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}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- To determine the concentration of an unknown copper(II) sulfate solution.
- To understand and apply Beer’s Law, which relates the absorbance of a solution to its concentration.
- To prepare and measure the absorbance of standard copper(II) sulfate solutions to construct a standard calibration curve.
- To use the standard curve—or its linear regression equation—to calculate the molar concentration of the unknown solution.
INTRODUCTION
The goal of this experiment is to determine the concentration of an unknown copper(II) sulfate solution by measuring how strongly it absorbs light. In colored solutions, absorbance increases as concentration increases; a more concentrated solution absorbs more light and transmits less than a more dilute one. This predictable behavior provides the basis for quantitative analysis using visible spectroscopy.
To obtain accurate measurements, it is first necessary to identify the wavelength at which the solution absorbs most strongly. This wavelength, known as \(\lambda_{\max}\), provides the greatest sensitivity because small changes in concentration produce measurable changes in absorbance.
Beer’s Law describes the relationship between absorbance and concentration. Once a set of standard solutions with known concentrations is prepared, their absorbance values are measured using a spectrophotometer. Each absorbance reflects the amount of light that passes through the solution and reaches a photocell inside the instrument.
Plotting absorbance versus concentration for these standard solutions produces a linear calibration curve, commonly called a Beer’s Law plot or standard curve. The slope of this line captures the proportionality between absorbance and concentration and can be used to determine the concentration of an unknown solution. A strong linear fit—indicated by a correlation coefficient \((r)\) close to 1.00 and a y-intercept \((b)\) near zero—demonstrates reliable adherence to Beer’s Law.
In this experiment, you will:
- To prepare a series of standard copper(II) sulfate solutions.
- To measure their absorbance values at \(\lambda_{\max}\).
- To construct a standard calibration curve using your spectrophotometer data.
- To measure the absorbance of an unknown copper(II) sulfate solution and determine its concentration using the standard curve or regression equation.
In this lab, you will calculate the concentration of an unknown. To do this accurately, your calibration curve must be linear.
- The Diagnostic: We use the Coefficient of Determination (\(R^2\)) to grade the straightness of the line.
- The Goal: An \(R^2\) of 1.000 is perfect. In this lab, if your \(R^2 < 0.98\), it implies your pipetting technique was inconsistent, and your calculated unknown concentration will likely be wrong.
Beer’s Law:
\[ A = \varepsilon b c \quad \text{or} \quad A = k c \text{ (for constant } \varepsilon \text{ and path length)} \]
Dilution Equation:
\[ C_1 V_1 = C_2 V_2 \]
- 1.1: Beer's Law - Experiment
- This page provides essential safety precautions and equipment needed for a UV-Vis spectrophotometry experiment analyzing 0.10 M copper sulfate. It outlines a six-part procedure: preparing solutions, calibrating the spectrophotometer, finding the maximum absorbance wavelength, collecting data for standards, analyzing with Beer's Law, and determining an unknown concentration. Emphasis is placed on accurate data handling and proper chemical disposal.
- 1.2: Beer's Law - Pre-lab
- This page covers solution concentration and spectroscopy, focusing on dilution calculations and Beer’s Law, which relates absorbance to concentration. It highlights the need for spectrometer calibration using a blank cuvette to ensure accuracy. The page also discusses using a linear regression from a Beer’s Law plot to find the concentration of unknown solutions and offers a data check to identify outliers and errors.
- 1.3: Beer's Law - Data and Report
- This page provides a laboratory procedure for determining the concentration of an unknown copper(II) sulfate solution using absorbance and Beer's Law. It emphasizes accurate measurements at the maximum absorbance wavelength, includes data tables, and discusses the significance of correlation coefficients and y-intercepts in linear regressions, highlighting potential experimental errors. Additionally, it offers instructions on proper cuvette handling to ensure precision in readings.