2: Determination of an Equilibrium Constant
- Page ID
- 516587
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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 apply Le Châtelier’s Principle to shift equilibrium conditions and drive the formation of \(\ce{Fe(SCN)^{2+}}\).
- To use spectrophotometry and Beer’s Law to determine the concentration of \(\ce{Fe(SCN)^{2+}}\) and calculate the proportionality constant \(k\).
- To construct and analyze a calibration curve by plotting absorbance versus concentration and interpret the slope for quantitative analysis.
- To calculate the equilibrium concentrations of \(\ce{Fe^{3+}}\), \(\ce{SCN^-}\), and \(\ce{Fe(SCN)^{2+}}\) in order to determine the equilibrium constant \(K_c\).
INTRODUCTION
This experiment allows you to determine the equilibrium constant for the formation of the iron(III) thiocyanate complex ion, \(\ce{Fe(SCN)^{2+}}\), and to apply Le Châtelier’s Principle to control the position of equilibrium. When \(\ce{Fe^{3+}}\) and \(\ce{SCN^-}\) are mixed in aqueous solution, they form the blood-red complex ion \(\ce{Fe(SCN)^{2+}}\):
\[ \ce{Fe^{3+}(aq)} + \ce{SCN^-(aq)} \rightleftharpoons \ce{Fe(SCN)^{2+}(aq)} \]
colorless colorless blood-red
The complex ion is highly colored and easily detected by spectrophotometry. Because the reactants are essentially colorless, absorbance measurements directly correspond to the concentration of \(\ce{Fe(SCN)^{2+}}\) without interference.
The equilibrium constant for the reaction is given by:
\[ K_c = \frac{[\ce{Fe(SCN)^{2+}}]_{\text{eq}}} {[\ce{Fe^{3+}}]_{\text{eq}} \,[\ce{SCN^-}]_{\text{eq}}} \]
To determine \(K_c\), the equilibrium concentrations must be known. Beer’s Law provides a direct method for determining \(\ce{Fe(SCN)^{2+}}\) concentration from absorbance measurements:
\[ A = k c \]
However, the proportionality constant \(k\) must first be determined using solutions of *known* \(\ce{Fe(SCN)^{2+}}\) concentration. This is complicated by the fact that the complex ion participates in the equilibrium itself. Stoichiometric mixing does not guarantee a known concentration of product.
This difficulty is resolved by Le Châtelier’s Principle. By adding a large excess of \(\ce{Fe^{3+}}\), the equilibrium shifts so far to the right that essentially all \(\ce{SCN^-}\) is converted into \(\ce{Fe(SCN)^{2+}}\). Under these conditions, the concentration of the complex ion is effectively equal to the initial concentration of the limiting reagent, \(\ce{SCN^-}\).
In the experiment, you will prepare solutions containing known amounts of \(\ce{Fe(SCN)^{2+}}\) and measure their absorbances at approximately 450 nm, the wavelength of maximum absorbance. Plotting absorbance versus concentration produces a straight line whose slope is the Beer’s Law constant \(k\).
After establishing \(k\), you will measure the absorbance of equilibrium mixtures prepared with various starting concentrations of \(\ce{Fe^{3+}}\) and \(\ce{SCN^-}\). From these results, equilibrium concentrations will be determined and used to calculate the equilibrium constant \(K_c\) for each trial.
You will calculate \(K_c\) five times. You might expect to get the exact same number every time, but experimental noise prevents this.
The Coefficient of Variation (CV): To determine if your equilibrium constant is truly "constant," we calculate the CV (Standard Deviation divided by the Average). A low CV (below 5%) proves that your technique was precise and the reaction follows the equilibrium model well.
Beer’s Law:
\[ A = \varepsilon b c \quad \text{or} \quad A = k c \]
Dilution Equation:
\[ C_1 V_1 = C_2 V_2 \]
- 2.1: Determination of an Equilibrium Constant - Experiment
- This page outlines a laboratory procedure for determining Beer's Law and equilibrium constants using iron(III) thiocyanate solutions. It includes two parts: Part A involves preparing test tubes with different reagent concentrations and measuring their absorbance with a spectrophotometer, while Part B focuses on the impact of increasing KSCN concentrations on absorbance as per Le Châtelier’s Principle. It also highlights the importance of following proper disposal protocols for thiocyanate waste.
- 2.2: Determination of an Equilibrium Constant - Pre-lab
- This page covers the preparation and analysis of reference solutions with \(\ce{Fe^{3+}}\) and \(\ce{SCN^-}\) ions, focusing on equilibrium concentrations and LeChatelier’s Principle. It highlights how the initial \(\ce{SCN^-}\) concentration affects the equilibrium concentration of \(\ce{Fe(SCN)^{2+}}\). The page includes a procedure for calculating concentrations using the dilution equation and discusses how varying \(\ce{SCN^-}\) concentrations influence the color intensity of the solutions.
- 2.3: Determination of an Equilibrium Constant - Data and Report
- This page outlines an experiment analyzing Beer’s Law and the equilibrium constant for iron(III) thiocyanate, detailing data collection methods such as absorbance measurements. It highlights the need for "Sanity Checks" in calculations and presents results in a comparison table of equilibrium concentrations and constants.