concentration of a saturated solution of calcium iodate using a redox titration.
- To determine the solubility product for calcium iodate and compare it to the known value.
INTRODUCTION
In chemistry, the solubility of a compound refers to the maximum amount of solute that can dissolve in a given solvent at equilibrium, forming a saturated solution. For slightly soluble ionic compounds, this equilibrium is described by the solubility product constant (\( K_{\text{sp}} \)), a fundamental equilibrium constant that quantifies the extent to which a solid dissolves in solution.
For calcium iodate, \( \ce{Ca(IO3)2} \), the equilibrium in a saturated solution is represented as:
\[ \ce{Ca(IO3)2 (s) <=> Ca^{2+} (aq) + 2 IO3^- (aq)} \]
The solubility product expression is given by:
\[ K_{\text{sp}} = [\ce{Ca^{2+}}][\ce{IO3^-}]^2 \]
where \( [\ce{Ca^{2+}}] \) and \( [\ce{IO3^-}] \) are the molar concentrations of the dissociated ions in equilibrium.
To determine the solubility of calcium iodate experimentally, we need to measure the concentration of iodate ions in a saturated solution. This is achieved through a redox titration using a standardized sodium thiosulfate (\(\ce{Na2S2O3}\)) solution in the presence of potassium iodide (\(\ce{KI}\)) and starch indicator.
The reaction between iodate ions and potassium iodide in acidic solution generates molecular iodine:
\[ \ce{IO3^- + 5 I^- + 6 H^+ -> 3 I2 + 3 H2O} \]
The molecular iodine (\(\ce{I2}\)) is then titrated with sodium thiosulfate, which reduces it back to iodide:
\[ \ce{I2 + 2 S2O3^{2-} -> 2 I^- + S4O6^{2-}} \]
where \( \ce{S4O6^{2-}} \) is the tetrathionate ion.
Since the amount of thiosulfate used directly correlates with the amount of iodate originally present in solution, this titration allows us to calculate the molarity of iodate ions, determine the solubility of calcium iodate, and compute its solubility product constant (\( K_{\text{sp}} \)).
Additionally, this experiment explores the concept that the solubility of a slightly soluble salt is independent of the volume of water used to dissolve it, meaning that different volumes of solvent should yield the same solubility value when equilibrium is reached.
In this redox titration, the stoichiometry is not 1:1. You must trace the electrons carefully:
- Step 1: 1 mole of \(\ce{IO3^-}\) produces 3 moles of \(\ce{I2}\).
- Step 2: Each mole of \(\ce{I2}\) consumes 2 moles of thiosulfate (\(\ce{S2O3^{2-}}\)).
- Result: It takes 6 moles of thiosulfate to titrate every 1 mole of iodate. If you forget this factor of 6, your calculated \(K_{sp}\) will be off by a factor of \(6^3\) (216 times)!
Solubility Product Constant (\(K_{sp}\)):
\[ K_{sp} = [\ce{Ca^{2+}}][\ce{IO3^-}]^2 \]
Titration Stoichiometry (The 1:6 Ratio):
Because 1 mole of iodate produces 3 moles of iodine, which consume 6 moles of thiosulfate:
\[ \text{mol } \ce{IO3^-} = \frac{1}{6} \times (\text{mol } \ce{S2O3^{2-}}) \]
Calculating \(K_{sp}\) from Molar Solubility (\(s\)):
If \(s\) is the molar solubility of \(\ce{Ca(IO3)2}\), then \([\ce{Ca^{2+}}] = s\) and \([\ce{IO3^-}] = 2s\).
\[ K_{sp} = (s)(2s)^2 = 4s^3 \]
- 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.