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Earlier we noted that a response surface can be described mathematically by an equation relating the response to its factors. If a series of experiments is carried out in which we measure the response for several combinations of factor levels, then linear regression can be used to fit an equation describing the respons... | {
"Header 1": "**14A.3 Mathematical Models of Response Surfaces**",
"token_count": 1787,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Estimates for these parameters are given by the following equations
$$\beta_0 \approx b_0 = \frac{1}{n} \sum R_i$$
14.5
$$\beta_a \approx b_a = \frac{1}{n} \sum A_i^* R_i$$
14.6
$$\beta_b \approx b_b = \frac{1}{n} \sum_i B_i^* R_i$$
14.7
Table 14.4 Example of Uncoded and Coded Factor Levels and Responses for a ... | {
"Header 1": "**14A.3 Mathematical Models of Response Surfaces**",
"token_count": 699,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Equation 14.9 gives the empirical model of the response surface for the data in Table 14.4 when the factors are in coded form. Convert the equation to its uncoded form.
#### SOLUTION
To convert the equation to its uncoded form, it is necessary to solve equation 14.3 for each factor. Values for $c_f$ and $d_f$ a... | {
"Header 1": "EXAMPLE 14.3",
"token_count": 945,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Table 14.5 lists the uncoded factor levels, coded factor levels, and responses for a 2<sup>3</sup> factorial design. Determine the coded and uncoded empirical model for the response surface based on equation 14.10.
#### SOLUTION
We begin by calculating the estimated parameters using equations 14.6–14.9 and 14.11–14... | {
"Header 1": "EXAMPLE 14.4",
"token_count": 2035,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
At the beginning of this section we noted that the concentration of vanadium can be determined spectrophotometrically by making the solution acidic with H2SO4 and reacting with H2O2 to form a reddish brown compound with the general formula (VO)2(SO4)3. Palasota and Deming7 studied the effect on the absorbance of the re... | {
"Header 1": "**EXAMPLE 14.5**",
"token_count": 1107,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In many cases an optimized method may produce excellent results in the laboratory developing the method, but poor results in other laboratories. This is not surprising since a method is often optimized by a single analyst under an ideal set of conditions, in which the sources of reagents, equipment, and instrumentation... | {
"Header 1": "**14B.3 Ruggedness Testing**",
"token_count": 1629,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### SOLUTION
The effect of a change in level for each factor is calculated using equation 14.15
$$E_{A} = \frac{R_{1} + R_{2} + R_{3} + R_{4}}{4} - \frac{R_{5} + R_{6} + R_{7} + R_{8}}{4} = 0.30$$
$$E_{B} = \frac{R_{1} + R_{2} + R_{5} + R_{6}}{4} - \frac{R_{3} + R_{4} + R_{7} + R_{8}}{4} = 0.05$$
$$E_{C} = \... | {
"Header 1": "**14B.3 Ruggedness Testing**",
"token_count": 714,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
For an analytical method to be of use, it must be capable of producing results with acceptable accuracy and precision. The process of verifying a method as described in the previous section determines whether the method meets this goal for a single analyst. A further requirement for a standard method is that an analysi... | {
"Header 1": "**14C Validating the Method as a Standard Method**",
"token_count": 550,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The design of a collaborative test must provide the additional information needed to separate the effect of random error from that due to systematic errors introduced by the analysts. One simple approach, which is accepted by the Association of Official Analytical Chemists, is to have each analyst analyze two samples, ... | {
"Header 1": "**14C.1 Two-Sample Collaborative Testing**",
"token_count": 1724,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Analyst | $D_i$ | $T_i$ |
|---------|-------|-------|
| 1 | 15.6 | 474.4 |
| 2 | -2.3 | 497.1 |
| 3 | 5.6 | 486.4 |
| 4 | 9.4 | 480.4 |
| 5 | -6.0 | 517.4 |
| 6 | 8.6 | 487.4 |
| 7 | -6.3 | 504.7 |
| 8 | 0.8 | 449.4 |
| 9 | 8.7 | 501.3 |
| 10 ... | {
"Header 1": "**14C.1 Two-Sample Collaborative Testing**",
"token_count": 2006,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The variability in the results shown in Table 14.7 arises from two sources: indeterminate errors associated with the analytical procedure that are experienced equally by all analysts, and systematic or determinate errors introduced by the analysts.
One way to view the data in Table 14.7 is to treat it as a single sys... | {
"Header 1": "**14C.1 Two-Sample Collaborative Testing**",
"token_count": 2037,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### SOLUTION
To begin, we calculate the global mean and variance and the means for each analyst. These results are
$$\overline{\overline{X}} = 95.87$$
$\overline{\overline{s}^2} = 5.506$ $\overline{X}_A = 94.56$ $\overline{X}_B = 99.88$ $\overline{X}_C = 94.77$ $\overline{X}_D = 94.75$
Using these valu... | {
"Header 1": "**14C.1 Two-Sample Collaborative Testing**",
"token_count": 1109,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 14.10
Determine the source of the significant difference for the data in Example 14.9.
#### SOLUTION
Individual comparisons using Fisher's least significant difference test are based on the following null hypothesis and one-tailed alternative hypothesis
$$H_0: \overline{X}_i = \overline{X}_i \qquad... | {
"Header 1": "0",
"token_count": 1603,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
One of the goals of analytical chemistry is to develop new analytical methods that are recognized or accepted as being standard methods. In this chapter we considered how a standard method is developed, including finding the optimum experimental conditions, verifying that the method produces acceptable precision and ac... | {
"Header 1": "**14E SUMMARY**",
"token_count": 559,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
*The following set of experiments provides practical examples of the optimization of experimental conditions. Examples include simplex optimization, factorial designs used to develop empirical models of response surfaces, and the fitting of experimental data to theoretical models of the... | {
"Header 1": "**14F** *Suggested* **EXPERIMENTS**",
"token_count": 220,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Continued from page 699
Leggett, D. L. "Instrumental Simplex Optimization," *J. Chem. Educ.* **1983**, *60*, 707–710.
A variable-size simplex optimization of a gas chromatographic separation using oven temperature and carrier gas flow rate as factors is described in this experiment.
Oles, P. J. "Fractional Factor... | {
"Header 1": "Experiments",
"token_count": 868,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **1.** For each of the following equations, determine the optimum response, using the one-factor-at-a-time searching algorithm. Begin the search at (0,0) with factor A, and use a step size of 1 for both factors. The boundary conditions for each response surface are $0 \le A \le 10$ and $0 \le B \le 10$ . Continue ... | {
"Header 1": "14G PROBLEMS",
"token_count": 1491,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
units) |
| 1 | –1 | –1 | –1 | 1.55 |
| 2 | 1 | –1 | –1 | 5.40 |
| 3 | –1 | 1 | –1 | 3.50 |
| 4 | 1 | 1 ... | {
"Header 1": "14G PROBLEMS",
"token_count": 1276,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
(b) Determine the coded equation for the response surface where samples/h is the response.
- (c) Based on the coded equations, do the conditions favoring sensitivity also improve the sampling rate? (d) What conditions would you choose if your goal is to optimize both sensitivity and sampling rate?
- **9.** Here is a ch... | {
"Header 1": "14G PROBLEMS",
"token_count": 1995,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The results for the ten trials are
Are the single-operator characteristics for this method acceptable?
**12.** A proposed gravimetric method was evaluated for its ruggedness by varying the following factors
| Factor A—sample size | A = 1 g | a = 1.1 g |
|-----------------------... | {
"Header 1": "14G PROBLEMS",
"token_count": 1245,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The following texts and articles provide an excellent discussion of optimization methods based on searching algorithms and mathematical modeling, including a discussion of the relevant calculations.
Bayne, C. K.; Rubin, I. B. *Practical Experimental Designs and Optimization Methods for Chemists.* VCH Publishers: Deer... | {
"Header 1": "**14H SUGGESTED READINGS**",
"token_count": 330,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- 1. *Vogel's Textbook of Quantitative Inorganic Analysis.* Longman: London, 1978; p. 752.
- 2. Sharaf, M. A.; Illman, D. L.; Kowalski, B. R. *Chemometrics.* Wiley-Interscience: New York, 1986.
- 3. Spendley, W.; Hext, G. R.; Himsworth, F. R. *Technometrics* **1962,** *4,* 441–461.
- 4. Deming, S. N.; Parker, L. R. *CR... | {
"Header 1": "**14I REFERENCES**",
"token_count": 1000,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**I**n Chapter 1 we noted that each field of chemistry brings a unique perspective to the broader discipline of chemistry. For analytical chemistry this perspective was identified as an approach to solving problems, which was presented as a five-step process: (1) Identify and define the problem; (2) Design the experime... | {
"Header 1": "Quality Assurance",
"token_count": 532,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Quality control encompasses all activities used to bring a system into statistical control. The most important facet of quality control is a set of written directives describing all relevant laboratory-specific, technique-specific, sample-specific, method-specific, and protocol-specific operations. <sup>1,3,6</sup> Goo... | {
"Header 1": "15A Quality Control",
"token_count": 477,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Provide an SOP for the determination of cadmium in lake sediments by atomic absorption spectrophotometry using a normal calibration curve.
#### *SOLUTION*
Sediment samples should be collected using a bottom grab sampler and stored at 4 °C in acid-washed polyethylene bottles during transportation to the laboratory. ... | {
"Header 1": "**EXAMPLE 15.1**",
"token_count": 693,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The most useful methods for quality assessment are those that are coordinated by the laboratory and that provide the analyst with immediate feedback about the system's state of statistical control. Internal methods of quality assessment included in this section are the analysis of duplicate samples, the analysis of bla... | {
"Header 1": "15B.1 Internal Methods of Quality Assessment",
"token_count": 311,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Analyte | Limits for Spike Recovery (%) | (d) <sub>r</sub> When [Analyte] < $20 \times MDL$ (±%) | ( <i>d</i> ) <sub>r</sub> When [Analyte] > 20 $\times$ MDL (±%) |
|----------------------|-------------------------------|--------------------------------------------------------|---------------------------... | {
"Header 1": "Table 15.1 Selected Quality Assessment Limits for the Analysis of Waters and Wastewaters",
"token_count": 388,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
To evaluate the precision for the determination of potassium in blood serum, duplicate analyses were performed on six samples, yielding the following results.
| Duplicate | <i>X</i> <sub>1</sub> | $X_2$ |
|-----------|-----------------------|-------|
| 1 | 160 | 147 |
| 2 | 196 ... | {
"Header 1": "EXAMPLE 15.2",
"token_count": 1843,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
With a prescriptive approach to quality assessment, duplicate samples, blanks, standards, and spike recoveries are measured following a specific protocol. The result for each analysis is then compared with a single predetermined limit. If this limit is exceeded, an appropriate corrective action is taken. Prescriptive a... | {
"Header 1": "**15C.1 Prescriptive Approach**",
"token_count": 1094,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In a performance-based approach to quality assurance, a laboratory is free to use its experience to determine the best way to gather and monitor quality assessment data. The quality assessment methods remain the same (duplicate samples, blanks, standards, and spike recoveries) since they provide the necessary informati... | {
"Header 1": "**15C.2 Performance-Based Approach**",
"token_count": 1908,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 15.5
Construct a precision control chart using the following 20 ranges, each determined from a duplicate analysis of a 10-ppm calibration standard
| Sample: | 1 | 2 | 3 | 4 | 5 |
|---------|------|------|------|------|------|
| Result: | 0.36 | 0.09 | 0.11 | 0.06 | 0.25 |
| Sample: | 6... | {
"Header 1": "**15C.2 Performance-Based Approach**",
"token_count": 2006,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Few analyses are so straightforward that high-quality results are easily obtained. Good analytical work requires careful planning and an attention to detail. Creating and maintaining a quality assurance program is one way to help ensure the quality of analytical results. Quality assurance programs usually include eleme... | {
"Header 1": "**15E SUMMARY**",
"token_count": 242,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
*The following three experiments introduce aspects of quality assurance and quality control.*
Bell, S. C.; Moore, J. "Integration of Quality Assurance/ Quality Control into Quantitative Analysis," *J. Chem. Educ.* **1998,** *75,* 874–877.
The use of several QA/QC methods is describe... | {
"Header 1": "**15F Suggested EXPERIMENTS**",
"token_count": 357,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **1.** Make a list of good laboratory practices for the lab accompanying this course (or another lab if this course does not have an associated laboratory). Explain the rationale for each item on your list.
- **2.** Write directives outlining good measurement practices for (a) a buret, (b) a pH meter, and (c) a spect... | {
"Header 1": "**15G PROBLEMS**",
"token_count": 1667,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**9.** The following data were obtained for the duplicate analysis of a stable standard.14
| Sample | X1<br>(ppm) | X2<br>(ppm) | Sample | X1<br>(ppm) | X2<br>(ppm) |
|--------|-------------|-------------|--------|-------------|-------------|
| 1 | 50 | 46 | 14 | 36 | 36 ... | {
"Header 1": "**15G PROBLEMS**",
"token_count": 490,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The following texts and articles may be consulted for an additional discussion of the various aspects of quality assurance and quality control.
Amore, F. "Good Analytical Practices," *Anal. Chem.* **1979,** *51,* 1105A–1110A.
Barnard, Jr. A. J.; Mitchell, R. M.; Wolf, G. E. "Good Analytical Practices in Quality Con... | {
"Header 1": "**15H SUGGESTED READINGS**",
"token_count": 378,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- 1. Taylor, J. K. *Anal. Chem.* **1981,** *53,* 1588A–1596A
- 2. Taylor, J. K. *Anal. Chem.* **1983,** *55,* 600A–608A.
- 3. Taylor, J. K. *Am. Lab.* October **1985,** 67–75.
- 4. Nadkarni, R. A. *Anal. Chem.* **1991,** *63,* 675A–682A.
- 5. Valcárcel, M.; Ríos, A. *Trends Anal. Chem.* **1994,** *13,* 17–23.
- 6. ACS ... | {
"Header 1": "**15I REFERENCES**",
"token_count": 621,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### **Single-Sided Normal Distributiona**
| u | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
|-----|----------|--------|---------|--------|---------|--------|---------|--------|---------|--------|
| 0.0 | 0.5000 | 0.4960 | 0.4920 | 0.4880 | 0.4840 | 0.4801 | 0... | {
"Header 1": "Appendix 1A",
"token_count": 3615,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### *t***-Tablea**
| Value of t for confidence interval of:<br>Critical value of ötö for α values of:<br>Degrees of Freedom | 90%<br>0.10 | 95%<br>0.05 | 98%<br>0.02 | 99%<br>0.01 |
|--------------------------------------------------------------------------------------------------------|-------------|-------------|-... | {
"Header 1": "Appendix 1B",
"token_count": 789,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Appendix 1C.1 *F***-Table for One-Tailed Test at** α **= 0.05 (95% Confidence Level)**
| a<br>ν2/ν1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 15 | 20 | Ç |
|------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|... | {
"Header 1": "Appendix 1B",
"token_count": 2193,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Appendix 1C.2 *F***-Table for Two-Tailed Test at** α **= 0.05 (95% Confidence Level)**
| a<br>ν2/ν1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 15 | 20 | Ç |
|------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------... | {
"Header 1": "Appendix 1B",
"token_count": 2337,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### **Critical Values for** *Q-***Test**
| N/α | 0.1 | 0.05 | 0.04 | 0.02 | 0.01 |
|-----|-------|-------|-------|-------|-------|
| 3 | 0.941 | 0.970 | 0.976 | 0.988 | 0.994 |
| 4 | 0.765 | 0.829 | 0.846 | 0.889 | 0.926 |
| 5 | 0.642 | 0.710 | 0.729 | 0.780 | 0.821 |
| 6 | 0.560 | 0.625 | 0.644 | 0.69... | {
"Header 1": "Appendix 1D",
"token_count": 386,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### **Random Number Table**
| 23733 | 43499 | 92848 | 39382 | 65423 | 52443 | 41812 | 90777 | 42345 | 39906 |
|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| 57880 | 74874 | 94181 | 90599 | 55012 | 18321 | 18766 | 31656 | 22117 | 31932 |
| 16446 | 72008 | 81701 | 90740 | 56193 | 1... | {
"Header 1": "Appendix 1E",
"token_count": 1469,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**A**ll compounds should be of the highest available purity. Metals should be cleaned with dilute acid to remove surface impurities and rinsed with distilled water. Unless otherwise indicated, compounds should be dried to
constant weight at 110 °C. Most compounds can be dissolved in dilute acid (1:1 HCl or 1:1 HNO3),... | {
"Header 1": "Recommended Reagents for Preparing Primary Standards",
"token_count": 822,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| FW<br>Element | Compound | (g/mol) | Comments |
|---------------|----------------|---------|---------------------------------------------------------------------------------------------|
| magnesium | Mg metal | 24.305 ... | {
"Header 1": "Recommended Reagents for Preparing Primary Standards",
"Header 3": "**730** Modern Analytical Chemistry",
"token_count": 828,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Bromide (Br <sup>-</sup> ) | $pK_{sp}$ | $K_{sp}$ | Cyanide (CN <sup>-</sup> ) | $pK_{sp}$ | $K_{sp}$ |
|--------------------------------------------|--------------------------|-----------------------|----------------------------... | {
"Header 1": "**Solubility Products**",
"token_count": 2192,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Hydroxide (OH⁻) | p <i>K</i> <sub>sp</sub> | $K_{sp}$ | Sulfate (SO <sub>4</sub> <sup>2-</sup> ) | $pK_{sp}$ | $K_{sp}$ |
|---------------------------------------------------------------------|--------------------------|----------... | {
"Header 1": "**Solubility Products**",
"Header 3": "**Solubility Products—continued**",
"token_count": 2035,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### **Acid Dissociation Constants**
| Compound | Conjugate Acid | p <i>K</i> <sub>a</sub> | <b>K</b> a |
|--------------|---------------------------------------------|-----------------------------|----------------------------------------------|
|... | {
"Header 1": "Appendix 3B",
"token_count": 1470,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Compound | Conjugate Acid | pKa | Ka ... | {
"Header 1": "Appendix 3B",
"Header 3": "**Acid Dissociation Constants—***continued*",
"token_count": 4955,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### **Metal–Ligand Formation Constants**
| Acetate | | | | | | |
|---------|--------|--------|--------|--------|--------|--------|
| CH3COO– | log K1 | log K2 | log K3 | log K4 | log K5 | log K6 |
| Mg2+ | 1.27 | | | | | |
| Ca2+ | ... | {
"Header 1": "Appendix 3C",
"token_count": 4655,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Aluminum | <i>E</i> ° (V) | <i>E</i> °′<br>(V) | Bromine | <i>E</i> ° (V) | | <i... | {
"Header 1": "Standard Reduction Potentials<sup>a</sup>",
"token_count": 1756,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
200, | | | | | 1.44 | 1 M H <sub>2</... | {
"Header 1": "Standard Reduction Potentials<sup>a</sup>",
"token_count": 780,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| $Cr^{3+} + e^{-} \rightleftharpoons Cr^{2+}$ $-0.424$ $Fe^{2+} + 2e^{-} \rightleftharpoons Fe(s)$ $Cr^{2+} + 2e^{-} \rightleftharpoons Cr(s)$ $-0.90$ $Fe^{3+} + 3e^{-} \rightleftharpoons Fe(s)$ $Cr_2O_7^{2-} + 14H^+ + 6e^- \rightleftharpoons 2Cr^{3+} + 7H_2O$ 1.36 $Fe^{3+} + e^- \rightleftharpoons Fe^{2+}$ ... | {
"Header 1": "Standard Reduction Potentials<sup>a</sup>—continued",
"token_count": 11369,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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J.; Parsons, R.; Jordon, J., eds. Standard Potentials in Aqueous Solutions. Dekker: New York, 1985; Milazzo, G.; Caroli, S.; Sharma, V. K. Tables of Standard Electrode Potentials. Wiley: London, 1978; Swift, E. H.; Butler, E. A. Quantitative Measurements and Chemical Equilibria. Freeman: New York, 1972.
a Solids, gas... | {
"Header 1": "Standard Reduction Potentials<sup>a</sup>—continued",
"token_count": 296,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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| Element | E <sub>1/2</sub><br>(volts vs. SCE) | Matrix |
|----------------------------------------------|-------------------------------------|-------------------------------------------------------------|
| $Al^{3+} + 3e^- \rig... | {
"Header 1": "Selected Polarographic Half-Wave Potentials<sup>a</sup>",
"token_count": 1043,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Balancing a redox reaction is often more challenging than balancing other types of reactions, because we must balance both electrons and elements. Perhaps the simplest way to balance a redox reaction is by the half-reaction method, which consists of the following steps.
- 1. Identify the oxidizing and reducing agents... | {
"Header 1": "Balancing Redox Reactions",
"token_count": 266,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Balance the following redox reactions.
(a)
$$\operatorname{Cr}_2\operatorname{O}_7^{2-}(aq) + \operatorname{Zn}(s) \rightleftharpoons \operatorname{Cr}^{3+}(aq) + \operatorname{Zn}^{2+}(aq)$$
(acidic solution)
(b)
$$MnO_4^-(aq) + S^{2-}(aq) \rightleftharpoons MnO_2(s) + S(s)$$
(basic solution)
#### *SOLUTION*
W... | {
"Header 1": "**EXAMPLE A4.1**",
"token_count": 873,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
reaction's equilibrium position defines the extent to which the reaction can occur. For example, we expect a reaction with a large equilibrium constant, such as the dissociation of HCl in water
$$HCl(aq) + H_2O(\ell) \rightleftharpoons H_3O^+(aq) + Cl^-(aq)$$
to proceed nearly to completion. The magnitude of an equ... | {
"Header 1": "Review of Chemical Kinetics",
"token_count": 231,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A study of the kinetics of a chemical reaction begins with the measurement of its reaction rate. Consider, for example, the general reaction shown in the following equation, involving the aqueous solutes A, B, C, and D, with stoichiometries of *a*, *b*, *c*, and *d*.
$$aA + bB \rightleftharpoons cC + dD$$
A5.1
The ... | {
"Header 1": "A5.1 Chemical Reaction Rates",
"token_count": 647,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In this section we review the application of kinetics to several simple chemical reactions, focusing on how the integrated form of the rate law can be used to determine reaction orders. In addition, we consider how rate laws for more complex systems can be determined.
**First-Order Reactions** The simplest case is a ... | {
"Header 1": "A5.3 Kinetic Analysis of Selected Reactions",
"token_count": 857,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The following data were obtained during a kinetic study of the hydration of *p*-methoxyphenylacetylene by measuring the relative amounts of reactants and products by nuclear magnetic resonance (NMR).1
| Time<br>(min) | p-Methoxyphenylacetylene<br>(%) |
|---------------|---------------------------------|
| 67 ... | {
"Header 1": "**EXAMPLE A5.1**",
"token_count": 776,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The following data were collected during a kinetic study of the iodination of acetone by measuring the concentration of unreacted I2 in solution.2
| Experiment<br>Number | [C3H6O]<br>(M) | [H+]<br>(M) | [I2]<br>(M) | Rate<br>(M s–1) |
|----------------------|----------------|-------------|-------------|--------------... | {
"Header 1": "**EXAMPLE A5.2**",
"token_count": 731,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
solution to the problem of separating solutes with similar distribution ratios was introduced by Craig in the 1940s. The technique, which is known as a countercurrent liquid–liquid extraction, is outlined in Figure A6.1 and discussed in detail in this appendix. In contrast to a simple liquid–liquid extraction, in which... | {
"Header 1": "**Countercurrent Separations**",
"token_count": 1978,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Since the volumes of the lower and upper phases are equal, we get
$$q_{\rm A} = \frac{1}{D_{\rm A} + 1} = \frac{1}{5 + 1} = 0.167$$
and
$$q_{\rm B} = \frac{1}{D_{\rm B} + 1} = \frac{1}{0.5 + 1} = 0.667$$
Thus, $p_A$ is 0.833 and $p_B$ is 0.333. For solute A, the fraction present in tubes 5, 10, 15, 20, 25, ... | {
"Header 1": "**Countercurrent Separations**",
"token_count": 2001,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **1.** (a) 3; (b) 3; (c) 5; (d) 3; (e) 4; (f) 3
- **2.** (a) 0.894; (b) 0.893; (c) 0.894; (d) 0.900; (e) 0.0891
- **3.** (a) 12.01 g/mol; (b) 16.0 g/mol; (c) 6.022 × 1023 mol–1; (d) 9.65 × 104 C/mol
- **4.** (a) 71.9; (b) 39.8; (c) 6.1 × 103; (d) 55; (e) 2.57 × 10–2; (f) –4.185; (g) 7.2 × 10–8; (h) 5.30 × 10–13
- **5... | {
"Header 1": "**Chapter 2**",
"token_count": 829,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **2.** (a) 5 ng
- **3.** (a) 1.6 ppm–1; (b) 0.55 ppm–1; (c) 0.35; (d) analyte; (e) *C*I/*C*<sup>A</sup> < 0.029
- **4.** 2.01 ppm
- **5.** –1.0
- **6.** With ascorbic acid, *K*A,I = 30; with methionine, *K*A,I = –2.7 × 10–3
- **7.** (a) 4.4; (b) ascorbic acid; (c) 4.4 × 10–3 M
- **8.** (a) 66.5 A/M; (b) –7.9 × 10–3; ... | {
"Header 1": "**Chapter 3**",
"token_count": 2022,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Because t(0.05, 3) is 3.18, there is no evidence for a significant difference between the values.
- **16.** $\mu$ A = 2.61 $\mu$ A + (14.43 $\mu$ A ppm<sup>-1</sup>) × (ppm Tl added)
- 1. (a) $K = \frac{[NH_4^+][Cl^-]}{[NH_3][HCl]} = 1.75 \times 10^9$
- (c) $K = \frac{[Cd(CN)_4^{2-}][Y^{4-}]}{[CdY^{2-}][CN^{-}]^... | {
"Header 1": "**Chapter 3**",
"token_count": 2018,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
three extractions
- **29.** pH > 10.1
- **30.** (a) 4.8% of HA extracted, 99.6% of HB extracted; (b) aqueous; (c) $R_{\rm HA} = 95.2\%$ , $R_{\rm HB} = 0.4\%$ ; (d) $4.2 \times 10^{-3}$ ; (e) -2.81%
- **31.** (a) lower concentrations of $I^-$ increase extraction efficiency; (b) $D = K_D/(1 + K_f[I^-]_{aq})$
- **3... | {
"Header 1": "**Chapter 3**",
"token_count": 1256,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Average Depth (cm) | % w/w<br>Organic Matter |
|-----|--------------------|-------------------------|
| | 1 | 14.0 |
| | 3 | 16.8 |
| | 5 | 34.0 |
| | 7 | 26.9 ... | {
"Header 1": "**Chapter 3**",
"token_count": 1929,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Concentration<br>(M) | Absorbance<br>(a) | Absorbance<br>(b) | Absorbance<br>(c) |
|----|----------------------|-------------------|-------------------|-------------------|
| | 1.0 × 10–5 | 0.020 | 0.009 | 0.014 |
| | 3.0 × 10–5 | 0.060 | 0.035... | {
"Header 1": "**Chapter 3**",
"token_count": 2019,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
(a) -0.059 V; (b) -0.512 V; (c) 2.10 V
- **3.** 0.211 M I<sup>-</sup>
- **4.** $Zn(s) + 2H^{+}(aq) \rightleftharpoons Zn^{2+}(aq) + H_{2}(g)$
- 5. $7.11 \times 10^{-3}$ ; $1.3 \times 10^{-5}$ M benzoate
- the membrane responds only to the protonated form of cocaine
- **9.** (a) $2 \times 10^{-3}$ M to $1 \times ... | {
"Header 1": "**Chapter 3**",
"token_count": 1959,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
(b) 0.83 M HCO<sub>3</sub><sup>-</sup>, 0.25 mM Cl<sup>-</sup>, 0.0030 mM NO<sub>2</sub><sup>-</sup>, 0.12 mM NO<sub>3</sub><sup>-</sup>, 0.32 mM Ca<sup>2+</sup>, 0.11 mM Mg<sup>2+</sup>, 0.19 mM SO<sub>4</sub><sup>2-</sup>; (c) 0.77 M HCO<sub>3</sub><sup>-</sup>; (d) 1.00
- **28.** 74.5 ppm Cl<sup>-</sup>, 3.39 ppm NO... | {
"Header 1": "**Chapter 3**",
"token_count": 1325,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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(a) 2.52%; (b) 68 samples/h; (c) 94.8% w/w cocaine
- **28.** $6.27 \times 10^{-4} \text{ M H}_2\text{SO}_4$
- **3.** *R* = 4.00 + 1.20*B*\* + 0.72*A\*B\*, R* = 4.00 0.40*A* + 0.08*AB*
- **4.** (a) *R* = 52.610 + 23.755Ca\* 15.875Al\* 6.200Ca\*Al\*; (b) 16.9 ppm Al
- **5.** (a) *R* = 38.1 3.6*X*\* + 0.1*Y*\* + 8.1*Z*... | {
"Header 1": "**Chapter 3**",
"token_count": 1122,
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- **absorbance** the attenuation of photons as they pass through a sample (*A*). (*p. 373*)
- **absorbance spectrum** a graph of a sample's absorbance of electromagnetic radiation versus wavelength (or frequency or wavenumber). (*p. 373*)
- **accuracy** a measure of the agreement between an experimental result and its ... | {
"Header 1": "**A**",
"token_count": 888,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **background correction** in atomic absorption spectroscopy, the correction of the net absorbance from that due to the sample matrix. (*p. 419*)
- **back titration** a titration in which a reagent is added to a solution containing the analyte, and the excess reagent remaining after its reaction with the analyte is de... | {
"Header 1": "**B**",
"token_count": 520,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **calibration** the process of ensuring that the signal measured by a piece of equipment or an instrument is correct. (*p. 47*)
- **calibration curve** the result of a standardization showing graphically how a method's signal changes with respect to the amount of analyte. (*p. 47*)
- **capacity factor** a measure of ... | {
"Header 1": "**C**",
"token_count": 1360,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **dark current** the background current present in a photon detector in the absence of radiation from the source. (*p. 379*)
- **degrees of freedom** the number of independent values on which a result is based (ν). (*p. 80*)
- **desiccant** a drying agent. (*p. 29*)
- **desiccator** a closed container containing a de... | {
"Header 1": "**D**",
"token_count": 604,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **effective bandwidth** the width of the band of radiation passing through a wavelength selector measured at half the band's height. (*p. 376*)
- **electrical double layer** the interface between a positively or negatively charged electrode and the negatively or positively charged layer of solution in contact with th... | {
"Header 1": "**E**",
"token_count": 1115,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **factor** a property of a system that is experimentally varied and that may affect the response. (*p. 667*)
- **factor level** a factor's value. (*p. 667*)
- **faradaic current** any current in an electrochemical cell due to an oxidation or reduction reaction. (*p. 510*)
- **Faraday's law** the current or charge pas... | {
"Header 1": "**F**",
"token_count": 680,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **galvanostat** a device used to control the current in an electrochemical cell. (*p. 464*)
- **gamma ray** high-energy radiation emitted by nuclei (γ). (*p. 642*) **gas chromatography** a chromatographic technique in which the mobile phase is a gas. (*p. 563*)
- **gas–liquid chromatography** a chromatographic techni... | {
"Header 1": "**G**",
"token_count": 520,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**half-life** the time required for half of the initial number of a radioactive isotope's atoms to disintegrate (*t*1/2). (*p. 643*)
- **hanging mercury drop electrode** an electrode in which a drop of Hg is suspended from a capillary tube. (*p. 509*)
- **headspace sampling** the sampling of the vapor phase overlying... | {
"Header 1": "**H**",
"token_count": 337,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **inclusion** a coprecipitated impurity in which the interfering ion occupies a lattice site in the precipitate. (*p. 238*)
- **inclusion limit** in size-exclusion chromatography, the smallest solute that can be separated from other solutes; all smaller solutes elute together. (*p. 593*)
- **indeterminate error** any... | {
"Header 1": "**I**",
"token_count": 677,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **laboratory sample** sample taken into the lab for analysis after processing the gross sample. (*p. 199*)
- **ladder diagram** a visual tool for evaluating systems at equilibrium. (*p. 150*)
- **Le Châtelier's principle** when stressed, a system that was at equilibrium returns to its equilibrium state by reacting in... | {
"Header 1": "**L**",
"token_count": 567,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **manifold** the complete system of tubing for merging together samples and reagents in a flow injection analysis. (*p. 652*)
- **masking** a pseudo-separation method in which a species is prevented from participating in a chemical reaction by binding it with a masking agent in an unreactive complex. (*p. 207*)
- **m... | {
"Header 1": "**M**",
"token_count": 1477,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **occlusion** a coprecipitated impurity trapped within a precipitate as it forms. (*p. 239*)
- **Ohm's law** the statement that the current moving through a circuit is proportional to the applied potential and inversely proportional to the circuit's resistance (*E* = *iR*). (*p. 463*)
- **on-column injection** the di... | {
"Header 1": "**O**",
"token_count": 275,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **packed column** a wide-bore column containing a particulate packing material. (*p. 564*)
- **paired data** two sets of data consisting of results obtained using several samples drawn from different sources. (*p. 88*)
- **paired** *t***-test** statistical test for comparing paired data to determine if their differen... | {
"Header 1": "**P**",
"token_count": 1314,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **qualitative analysis** an analysis in which we determine the identity of the constituent species in a sample. (*p. 8*)
- **quality assessment** the steps taken to evaluate whether an analysis is under statistical control. (*p. 708*)
- **quality assurance** the steps taken during an analysis to ensure that the analy... | {
"Header 1": "**Q**",
"token_count": 279,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **random sample** a sample collected at random from the target population. (*p. 183*)
- **range** the numerical difference between the largest and smallest values in a data set (*w*). (*p. 56*)
- **rate** the change in a property's value per unit change in time; the rate of a reaction is a change in concentration per... | {
"Header 1": "**R**",
"token_count": 936,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **salt bridge** a connection between two solutions that allows the movement of current in the form of ionic charge. (*p. 466*)
- **sample** those members of a population that we actually collect and analyze. (*p. 71*)
- **sampling error** an error introduced during the process of collecting a sample for analysis. (*p... | {
"Header 1": "**S**",
"token_count": 2097,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **tailing** a tail at the end of a chromatographic peak, usually due to the presence of highly active sites in the stationary phase. (*p. 555*)
- **technique** a chemical or physical principle that can be used to analyze a sample. (*p. 36*)
- **temperature programming** the process of changing the column's temperatur... | {
"Header 1": "**T**",
"token_count": 920,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **validation** the process of verifying that a procedure yields acceptable results. (*p.* 47)
- **van Deemter equation** an equation showing the effect of the mobile phase's flow rate on the height of a theoretical plate. (*p*. 561)
- **variance** the square of the standard deviation ( $s^2$ ). (p. 57) **vibrational ... | {
"Header 1": "٧",
"token_count": 357,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Absorbance, 384–385, 373 concentration and, 385–386, 385*f* and end point in complexation titration, 324, 324*f* spectrum, 373, 373*f* Absorption of electromagnetic radiation, 380–384 filters, 376 of infrared *versus* UV/visible radiation, 381, 381*f* lines for copper, 416, 418*t* for sodium, 384, 384*f* of photons, en... | {
"Header 1": "**A**",
"token_count": 1622,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Analysis, 36. See also specific types of analysis | Analytical perspective, 5–8, 6f | Atomic emission spectroscopy, 373t, 434–441 |
|---------------------------------------------------|--------------------------------------------------|-------------------------------------------------------... | {
"Header 1": "**A**",
"Header 3": "**782** Index",
"token_count": 1725,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
See Data | instrumentation in, 412–415 | single-arm mechanical, 25, 26f |
| Analytical method(s) | precision in, 422 | Band broadening, 553 |
| accuracy in, 38... | {
"Header 1": "**A**",
"Header 3": "**782** Index",
"token_count": 1258,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
See Capillary gel electrophoresis (CGE) |
| Beryllium, standard reduction potentials | Calmagite, 323t | Characteristic concentrations, 416 |
| for, 743t | Calomel electrodes, saturated, 472, 473f | for copper, 416, 41... | {
"Header 1": "**A**",
"Header 3": "**782** Index",
"token_count": 1814,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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for, 734*t*
| sensitivity in, 640 | Chromium | titrants in, selection and standardization of, 327 |
|--------------------------------------------------------------------|----... | {
"Header 1": "**A**",
"Header 3": "**784** Index",
"token_count": 1750,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
See Size-exclusion | Complexation reactions, 144–145 | and background correction, 419 |
| chromatography | effect on solubility, 165–167 ... | {
"Header 1": "**A**",
"Header 3": "**784** Index",
"token_count": 1928,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
See Normal distribution |
| evaluation of, 507–508 | Desiccant, 29 | of measurements and results, 70–82 |
| precis... | {
"Header 1": "**A**",
"Header 3": "**784** Index",
"token_count": 1327,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| ladder diagram for, 315, 315f | Electrolysis time, in controlled-potential | by monitoring pH, 290–293, 291f–292f |
|-----------------------------------------------|--------------------------------------------------|----------------------------------------------|
| metal-EDTA formation c... | {
"Header 1": "**A**",
"Header 3": "**786** Index",
"token_count": 1742,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
See also Atomic | regression, 122–124, 124f |
| metallic, 473–475 | emission entries | van Deemter, 561 |
| ion-selective, 322, 475 | gamma-ray, 645, 645f ... | {
"Header 1": "**A**",
"Header 3": "**786** Index",
"token_count": 2002,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
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