5: Standardizing Analytical Methods
- Page ID
- 127235
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The American Chemical Society’s Committee on Environmental Improvement defines standardization as the process of determining the relationship between the signal and the amount of analyte in a sample. In Chapter 3 we defined this relationship as
\[S_{total} = k_A n_A + S_{reag} \text{ or } S_{total} = k_A C_A + S_{reag} \nonumber\]
where Stotal is the signal, nA is the moles of analyte, CA is the analyte’s concentration, kA is the method’s sensitivity for the analyte, and Sreag is the contribution to Stotal from sources other than the sample. To standardize a method we must determine values for kA and Sreag. Strategies for accomplishing this are the subject of this chapter.
- 5.1: Analytical Signals
- This page discusses the standardization of analytical methods using standards containing known analyte amounts. It emphasizes the importance of reagent and glassware quality. The text explains primary standards, like K???Cr???O???, and secondary standards, like NaOH, and mentions the role of solvents. It also covers preparing standard solutions through direct transfer or serial dilution, noting potential errors.
- 5.2: Calibrating the Signal
- The accuracy in determining kA and Sreag relies on precise signal measurement, using calibrated equipment like balances and spectrophotometers. Calibrating involves adjusting the measured signal, Stotal, to match a known standard signal, Sstd. For example, balances are calibrated using reference weights, while spectrophotometers are checked by measuring absorbance of specific solutions.
- 5.3: Determining the Sensitivity
- This page focuses on the process of standardizing an analytical method by determining the analyte's sensitivity, \(k_A\). It covers single-point and multiple-point standardizations, explaining that while single-point standardization is simpler, it has drawbacks due to potential errors and non-linearity in signal response. Multiple-point standardization, through calibration curves and methods like linear regression, offers a more accurate approach.
- 5.4: Linear Regression and Calibration Curves
- This page discusses different approaches to identifying the relationship between signal and concentration in quantitative analysis. It outlines methodologies for single-point and multiple-point external standardization, emphasizing the limitations and considerations for each, such as determinate errors. It further delves into unweighted and weighted linear regression techniques, detailing equations for calculating slope and y-intercept while addressing error management.
- 5.5: Compensating for the Reagent Blank
- The page discusses the importance of selecting an appropriate reagent blank to correct signals in analytical methods. It explores different approaches to blank correction, including calibration and reagent blanks. The study highlights that different methods yield varying results, emphasizing the significance of a proper blank choice.
- 5.6: Using Excel and R for a Linear Regression
- The page details methods for performing linear regression analysis using Excel and R. It explains how to fit a straight-line model to data, obtain relevant statistical information, and visualize the regression model using Excel. Three approaches in Excel include using built-in functions, employing Data Analysis ToolPak, and programming formulas directly into a spreadsheet.
- 5.7: Problems
- The page contains a set of analytical chemistry problems focused on topics such as serial dilution, uncertainty calculation, analyte concentration determination, calibration curves, standard addition method, and linear regression analysis. Each problem poses a complex scenario often involving quantitative chemical analysis and requires application of statistical methods or chemical calculations to solve.
- 5.8: Additional Resources
- The text provides a comprehensive list of resources and references for understanding various standardization methods, linear regression, and calibration techniques in analytical chemistry. It covers topics like external standards, standard additions, internal standards, linear and nonlinear regression, handling of errors and outliers, multivariate calibration, method blanks, and computational packages for regression analyses.
- 5.9: Chapter Summary and Key Terms
- The page discusses quantitative analysis techniques for measuring a signal, Stotal, to calculate an analyte's amount using specific equations. It emphasizes eliminating errors by calibrating equipment and instruments, with manufacturers generally providing calibration standards and methods. Standardization strategies such as external standards, standard additions, and internal standards are highlighted.