1: Beer's Law
- Page ID
- 516576
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\dsum}{\displaystyle\sum\limits} \)
\( \newcommand{\dint}{\displaystyle\int\limits} \)
\( \newcommand{\dlim}{\displaystyle\lim\limits} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)PURPOSE
- To determine the concentration of an unknown copper(II) sulfate solution.
- To understand and apply Beer's Law, which describes the direct relationship between a solution's absorbance and its concentration.
- To prepare and test the absorbance of standard copper(II) sulfate solutions to create a standard curve (a graph of absorbance versus concentration).
- To calculate the molar concentration of the unknown copper(II) sulfate solution using either graphical interpolation on the standard curve or the slope of the Beer's Law curve.
INTRODUCTION
The primary objective of this experiment is to determine the concentration of an unknown copper(II) sulfate solution. This determination relies on the fundamental principle that the concentration of a colored solution is directly related to its ability to absorb light. Specifically, a solution with a higher concentration of a colored substance will absorb more light and transmit less than a solution with a lower concentration.
To quantify this relationship, an appropriate wavelength for measurements is first identified from the absorbance spectrum of the solution. This optimal wavelength, known as λmax, is where the solution absorbs light most strongly, providing the most sensitive measurements.
The core theoretical concept underpinning this experiment is Beer's Law, which describes the direct relationship between a solution's absorbance and its concentration. To establish this relationship, standard solutions of copper(II) sulfate with precisely known concentrations are prepared. Each solution's absorbance is then measured; this value is computed based on the amount of light that penetrates the solution and strikes a photocell within a Spectrophotometer.
When these measured absorbance values are plotted against their corresponding concentrations for the standard solutions, a direct and linear relationship is expected to result. This graphical representation is referred to as a Beer's Law curve or standard curve. The slope of this curve is crucial as it embodies the quantitative relationship between absorbance and concentration.
Ultimately, by measuring the absorbance of the unknown copper(II) sulfate solution, its concentration can be determined. This can be achieved graphically by locating the unknown's absorbance on the vertical axis of the established standard curve and finding the corresponding concentration on the horizontal axis. Alternatively, the slope of the Beer’s Law curve derived from the standard solutions can be used for this calculation. A high-quality linear regression fit, indicated by a correlation coefficient (r) close to 1.00 and a y-intercept (b) close to zero, signifies a strong, reliable relationship that passes through or near the origin.
In this experiment, you will
- Prepare and test the absorbance of five standard copper(II) sulfate solutions.
- Calculate a standard curve from the test results of the standard solutions.
- Test the absorbance of a copper(II) sulfate solution of unknown molar concentration.
- Calculate the molar concentration of the unknown copper(II) sulfate solution.
Beer's Law:
\[ A=\varepsilon bc\ \ \ \ \ or\ \ \ \ \ A = kc \text{ (for a fixed }\varepsilon\text{ and path-length)} \]
Dilution Equation:
\[ C_1V_1 = C_2V_2 \]
- 1.1: Beer's Law - Experiment
- This page provides safety precautions and essential equipment for UV-Vis spectrophotometry experiments with copper(II) sulfate solutions. It includes steps for preparing standard solutions, calibrating the spectrophotometer, and gathering absorbance data. Additionally, it outlines a procedure for applying Beer's Law to analyze the standards, graphing absorbance against concentration, and calculating the concentration of an unknown solution using linear regression.
- 1.2: Beer's Law - Pre-lab
- This page covers solution preparation and spectrophotometry, focusing on calculating the final concentration of diluted solutions using a dilution formula. It discusses Beer’s Law, linking absorbance and concentration, and highlights the importance of calibrating a spectrometer with a blank for accurate results. The page also explains using a linear regression equation from a Beer’s Law plot to find the concentration of an unknown copper(II) sulfate solution.
- 1.3: Beer's Law - Data and Report
- This page details a laboratory experiment employing Beer's Law to ascertain the concentration of an unknown copper(II) sulfate solution through absorbance measurements at \(\lambda_{\text{max}}\). It features a data table of absorbance versus concentration, a linear regression curve fitting section, and post-lab questions discussing the significance of \(\lambda_{\text{max}}\), the relevance of regression parameters on data quality, and cuvette handling effects on absorbance results.