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"Header 1": "**Glossary**",
"Header 2": "**Answer Key**",
"token_count": 2433,
"source_pdf": "datasets/websources/biochem/Microbiology-LR.pdf"
} |
*A Division of The McGraw-Hill Companies*
#### MODERN ANALYTICAL CHEMISTRY
Copyright © 2000 by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed... | {
"Header 1": "*McGraw-Hill Higher Education*",
"token_count": 719,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
2C.5 Conservation of Electrons 23 2C.6 Using Conservation Principles in Stoichiometry Problems 23
| Introduction<br>1 | 2D<br>Basic Equipment and Instrumentation<br>25 | | |
|----------------------------------------------|--------------------------------------------------|--|--|
| ... | {
"Header 1": "Contents **Contents**",
"token_count": 2511,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **6A Reversible Reactions and Chemical Equilibria 136**
- **6B Thermodynamics and Equilibrium Chemistry 136**
- **6C Manipulating Equilibrium Constants 138**
- **6D Equilibrium Constants for Chemical Reactions 139**
- 6D.1 Precipitation Reactions 139
- 6D.2 Acid–Base Reactions 140
- 6D.3 Complexation Reactions 144
- ... | {
"Header 1": "Equilibrium Chemistry 135",
"token_count": 507,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **7A The Importance of Sampling 180**
- **7B Designing a Sampling Plan 182**
- 7B.1 Where to Sample the Target Population 182
- 7B.2 What Type of Sample to Collect 185
- 7B.3 How Much Sample to Collect 187
- 7B.4 How Many Samples to Collect 191
- 7B.5 Minimizing the Overall Variance 192
- **7C Implementing the Sampli... | {
"Header 1": "Obtaining and Preparing Samples for Analysis 179",
"token_count": 5303,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Margin notes direct students to colorplates located toward the middle of the book
Modern Analytical Chemistry
either case, the calibration curve provides a means for relating S<sub>samp</sub> to the ana-
A second spectrophotometric method for the quantitative determination of Pb<sup>2+</sup> levels in blood gives... | {
"Header 1": ". . . in Chapter",
"Header 3": "**Margin Notes**",
"token_count": 423,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Each example problem includes a detailed solution that helps students in applying the chapter's material to practical problems.
Modern Analytical Chemistry
An additional problem is encountered when the isolated solid is nonstoichiometric. For example, precipitating Mn<sup>2+</sup> as Mn(OH)<sub>2</sub>, followed by... | {
"Header 1": "**Examples of Typical Problems**",
"token_count": 1806,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In a quantitative analysis, we measure a signal and calculate the amount of analyte using one of the following equations.
$$S_{\text{meas}} = kn_{\text{A}} + S_{\text{reag}}$$
$S_{meas} = kC_A + S_{reag}$
To obtain accurate results we must eliminate determinate errors affecting the measured signal, $S_{\rm meas}... | {
"Header 1": ". . . End of Chapter",
"Header 3": "> 5F SUMMARY",
"token_count": 1321,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The references cited in the chapter are provided so the student can access them for further information
chemistry has been discussed by many prominent analytical chemists. Several notable examples follow.
Hieftie, G. M. "The Two Sides of Analytical Chemistry." Anal.
- Laitinen, H. A. "Analytical Chemistry in a Ch... | {
"Header 1": "References -",
"token_count": 1078,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**A**s currently taught, the introductory course in analytical chemistry emphasizes quantitative (and sometimes qualitative) methods of analysis coupled with a heavy dose of equilibrium chemistry. Analytical chemistry, however, is more than equilibrium chemistry and a collection of analytical methods; it is an approach... | {
"Header 1": "**Preface** Preface",
"token_count": 511,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Key features set this textbook apart from others currently available.
- *A stronger emphasis on the evaluation of data.* Methods for characterizing chemical measurements, results, and errors (including the propagation of errors) are included. Both the binomial distribution and normal distribution are presented, and t... | {
"Header 1": "**Key Features of This Textbook**",
"token_count": 777,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Equilibrium chemistry often receives a significant emphasis in the introductory analytical chemistry course. While an important topic, its overemphasis can cause students to confuse analytical chemistry with equilibrium chemistry. Although attention to solving equilibrium problems is important, it is equally important ... | {
"Header 1": "**The Role of Equilibrium Chemistry in Analytical Chemistry**",
"token_count": 204,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The textbook's organization can be divided into four parts. Chapters 1–3 serve as an introduction, providing an overview of analytical chemistry (Chapter 1); a review of the basic tools of analytical chemistry, including significant figures, units, and stoichiometry (Chapter 2); and an introduction to the terminology u... | {
"Header 1": "**Organization**",
"token_count": 463,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Before beginning an academic career I was, of course, a student. My interest in chemistry and teaching was nurtured by many fine teachers at Westtown Friends School, Knox College, and the University of North Carolina at Chapel Hill; their collective influence continues to bear fruit. In particular, I wish to recognize ... | {
"Header 1": "**Acknowledgments**",
"token_count": 883,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
*"Analytical chemistry is what analytical chemists do."\**
We begin this section with a deceptively simple question. What is analytical chemistry? Like all fields of chemistry, analytical chemistry is too broad and active a discipline for us to easily or completely define in an introductory textbook. Instead, we will... | {
"Header 1": "**1A What Is Analytical Chemistry?**",
"token_count": 739,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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**Figure 1.2** Analytical scheme outlined by Hillebrand and Lundell4 for the gravimetric analysis of Ni in ores (DMG = dimethylgloxime). The factor of 0.2031 in the equation for %Ni accounts for the difference in the formula weights of
Ni(DMG)2 and Ni; see Chapter 8 for more
details. ... | {
"Header 1": "**1A What Is Analytical Chemistry?**",
"Header 3": "**4** Modern Analytical Chemistry",
"token_count": 580,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Having noted that each field of chemistry brings a unique perspective to the study of chemistry, we now ask a second deceptively simple question. What is the "analytical perspective"? Many analytical chemists describe this perspective as an analytical approach to solving problems.7 Although there are probably as many d... | {
"Header 1": "**1B The Analytical Perspective**",
"token_count": 1877,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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In Section 1A we indicated that analytical chemistry is more than a collection of qualitative and quantitative methods of analysis. Nevertheless, many problems on which analytical chemists work ultimately involve either a qualitative or quantitative measurement. Other problems may involve characterizing a sample's chem... | {
"Header 1": "**1C Common Analytical Problems**",
"token_count": 615,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **1.** For each of the following problems indicate whether its solution requires a qualitative, quantitative, characterization, or fundamental study. More than one type of analysis may be appropriate for some problems.
- a. A hazardous-waste disposal site is believed to be leaking contaminants into the local groundwa... | {
"Header 1": "**1F PROBLEMS**",
"token_count": 236,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The role of analytical chemistry within the broader discipline of chemistry has been discussed by many prominent analytical chemists. Several notable examples follow.
Baiulescu, G. E.; Patroescu, C.; Chalmers, R. A. *Education and Teaching in Analytical Chemistry.* Ellis Horwood: Chichester, 1982.
Hieftje, G. M. "T... | {
"Header 1": "**1G SUGGESTED READINGS**",
"token_count": 569,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- 1. Ravey, M. *Spectroscopy* **1990,** *5(7),* 11.
- 2. de Haseth, J. *Spectroscopy* **1990,** *5(7),* 11.
- 3. Fresenius, C. R. *A System of Instruction in Quantitative Chemical Analysis.* John Wiley and Sons: New York, 1881.
- 4. Hillebrand, W. F.; Lundell, G. E. F. *Applied Inorganic Analysis,* John Wiley and Sons:... | {
"Header 1": "**1H REFERENCES**",
"token_count": 617,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Imagine that you find the following instructions in a laboratory procedure: "Transfer 1.5 of your sample to a 100 volumetric flask, and dilute to volume." How do you do this? Clearly these instructions are incomplete since the units of measurement are not stated. Compare this with a complete instruction: "Transfer 1.5 ... | {
"Header 1": "**2A.1 Fundamental Units of Measure**",
"token_count": 1333,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Recording a measurement provides information about both its magnitude and uncertainty. For example, if we weigh a sample on a balance and record its mass as 1.2637 g, we assume that all digits, except the last, are known exactly. We assume that the last digit has an uncertainty of at least $\pm 1$ , giving an absolute... | {
"Header 1": "2A.2 Significant Figures",
"token_count": 1511,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Both molarity and formality express concentration as moles of solute per liter of solution. There is, however, a subtle difference between molarity and formality. **Molarity** is the concentration of a particular chemical species in solution. **Formality**, on the other hand, is a substance's total concentration in sol... | {
"Header 1": "2B.I Molarity and Formality",
"token_count": 1860,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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(a)
$$EW = \frac{FW}{n} = \frac{97.994}{3} = 32.665$$
$N = n \times M = 3 \times 6.0 = 18 \text{ N}$
(b) $EW = \frac{FW}{n} = \frac{97.994}{2} = 48.997$ $N = n \times M = 2 \times 6.0 = 12 \text{ N}$
(c) $EW = \frac{FW}{n} = \frac{97.994}{1} = 97.994$ $N = n \times M = 1 \times 6.0 = 6.0 \text{ N}$
(b) EW =
$... | {
"Header 1": "2B.I Molarity and Formality",
"token_count": 877,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The units of concentration most frequently encountered in analytical chemistry are molarity, weight percent, volume percent, weight-to-volume percent, parts per million, and parts per billion. By recognizing the general definition of concentration given in equation 2.1, it is easy to convert between concentration units... | {
"Header 1": "2B.5 Converting Between Concentration Units",
"token_count": 873,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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#### EXAMPLE 2.4
What is pNa for a solution of $1.76 \times 10^{-3}$ M Na<sub>3</sub>PO<sub>4</sub>?
#### SOLUTION
Since each mole of Na<sub>3</sub>PO<sub>4</sub> contains three moles of Na<sup>+</sup>, the concentration of Na<sup>+</sup> is
$$[Na^+] = \frac{3 \text{ mol } Na^+}{\text{mol } Na_3 PO_4} \times ... | {
"Header 1": "9",
"token_count": 291,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A balanced chemical reaction indicates the quantitative relationships between the moles of reactants and products. These stoichiometric relationships provide the basis for many analytical calculations. Consider, for example, the problem of determining the amount of oxalic acid, $H_2C_2O_4$ , in rhubarb. One method for... | {
"Header 1": "**2C** Stoichiometric Calculations",
"token_count": 1222,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The easiest principle to appreciate is conservation of mass. Except for nuclear reactions, an element's total mass at the end of a reaction must be the same as that present at the beginning of the reaction; thus, an element serves as the most fundamental reaction unit. Consider, for example, the combustion of butane to... | {
"Header 1": "**2C.1 Conservation of Mass**",
"token_count": 414,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In an acid–base reaction, the reaction unit is the proton. For an acid, the number of reaction units is given by the number of protons that can be donated to the base; and for a base, the number of reaction units is the number of protons that the base can accept from the acid. In the reaction between H3PO4 and NaOH, fo... | {
"Header 1": "**2C.3 Conservation of Protons**",
"token_count": 701,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 2.7
Rework Example 2.6 using conservation principles.
#### SOLUTION
Conservation of electrons for this redox reaction requires that
moles
$$Fe^{3+} = 2 \times moles H_2C_2O_4$$
which can be transformed by writing moles as the product of molarity and volume or as grams per formula weight.
$$M_{F... | {
"Header 1": "**O**",
"token_count": 384,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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#### EXAMPLE 2.8
One quantitative analytical method for tetraethylthiuram disulfide, $C_{10}H_{20}N_2S_4$ (Antabuse), requires oxidizing the sulfur to $SO_2$ , and bubbling the resulting $SO_2$ through $H_2O_2$ to produce $H_2SO_4$ . The $H_2SO_4$ is then reacted with NaOH according to the reaction
$$H_2S... | {
"Header 1": "0",
"token_count": 986,
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Measurements are made using appropriate equipment or instruments. The array of equipment and instrumentation used in analytical chemistry is impressive, ranging from the simple and inexpensive, to the complex and costly. With two exceptions, we will postpone the discussion of equipment and instrumentation to those chap... | {
"Header 1": "2D Basic Equipment and Instrumentation",
"token_count": 862,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Analytical chemists use a variety of glassware to measure volume, several examples of which are shown in Figure 2.4. The type of glassware used depends on how exact the volume needs to be. Beakers, dropping pipets, and graduated cylinders are used to measure volumes approximately, typically with errors of several perce... | {
"Header 1": "**2D.2 Equipment for Measuring Volume**",
"token_count": 1107,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Many materials need to be dried prior to their analysis to remove residual moisture. Depending on the material, heating to a temperature of 110–140 °C is usually sufficient. Other materials need to be heated to much higher temperatures to initiate thermal decomposition. Both processes can be accomplished using a labora... | {
"Header 1": "**2D.3 Equipment for Drying Samples**",
"token_count": 524,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Describe how you would prepare the following three solutions: (a) 500 mL of approximately 0.20 M NaOH using solid NaOH; (b) 1 L of 150.0 ppm $\rm Cu^{2+}$ using Cu metal; and (c) 2 L of 4% v/v acetic acid using concentrated glacial acetic acid.
#### SOLUTION
(a) Since the concentration only needs to be known to t... | {
"Header 1": "**2E Preparing Solutions**",
"Header 3": "EXAMPLE 2.9",
"token_count": 1549,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Finally, we cannot end a chapter on the basic tools of analytical chemistry without mentioning the laboratory notebook. Your laboratory notebook is your most important tool when working in the lab, providing a complete record of all your work. If kept properly, you should be able to look back at your laboratory noteboo... | {
"Header 1": "2F The Laboratory Notebook",
"token_count": 321,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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balance (p. 25) concentration (p. 15) desiccant (p. 29) desiccator (p. 29) dilution (p. 31) equivalent (p. 17) equivalent weight (p. 17) formality (p. 15) formula weight (p. 17) meniscus (p. 29) molality (p. 18) molarity (p. 15)
```
normality (p. 16) quantitative transfer (p. 30) volume percent (p. 18) parts per bill... | {
"Header 1": "S 2G KEY TERMS",
"token_count": 243,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
There are a few basic numerical and experimental tools with which you must be familiar. Fundamental measurements in analytical chemistry, such as mass and volume, use base SI units, such as the kilogram (kg) and the liter (L). Other units, such as power, are defined in terms of these base units. When reporting measurem... | {
"Header 1": "3",
"Header 3": "**2H SUMMARY**",
"token_count": 308,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- Indicate how many significant figures are in each of the following numbers.
- a. 903d. 0.0903
- b. 0.903 e. 0.09030
- c. 1.0903f. $9.03 \times 10^2$
- 2. Round each of the following to three significant figures.
- a. 0.89377
- b. 0.89328
- c. 0.89350
- d. 0.8997
- e. 0.08907
- **3.** Round each of the following to... | {
"Header 1": "3",
"Header 3": "21 PROBLEMS",
"token_count": 1929,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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**A**nalytical chemists converse using terminology that conveys specific meaning to other analytical chemists. To discuss and learn analytical chemistry you must first understand its language. You are probably already familiar with some analytical terms, such as "accuracy" and "precision," but you may not have placed t... | {
"Header 1": "The Language of Analytical Chemistry",
"token_count": 280,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The first important distinction we will make is among the terms "analysis," "determination," and "measurement." An **analysis** provides chemical or physical information about a sample. The components of interest in the sample are called **analytes,** and the remainder of the sample is the **matrix.** In an analysis we... | {
"Header 1": "**3A Analysis, Determination, and Measurement**",
"token_count": 280,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Suppose you are asked to develop a way to determine the concentration of lead in drinking water. How would you approach this problem? To answer this question it helps to distinguish among four levels of analytical methodology: techniques, methods, procedures, and protocols.1
A **technique** is any chemical or physica... | {
"Header 1": "**3B Techniques, Methods, Procedures, and Protocols**",
"token_count": 682,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Analyzing a sample generates a chemical or physical **signal** whose magnitude is proportional to the amount of analyte in the sample. The signal may be anything we can measure; common examples are mass, volume, and absorbance. For our purposes it is convenient to divide analytical techniques into two general classes b... | {
"Header 1": "**3C Classifying Analytical Techniques**",
"token_count": 950,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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A method is the application of a technique to a specific analyte in a specific matrix. Methods for determining the concentration of lead in drinking water can be developed using any of the techniques mentioned in the previous section. Insoluble lead salts such as PbSO4 and PbCrO4 can form the basis for a gravimetric me... | {
"Header 1": "**3D Selecting an Analytical Method**",
"token_count": 228,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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**Accuracy** is a measure of how closely the result of an experiment agrees with the expected result. The difference between the obtained result and the expected result is usually divided by the expected result and reported as a percent relative error
$$\% Error = \frac{obtained result - expected result}{expected res... | {
"Header 1": "**3D.1 Accuracy**",
"token_count": 232,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Figure 3.5
Two determinations of the concentration of K+ in serum, showing the effect of precision. The data in (a) are less scattered and, therefore, more precise than the data in (b).
#### 3D.2 Precision
When a sample is analyzed several times, the individual results are rarely the same. Instead, the results ar... | {
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The ability to demonstrate that two samples have different amounts of analyte is an essential part of many analyses. A method's **sensitivity** is a measure of its ability to establish that such differences are significant. Sensitivity is often confused with a method's detection limit.<sup>4</sup> The **detection limit... | {
"Header 1": "3D.3 Sensitivity",
"token_count": 467,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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An analytical method is selective if its signal is a function of only the amount of analyte present in the sample. In the presence of an interferent, equations 3.1 and 3.2 can be expanded to include a term corresponding to the interferent's contribution to the signal, $S_{\rm I}$ ,
$$S_{\text{samp}} = S_A + S_I = k_... | {
"Header 1": "3D.3 Sensitivity",
"Header 3": "3D.4 Selectivity",
"token_count": 1325,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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#### EXAMPLE 3.2
Barnett and colleagues<sup>5</sup> developed a new method for determining the concentration of codeine during its extraction from poppy plants. As part of their study they determined the method's response to codeine relative to that for several potential interferents. For example, the authors found t... | {
"Header 1": "9",
"token_count": 816,
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Another way to narrow the choice of methods is to consider the scale on which the analysis must be conducted. Three limitations of particular importance are the amount of sample available for the analysis, the concentration of analyte in the sample, and the absolute amount of analyte needed to obtain a measurable signa... | {
"Header 1": "3D.6 Scale of Operation",
"token_count": 1049,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Finally, analytical methods can be compared in terms of their need for equipment, the time required to complete an analysis, and the cost per sample. Methods relying on instrumentation are equipment-intensive and may require significant operator training. For example, the graphite furnace atomic absorption spectroscopi... | {
"Header 1": "**3D.7 Equipment, Time, and Cost**",
"token_count": 244,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Unfortunately, the design criteria discussed earlier are not mutually independent.8 Working with smaller amounts of analyte or sample, or improving selectivity, often comes at the expense of precision. Attempts to minimize cost and analysis time may decrease accuracy. Selecting a specific method requires a careful bala... | {
"Header 1": "**3D.8 Making the Final Choice**",
"token_count": 288,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The accuracy of a method depends on its selectivity for the analyte. Even the best methods, however, may not be free from interferents that contribute to the measured signal. Potential interferents may be present in the sample itself or the reagents used during the analysis. In this section we will briefly look at how ... | {
"Header 1": "**3E.1 Compensating for Interferences**",
"token_count": 969,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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A sample was analyzed for the concentration of two analytes, A and B, under two sets of conditions. Under condition 1, the calibration sensitivities are
$$k_{A,1} = 76 \text{ ppm}^{-1}$$
$k_{B,1} = 186 \text{ ppm}^{-1}$
and for condition 2
$$k_{\rm A,2} = 33 \ \rm ppm^{-1}$$
$k_{\rm B,2} = 243 \ \rm ppm^{-1}$
T... | {
"Header 1": "**EXAMPLE 3.3**",
"token_count": 507,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Analytical chemists make a distinction between calibration and standardization.9 **Calibration** ensures that the equipment or instrument used to measure the signal is operating correctly by using a standard known to produce an exact signal. Balances, for example, are calibrated using a standard weight whose mass can b... | {
"Header 1": "**3E.2 Calibration and Standardization**",
"token_count": 267,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Before a procedure can provide useful analytical information, it is necessary to demonstrate that it is capable of providing acceptable results. **Validation** is an evaluation of whether the precision and accuracy obtained by following the procedure are appropriate for the problem. In addition, validation ensures that... | {
"Header 1": "**3E.4 Validation**",
"token_count": 306,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Earlier we noted that a protocol is a set of stringent written guidelines, specifying an exact procedure that must be followed if results are to be accepted by the agency specifying the protocol. Besides all the considerations taken into account when designing the procedure, a protocol also contains very explicit instr... | {
"Header 1": "**3F Protocols**",
"token_count": 475,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The importance of analytical methodology is evident when examining the results of environmental monitoring programs. The purpose of a monitoring program is to determine the present status of an environmental system and to assess longterm trends in the quality of the system. These are broad and poorly defined goals. In ... | {
"Header 1": "**3G The Importance of Analytical Methodology**",
"token_count": 521,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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| accuracy<br>(p. 38) |
|-------------------------------------|
| analysis<br>(p. 36) |
| analytes<br>(p. 36) |
| calibration<br>(p. 47) |
| calibration curve<br>(p. 47) |
| concentration techniques<br>(p. 38) |
| detection limit<br>(p. 39) |
... | {
"Header 1": "**3H KEY TERMS**",
"token_count": 302,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
1. When working with a solid sample, it often is necessary to bring the analyte into solution by dissolving the sample in a suitable solvent. Any solid impurities that remain are removed by filtration before continuing with the analysis. In a typical total analysis method, the procedure might read
After dissolving th... | {
"Header 1": "**3**J",
"Header 3": "3J PROBLEMS",
"token_count": 1856,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The following papers provide alternative schemes for classifying analytical methods
Booksh, K. S.; Kowalski, B. R. "Theory of Analytical Chemistry," *Anal. Chem.* **1994,** *66,* 782A–791A.
Phillips, J. B. "Classification of Analytical Methods," *Anal. Chem.* **1981,** *53,* 1463A–1470A.
Valcárcel, M.; Luque de C... | {
"Header 1": "**3K SUGGESTED READINGS**",
"token_count": 510,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- 1. Taylor, J. K. *Anal. Chem.* **1983,** *55,* 600A–608A.
- 2. Fitch, A.; Wang, Y.; Mellican, S.; et al. *Anal. Chem.* **1996,** *68,* 727A–731A.
- 3. Basset, J.; Denney, R. C.; Jeffery, G. H.; et al. *Vogel's Textbook of Quantitative Inorganic Analysis,* 4th ed. Longman: London, 1981, p. 8.
- 4. Ingle, J. D.; Crouch... | {
"Header 1": "**3L REFERENCES**",
"token_count": 772,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**A**problem dictates the requirements we place on our measurements and results. Regulatory agencies, for example, place stringent requirements on the reliability of measurements and results reported to them. This is the rationale for creating a protocol for regulatory problems. Screening the products of an organic syn... | {
"Header 1": "Evaluating Analytical Data",
"token_count": 218,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Let's begin by choosing a simple quantitative problem requiring a single measurement. The question to be answered is—What is the mass of a penny? If you think about how we might answer this question experimentally, you will realize that this problem is too broad. Are we interested in the mass of United State pennies or... | {
"Header 1": "4A Characterizing Measurements and Results",
"token_count": 720,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 4.1
What is the mean for the data in Table 4.1?
#### SOLUTION
To calculate the mean, we add the results for all measurements
$$3.080 + 3.094 + 3.107 + 3.056 + 3.112 + 3.174 + 3.198 = 21.821$$
and divide by the number of measurements
$$\overline{X} = \frac{21.821}{7} = 3.117 \text{ g}$$
The me... | {
"Header 1": "0",
"token_count": 550,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
If the mean or median provides an estimate of a penny's true mass, then the spread of the individual measurements must provide an estimate of the variability in the masses of individual pennies. Although spread is often defined relative to a specific measure of central tendency, its magnitude is independent of the cent... | {
"Header 1": "4A.2 Measures of Spread",
"token_count": 455,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 4.3
What are the standard deviation, the relative standard deviation, and the percent relative standard deviation for the data in Table 4.1?
#### **SOLUTION**
To calculate the standard deviation, we obtain the difference between the mean value (3.117; see Example 4.1) and each measurement, square the... | {
"Header 1": "ח",
"token_count": 566,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Accuracy is a measure of how close a measure of central tendency is to the true, or expected value, $\mu$ .<sup>†</sup> Accuracy is usually expressed as either an absolute error
$$E = \overline{X} - \mu$$
4.2
or a percent relative error, $E_r$ .
$$E_{\rm r} = \frac{\overline{X} - \mu}{\mu} \times 100$$
4.3
<s... | {
"Header 1": "4B.I Accuracy",
"token_count": 2035,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
bData for Eppendorf Digital Pipet 4710.
cData for Oxford Benchmate.
dData for Eppendorf Maxipetter 4720 with Maxitip P.
Volumetric glassware is categorized by class. Class A glassware is manufactured to comply with tolerances specified by agencies such as the National Institute of Standards and Technology. Tole... | {
"Header 1": "4B.I Accuracy",
"token_count": 644,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Mass Sample<br>(g) | True Mass of Analyte<br>(g) | Constant Error<br>Mass of Analyte Determined<br>(g)<br>(g) | | | | Percent Analyte Reported<br>(%w/w) |
|--------------------|-----------------------------|------------------------------------------------------------|-------|------|--|--------------------... | {
"Header 1": "**Table 4.5 Effect of Constant Positive Determinate Error on Analysis of Sample Containing 50% Analyte (%w/w)**",
"token_count": 897,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Mass Sample<br>(g) | True Mass of Analyte<br>(g) | Proportional Error<br>Mass of Analyte Determined<br>(%)<br>(g) | | Percent Analyte Reported<br>(%w/w) |
|--------------------|-----------------------------|----------------------------------------------------------------|-------|--------------------------------... | {
"Header 1": "**Table 4.6 Effect of Proportional Positive Determinate Error on Analysis of Sample Containing 50% Analyte (%w/w)**",
"token_count": 886,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance. Precision is commonly divided into two categories: repeatability and reproducibility. **Repeatability** is the precision obtained when all measurements are made by the same anal... | {
"Header 1": "**4B.2 Precision**",
"token_count": 1110,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Analytical chemists make a distinction between error and uncertainty.3 **Error** is the difference between a single measurement or result and its true value. In other words, error is a measure of bias. As discussed earlier, error can be divided into determinate and indeterminate sources. Although we can correct for det... | {
"Header 1": "**4B.3 Error and Uncertainty**",
"token_count": 515,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Suppose that you need to add a reagent to a flask by several successive transfers using a class A 10-mL pipet. By calibrating the pipet (see Table 4.8), you know that it delivers a volume of 9.992 mL with a standard deviation of 0.006 mL. Since the pipet is calibrated, we can use the standard deviation as a measure of ... | {
"Header 1": "**4C Propagation of Uncertainty**",
"token_count": 507,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The class A 10-mL pipet characterized in Table 4.8 is used to deliver two successive volumes. Calculate the absolute and relative uncertainties for the total delivered volume.
#### *SOLUTION*
The total delivered volume is obtained by adding the volumes of each delivery; thus
$$V_{\text{tot}} = 9.992 \text{ mL} + ... | {
"Header 1": "**EXAMPLE 4.5**",
"token_count": 235,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
When measurements are multiplied or divided, the relative uncertainty in the result is the square root of the sum of the squares of the relative uncertainties for the individual measurements. Thus, for the equations $R = A \times B \times C$ or $R = A \times B/C$ , or any other combination of multiplying and dividin... | {
"Header 1": "4C.3 Uncertainty When Multiplying or Dividing",
"token_count": 441,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Many chemical calculations involve a combination of adding and subtracting, and multiply and dividing. As shown in the following example, the propagation of uncertainty is easily calculated by treating each operation separately using equations 4.6 and 4.7 as needed.
67
#### EXAMPLE 4.7
For a concentration techniq... | {
"Header 1": "4C.4 Uncertainty for Mixed Operations",
"token_count": 607,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Many other mathematical operations are commonly used in analytical chemistry, including powers, roots, and logarithms. Equations for the propagation of uncertainty for some of these functions are shown in Table 4.9.
#### EXAMPLE 4.8
The pH of a solution is defined as
$$pH = -log[H^+]$$
where [H<sup>+</sup>] is ... | {
"Header 1": "4C.5 Uncertainty for Other Mathematical Functions",
"token_count": 768,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Given the complexity of determining a result's uncertainty when several measurements are involved, it is worth examining some of the reasons why such calculations are useful. A propagation of uncertainty allows us to estimate an ex-
pected uncertainty for an analysis. Comparing the expected uncertainty to that which ... | {
"Header 1": "4C.6 Is Calculating Uncertainty Actually Useful?",
"token_count": 669,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Which of the following methods for preparing a 0.0010 M solution from a 1.0 M stock solution provides the smallest overall uncertainty?
(a) A one-step dilution using a 1-mL pipet and a 1000-mL volumetric flask.
- (b) A two-step dilution using a 20-mL pipet and a 1000-mL volumetric flask for the first dilution and a... | {
"Header 1": "EXAMPLE 4.9",
"token_count": 552,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
An analysis, particularly a quantitative analysis, is usually performed on several replicate samples. How do we report the result for such an experiment when results for the replicates are scattered around a central value? To complicate matters further, the analysis of each replicate usually requires multiple measureme... | {
"Header 1": "4D The Distribution of Measurements and Results",
"token_count": 532,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In the previous section we introduced the terms "population" and "sample" in the context of reporting the result of an experiment. Before continuing, we need to understand the difference between a population and a sample. A **population** is the set of all objects in the system being investigated. These objects, which ... | {
"Header 1": "**4D.1 Populations and Samples**",
"token_count": 317,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
To predict the properties of a population on the basis of a sample, it is necessary to know something about the population's expected distribution around its central value. The distribution of a population can be represented by plotting the frequency of occurrence of individual values as a function of the values themse... | {
"Header 1": "**4D.2 Probability Distributions for Populations**",
"token_count": 509,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 4.10
Carbon has two common isotopes, <sup>12</sup>C and <sup>13</sup>C, with relative isotopic abundances of, respectively, 98.89% and 1.11%. (a) What are the mean and standard deviation for the number of <sup>13</sup>C atoms in a molecule of cholesterol? (b) What is the probability of finding a molecule... | {
"Header 1": "0",
"token_count": 1326,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The amount of aspirin in the analgesic tablets from a particular manufacturer is known to follow a normal distribution, with µ = 250 mg and σ<sup>2</sup> = 25. In a random sampling of tablets from the production line, what percentage are expected to contain between 243 and 262 mg of aspirin?
#### *SOLUTION*
The nor... | {
"Header 1": "**EXAMPLE 4.11**",
"token_count": 502,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
If we randomly select a single member from a population, what will be its most likely value? This is an important question, and, in one form or another, it is the fundamental problem for any analysis. One of the most important features of a population's probability distribution is that it provides a way to answer this ... | {
"Header 1": "4D.3 Confidence Intervals for Populations",
"token_count": 1834,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Pennies<br>in Circulationa | | | | | | |
|-------|---------------------------------------------------------------------------------------|-------|---------------|-------|---------------|-------|---------------|
| Penny | Weight<br>(g) ... | {
"Header 1": "4D.3 Confidence Intervals for Populations",
"token_count": 2023,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
7,8 If we could analyze every possible sample of equal size for a given population (e.g., every possible sample of five pennies), calculating their respective means and variances, the average mean and the average variance would equal $\mu$ and $\sigma^2$ . Although $\overline{X}$ and $s^2$ for any single sample ... | {
"Header 1": "4D.3 Confidence Intervals for Populations",
"token_count": 1488,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
There is a temptation when analyzing data to plug numbers into an equation, carry out the calculation, and report the result. This is never a good idea, and you should develop the habit of constantly reviewing and evaluating your data. For example, if analyzing five samples gives an analyte's mean concentration as 0.67... | {
"Header 1": "4D.6 A Cautionary Statement",
"token_count": 347,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In the previous section we noted that the result of an analysis is best expressed as a confidence interval. For example, a 95% confidence interval for the mean of five results gives the range in which we expect to find the mean for 95% of all samples of equal size, drawn from the same population. Alternatively, and in ... | {
"Header 1": "**4E Statistical Analysis of Data**",
"token_count": 237,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Let's consider the following problem. Two sets of blood samples have been collected from a patient receiving medication to lower her concentration of blood glucose. One set of samples was drawn immediately before the medication was administered; the second set was taken several hours later. The samples are analyzed and... | {
"Header 1": "**4E.1 Significance Testing**",
"token_count": 378,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A **significance test** is designed to determine whether the difference between two or more values is too large to be explained by indeterminate error. The first step in constructing a significance test is to state the experimental problem as a yesor-no question, two examples of which were given at the beginning of thi... | {
"Header 1": "**4E.2 Constructing a Significance Test**",
"token_count": 1504,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Since significance tests are based on probabilities, their interpretation is naturally subject to error. As we have already seen, significance tests are carried out at a significance level, $\alpha$ , that defines the probability of rejecting a null hypothesis that is true. For example, when a significance test is con... | {
"Header 1": "**4E.4** Errors in Significance Testing",
"token_count": 378,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
One approach for validating a new analytical method is to analyze a standard sample containing a known amount of analyte, $\mu$ . The method's accuracy is judged by determining the average amount of analyte in several samples, $\overline{X}$ , and using a significance test to compare it with $\mu$ . The null hypothe... | {
"Header 1": "4F.1 Comparing $\\bar{X}$ to $\\mu$",
"token_count": 2048,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Critical values of F for $\alpha=0.05$ are listed in Appendix 1C for both one-tailed and two-tailed significance tests.
#### EXAMPLE 4.17
A manufacturer's process for analyzing aspirin tablets has a known variance of 25. A sample of ten aspirin tablets is selected and analyzed for the amount of aspirin, yielding ... | {
"Header 1": "4F.1 Comparing $\\bar{X}$ to $\\mu$",
"token_count": 852,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The result of an analysis is influenced by three factors: the method, the sample, and the analyst. The influence of these factors can be studied by conducting a pair of experiments in which only one factor is changed. For example, two methods can be compared by having the same analyst apply both methods to the same sam... | {
"Header 1": "4F.4 Comparing Two Sample Means",
"token_count": 2029,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### SOLUTION
We begin by summarizing the mean and standard deviation for the data reported by each analyst. These values are
$$\overline{X}_{A} = 86.83\%$$
$s_{A} = 0.32$
$\overline{X}_{B} = 82.71\%$
$s_{B} = 2.16$
A two-tailed *F*-test of the following null and alternative hypotheses
$$H_0$$
: $s_A^2 = s_B^2... | {
"Header 1": "Examp",
"token_count": 2049,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
If this is not the case, a single sample with a larger error could result in a value of $d_i$ that is substantially larger than that for the remaining samples. Including this sample in the calculation of $\overline{d}$ and $s_d$ leads to a biased estimate of the true mean and standard deviation. For samples that ... | {
"Header 1": "Examp",
"token_count": 1303,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The focus of this chapter has been the evaluation of analytical data, including the use of statistics. In this final section we consider how statistics may be used to characterize a method's ability to detect trace amounts of an analyte.
A method's **detection limit** is the smallest amount or concentration of analyt... | {
"Header 1": "**46** Detection Limits",
"token_count": 1604,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
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