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Describe how you would perform this analysis using external standards and how you would perform this analysis using the method of standard additions.
- 16. Explain why each of the following decreases the analysis time in controlled-potential coulometry: a larger surface area for the working electrode; a smaller volum... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
Analysis of this solution gives peak currents of 12.3 $\mu A$ and of 20.2 $\mu A$ for Zn<sup>2+</sup> and Tl<sup>+</sup>, respectively. Report the %w/w Tl in the alloy.
- 26. Differential pulse voltammetry at a carbon working electrode is used to determine the concentrations of ascorbic acid and caffeine in drug fo... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
| treatment | groups removed<br>by treatment | groups<br>contributing to<br>ASV-labile metals | groups<br>contributing to<br>total metals |
|-----------|--------------------------------|------------------------------------------------|-------------------------------------------|
| 1 | none ... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
In 1977, when I was an undergraduate student at Knox College, my lab partner and I completed an experiment to study the voltammetric behavior of Cd<sup>2+</sup> (in 0.1 M KNO<sub>3</sub>) and Ni<sup>2+</sup> (in 0.2 M KNO<sub>3</sub>) at a dropping mercury electrode. The data in this problem are from my lab notebook. A... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
To find the activity of $I^-$ that gives a potential equivalent to a $NO_2^-$ activity of $2.75\times 10^{-4}$ , we note that
$$a_{NO_{2}} = K_{AI} \times a_{I}$$
Making appropriate substitutions
$$2.75 \times 10^{-4} = (6.3 \times 10^{-2}) \times a_{17}$$
and solving for $a_{T}$ gives its activity as $... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
$$-0.280 = -\frac{0.05916}{2} \log \beta_{P} - \frac{0.05916p}{2} \log(0.115)$$
$$-0.308 = -\frac{0.05916}{2} \log \beta_{P} - \frac{0.05916p}{2} \log(0.231)$$
To solve for the value of p, we first subtract the second equation from the first equation
$$0.028 = -\frac{0.05916p}{2}\log(0.115) - \left\{-\frac{0.05... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
- 12A [Overview of Analytical Separations](#page-771-1)
- 12B [General Theory of Column Chromatography](#page-776-1)
- 12C [Optimizing Chromatographic Separations](#page-785-1)
- 12D [Gas Chromatography](#page-793-1)
- 12E [High-Performance Liquid Chromatography](#page-813-1)
- 12F [Other Forms of Liquid Chromatography... | {
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A component whose distribution ratio favors the stationary phase requires more time to pass through the system. Given sufficient time and sufficient stationary and mobile phase, we can separate solutes even if they have similar distribution ratios.
There are many ways in which we can identify a chromatographic separa... | {
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A chromatographic peak's baseline width, *w*, as shown in Figure 12.9, is determined by extending tangent lines from the inflection points on either side of the peak through the baseline. Although usually we report *t*r and *w* using units of time, we can report them using units of volume by multiplying each by the mob... | {
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Because we may not know the exact volumes of the stationary phase and the mobile phase, we simplify equation 12.4 by dividing both the numerator and the denominator by $V_{\rm m}$ ; thus
$$f_{\rm m} = \frac{V_{\rm m}/V_{\rm m}}{DV_{\rm s}/V_{\rm m} + V_{\rm m}/V_{\rm m}} = \frac{1}{DV_{\rm s}/V_{\rm m} + 1} = \frac{... | {
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$$N = 16 \frac{t_{\rm r}^2}{w^2} = 16 \left(\frac{t_{\rm r}}{w}\right)^2$$
12.15
#### Example 12.4
A chromatographic analysis for the chlorinated pesticide Dieldrin gives a peak with a retention time of 8.68 min and a baseline width of 0.29 min. Calculate the number of theoretical plates? Given that the column is... | {
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$$R_{AB} = \frac{\sqrt{N_B}}{4} \times \frac{t_{r,B} - t_{r,A}}{t_{r,B}}$$
12.18
Rearranging <u>equation 12.8</u> provides us with the following equations for the retention times of solutes *A* and *B*.
$$t_{\text{r,A}} = k_{\text{A}}t_{\text{m}} + t_{\text{m}}$$
and $t_{\text{r,B}} = k_{\text{B}}t_{\text{m}} + ... | {
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The intersections of the curves in Figure 12.17a show pH values where two solutes co-elute. For example, at a pH of 3.8 terephthalic acid and *p*-hydroxybenzoic acid elute as a single chromatographic peak.
Figure 12.17a shows that there are many pH values where some separation is possible. To find the optimum separat... | {
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**Figure 12.18** The effect of multiple paths on a solute's band broadening. The solute's initial band profile is rectangular. As this band travels through the column, individual solute molecules travel different paths, three of which are shown by the meandering colored paths (the actua... | {
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#### **12D Gas Chromatography**
In gas chromatography (GC) we inject the sample, which may be a gas or a liquid, into an gaseous mobile phase (often called the carrier gas). The mobile phase carries the sample through a packed or a capillary column that separates the sample's components based on their ability to pa... | {
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A capillary, or open tubular column is constructed from fused silica and is coated with a protective polymer coating. Columns range from 15–100 m in length with an internal diameter of approximately 150–300 µm. Figure 12.24 shows an example of a typical capillary column.
Capillary columns are of three principal types... | {
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An attractive approach to isolating analytes is a solid-phase microextraction (SPME). In one approach, which is illustrated in Figure 12.27, a fused-silica fiber is placed inside a syringe needle. The fiber, which is coated with a thin film of an adsorbent material, such as polydimethyl siloxane, is lowered into the ... | {
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In a splitless injection, which is useful for trace analysis, we close the split vent and allow all the carrier gas that passes through the glass liner to enter the column—this allows virtually all the sample to enters the column. Because the flow rate through the injector is low, significant precolumn band broadenin... | {
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We can achieve some degree of selectivity by monitoring one or more specific mass-to-charge ratios, a process called selective-ion monitoring. A mass spectrometer provides excellent detection limits, typically 25 fg to 100 pg, with a linear range of 10<sup>5</sup> orders of magnitude. Because we continuously record the... | {
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The 95% confidence interval is
$$\mu = \overline{X} \pm \frac{ts}{\sqrt{n}} = 1.5779 \pm \frac{(2.78)(0.0080)}{\sqrt{5}} = 1.5779 \pm 0.0099$$
Although there is a substantial variation in the individual peak areas for this set of replicate injections, the internal standard compensates for these variations, providin... | {
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Using an appropriate volumetric flask, prepare the standards by injecting at least 10 $\mu L$ of the working standard below the surface of the water and dilute to volume. Gently mix each standard three times only. Discard the solution in the neck of the volumetric flask and then transfer the remaining solution to a 4... | {
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Packed columns typically cost <\$200, and the cost of a capillary column is typically \$300–\$1000.
#### **12E High-Performance Liquid Chromatography**
In high-performance liquid chromatography (HPLC) we inject the sample, which is in solution form, into a liquid mobile phase. The mobile phase carries the sample th... | {
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For a normalphase separation, a solute of lower polarity spends proportionally less time in the polar stationary phase and elutes before a solute that is more polar. Given a particular stationary phase, retention times in normal-phase HPLC are controlled by adjusting the mobile phase's properties. For example, if the r... | {
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Four additional mobile Acid–base chemistry is not the only example of a secondary equilibrium reaction. Other examples include ion-pairing, complexation, and the interaction of solutes with micelles. We will consider the last of these in Section 12G.3 when we discuss micellar electrokinetic capillary chromatography.
... | {
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The working pump and the equilibrating pump each have a piston whose back and forth movement maintains a constant flow rate of up to several mL/min and provides the high output pressure needed to push the mobile phase through the chromatographic column. In this particular instrument, each pump sends its mobile phase
... | {
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A detector counts the ions and displays the mass spectrum.
There are several options for monitoring the chromatogram when using a mass spectrometer as the detector. The most common method is to continuously scan the entire mass spectrum and report the total signal for all ions reaching the detector during each scan. ... | {
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Second, some of the compounds in the serum may absorb too strongly to the stationary phase, degrading the column's performance. Finally, although an HPLC can separate and analyze complex mixtures, an analysis is difficult if the number of constituents exceeds the column's peak capacity.
- 2. One advantage of an HPLC an... | {
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The ion-exchange reaction of a monovalent cation, M<sup>+</sup>, at a strong acid exchange site is
$$-SO_3^-H^+(s) + M^+(aq) \Rightarrow -SO_3^-M^+(s) + H^+(aq)$$
The equilibrium constant for this ion-exchange reaction, which we call the selectivity coefficient, *K*, is
$$K = \frac{\{-SO_{3}^{-}M^{+}\}[H^{+}]}{... | {
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A stationary phase's size selectivity extends over a finite range. All solutes significantly smaller than the pores move through the column's entire volume and elute simultaneously, with a retention volume, *V*<sup>r</sup> , of
$$V_{\rm r} = V_{\rm i} + V_{\rm o}$$
12.31
where *V*<sup>i</sup> is the volume of mob... | {
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| Table 12.9 Critical Points for Selected Supercritical Fluids | | | | | |
|--------------------------------------------------------------|---------------------------|-------------------------|--|--|--|
| compound ... | {
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Below a pH of 2 there are few silanate ions and the zeta potential and the electroosmotic flow velocity approach zero. As the pH increases, both the zeta potential and the electroosmotic flow velocity increase. Second, the zeta potential is directly proportional to the thickness of the double layer. Increasing the buff... | {
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The inner diameter is typically 25–75 µm, which is smaller than the internal diameter of a capillary GC column, with an outer diameter of 200–375 µm.
The capillary column's narrow opening and the thickness of its walls are important. When an electric field is applied to the buffer solution, current flows through the ... | {
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Migration in electrophoresis occurs in response to an applied electric field. The ability to apply a large electric field is important because higher voltages lead to shorter analysis times [\(equation 12.42](#page-840-2)), more efficient separations [\(equation 12.43](#page-841-0)), and better resolution [\(equation... | {
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Micellar electrokinetic chromatography is used to separate a wide variety of samples, including mixtures of pharmaceutical compounds, vitamins, and explosives.
#### CAPILLARY GEL ELECTROPHORESIS (CGE)
In CAPILLARY GEL ELECTROPHORESIS the capillary tubing is filled with a polymeric gel. Because the gel is porous, a ... | {
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Capillary electrophoretic columns contain substantially more theoretical plates ( $\approx \! 10^6$ plates/m) than that found in HPLC ( $\approx \! 10^5$ plates/m) and capillary GC columns ( $\approx \! 10^3$ plates/m), providing unparalleled resolution and peak capacity. Separations in capillary electrophoresis are... | {
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<sup>16</sup> Evaluating plate height as a function of flow rate gave a van Deemter equation for which *A* is 1.65 mm, *B* is 25.8 mm•mL min<sup>-1</sup>, and *C* is 0.0236 mm•min mL<sup>-1</sup>.
- (a) Prepare a graph of H versus u for flow rates between 5-120 mL/min.
- (b) For what range of flow rates does each term ... | {
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The amount of camphor in an analgesic ointment is determined by GC using the method of internal standards.21 A standard sample is prepared by placing 45.2 mg of camphor and 2.00 mL of a 6.00 mg/mL internal standard solution of terpene hydrate in a 25-mL volumetric flask and diluting to volume with CCl4. When an approxi... | {
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- (a) Explain the change in each compound's retention time.
- (b) Prepare a single graph that shows retention time versus pH for each compound. Using your plot, identify a pH level that will yield an acceptable separation.
- 22. The composition of a multivitamin tablet is determined using an HPLC with a diode array U... | {
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| ion | $HCO_3^-$ | Cl <sup>-</sup> | $NO_2^-$ | $NO_3^-$ |
|-----------|-----------|--------------------|-------------|----------|
| peak area | 310.0 | 403.1 | 3.97 | 157.6 |
| ion | $Ca^{2+}$ | $\mathrm{Mg}^{2+}$ | $SO_4^{2-}$ | |
| peak area | 734.3 | 193.... | {
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| alkylpyridine | $\mu_{ep} (\text{cm}^2 \text{V}^{-1} \text{s}^{-1})$ |
|------------------|---------------------------------------------------------|
| 2-methylpyridine | $3.581 \times 10^{-4}$ |
| 2-ethylpyridine | $3.222 \times 10^{-4}$ |
| ... | {
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Using equation 12.27, we have
The data for this exercise were created so that the actual number of theoretical plates is 400 for solute 1 and 264 for solute 2. Given the resolution of my ruler's scale, my answer is pretty reasonable. Your measurements may be slightly different, but your answers should be close to the... | {
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- 13A [Kinetic Techniques versus Equilibrium Techniques](#page-871-1)
- 13B [Chemical Kinetics](#page-872-1)
- 13C [Radiochemistry](#page-896-1)
- 13D [Flow Injection Analysis](#page-904-1)
- 13E [Key Terms](#page-917-1)
- 13F [Chapter Summary](#page-917-2)
- 13G [Problems](#page-918-1)
- 13H [Solutions to Practice Exe... | {
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Step 1
$$H_2NO_3S$$
$NH_2 + NO_2^- + 2H^+$
$H_2NO_3S$
$NH_2 + NO_2^- + 2H^+$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3S$
$H_2NO_3... | {
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By the 1980s, improvements in instrumentation and data analysis methods compensated for these limitations, ensuring the further development of chemical kinetic methods of analysis.3
#### **13B.1 Theory and Practice**
Every chemical reaction occurs at a finite rate, which makes it a potential candidate for a chemica... | {
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1972, 44(12), 26A–41A.
<sup>6</sup> Javier, A. C.; Crouch, S. R.; Malmstadt, H. V. Anal. Chem. 1969, 41, 239-243.
**Figure 13.2** Classification of chemical kinetic methods of analysis adapted from Pardue, H. L. "Kinetic Aspects of Analytical Chemistry," *Anal. Chim. Acta* **1989**, *... | {
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$$[A]_0 = \frac{[P]_t}{1 - e^{-k't}} = \frac{0.0420 \text{ M}}{1 - e^{-(0.0726 \text{ s}^{-1})(10.0 \text{ s})}} = 0.0868 \text{ M}$$
A one-point fixed-time integral method has the advantage of simplicity because we need only a single measurement to determine the analyte's initial concentration. As with any method ... | {
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#### **Direct-Computation Rate Methods**
In a rate method we use the differential form of the rate law—[equation](#page-873-2) [13.1](#page-873-2) is one example of a differential rate law—to determine the analyte's concentration. As shown in Figure 13.4, the rate of a reaction at time *t*, (*rate*)*<sup>t</sup>* ... | {
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Because the concentration of creatinine in urine and serum is an important indication of renal function, a rapid method for its analysis is clinically important. In this method the rate of reaction between creatinine and picrate in an alkaline medium is used to determine the con-
**Fig... | {
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This presents us with a problem and an advantage. The problem is that rapidly and reproducibly mixing the sample and the reagent requires a dedicated instrument, which adds an additional expense to the analysis. The advantage is that a rapid, automated analysis allows for a high throughput of samples. Instruments for t... | {
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For example the reduction of $H_2O_2$ by $I^-$
$$2I^{-}(aq) + H_2O_2(aq) + 2H_3O^{+}(aq) \longrightarrow 4H_2O(l) + I_2(aq)$$
concentration of substrate
**Figure 13.10** Plot of equation 13.25 showing limits for the analysis of substrates and enzymes in an enzyme-catalyzed chemi... | {
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L.; Vandeginste, B. G. M.; Buydens, L. M. C. De Jong, S.; Lewi, P. J.; Smeyers-Verbeke, J. "Nonlinear Regression," which is Chapter 11 in Handbook of Chemometrics and Qualimetrics: Part A, Elsevier: Amsterdam, 1997, for additional details. The simplex algorithm described in Chapter 14 of this text also can be used to f... | {
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#### **Accuracy**
As noted earlier, a chemical kinetic method potentially is subject to larger errors than an equilibrium method due to the effect of uncontrolled or poorly controlled variables, such as temperature or pH. Although a directcomputation chemical kinetic method can achieve moderately accurate results (... | {
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#### SOLUTION
Extrapolating the linear part of the curve back to t = 0 gives $\ln[B]_0$ as -2.3, or a $[B]_0$ of 0.10 M. At t = 0, $\ln[C]_0$ is -1.2, which corresponds to a $[C]_0$ of 0.30 M. Because $[C]_0 = [A]_0 + [B]_0$ , the concentration of A in the original sample is 0.20 M.
#### TIME, COST, AND ... | {
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What is the molar concentration of $^{90}_{38}$ Sr in the sample? The half-life for $^{90}_{38}$ Sr is 28.1 yr.
#### SOLUTION
Solving equation 13.37 for $\lambda$ , substituting into equation 13.34, and solving for N gives
$$N = \frac{A \times t_{1/2}}{0.693}$$
Before we can determine the number of atoms of ... | {
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#### ISOTOPE DILUTION
Another important radiochemical method for the analysis of nonradioactive analytes is **ISOTOPE DILUTION**. An external source of analyte is prepared in a radioactive form with a known activity, $A_T$ , for its radioactive decay—we call this form of the analyte a **TRACER**. To prepare a samp... | {
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Another example is the dating of sediments collected from lakes by measuring the amount of $^{210}_{82}\text{Pb}$ that is present.
#### 13C.5 Evaluation
Radiochemical methods routinely are used for the analysis of trace analytes in macro and meso samples. The accuracy and precision of radiochemical methods genera... | {
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[Figure 13.22](#page-907-1) shows that if we inject a second sample at a time *T*′ after we inject the first sample, there is little overlap of the two FIA curves. By injecting samples at intervals of *T*′, we obtain the maximum possible sampling rate.
Peak heights and return times are influenced by the dispersion of... | {
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In the conventional method of analysis, COD is determined by refluxing the sample for 2 h in the presence of acid and a strong oxidizing agent, such as K2Cr2O7 or KMnO4. When refluxing is complete, the amount of oxidant consumed in the reaction is determined
**Figure 13.26** Two examples of a dualchannel manifold for... | {
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Acta* **1981**, *129*, 1–17.
| Table 13.3 | Selected Flow Injection Analysis Methods for Clinical Samples | | | |
|----------------------|---------------------------------------------------------------|-----------------------|---------... | {
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**Figure 13.30** Calibration curve and equation for the data in Example 13.13.
#### 13D.4 Evaluation
The majority of flow injection analysis applications are modifications of conventional titrimetric, spectrophotometric, and electrochemical methods of analysis; thus, it is appropriate to compare FIA methods to thes... | {
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The H2O2 produced by the oxidation of glucose reacts with I– , forming I2 as a product. The time required to produce a fixed amount of I2 is determined spectrophotometrically. The following data was reported for a set of calibration standards
| [glucose] (ppm) | | time (s) | |
|-----------------|-------|-... | {
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| time (min) | [C] (mM) |
|------------|----------|
| 1 | 0.313 |
| 6 | 0.200 |
| 11 | 0.136 |
| 16 | 0.098 |
| 21 | 0.074 |
| 26 | 0.058 |
| 31 | 0.047 |
| 36 | 0.038 |
| 41 | 0.032 |
| 46 | 0.027 |
| 51 ... | {
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A sample with an unknown concentration of HCl is analyzed five times, giving values of 7.43, 7.28, 7.41, 7.37, and 7.33 s for D*t*. Determine the concentration of HCl in the sample.
- 27. Milardovíc and colleagues used a flow injection analysis method with an amperometric biosensor to determine the concentration of... | {
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- 14A [Optimizing the Experimental Procedure](#page-929-0)
- 14B [Verifying the Method](#page-946-0)
- 14C [Validating the Method as a Standard Method](#page-950-0)
- 14D [Using Excel and R for an Analysis of Variance](#page-962-0)
- 14E [Key Terms](#page-965-0)
- 14F [Chapter Summary](#page-965-1)
- 14G [Problems](#pa... | {
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#### **Effectiveness and Efficiency**
A searching algorithm is characterized by its effectiveness and its efficiency. To be effective, a searching algorithm must find the response surface's global optimum, or at least reach a point near the global optimum. A searching algorithm may fail to find the global optimum f... | {
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$$R = 80 - 80 = 0$$
Figure 14.8 shows this **DEPENDENT** relationship between the two factors. Factors that are dependent are said to interact and the equation for the response surface' includes an interaction term that contains both factor A and factor B. The final term in equation 14.2, for example, accounts for ... | {
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Following Rule 1, we reject $v_1$ and replace it with a new vertex using equation 14.3 and equation 14.4; thus
$$a_{v_4} = 2 \times \frac{1.00 + 0.50}{2} - 0 = 1.50$$
$$b_{v_4} = 2 \times \frac{0 + 0.87}{2} - 0 = 0.87$$
The following table gives the vertices of the second simplex.
| vertex | а | b | res... | {
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A $2^2$ factorial design requires four experiments and a $2^3$ factorial design requires eight experiments.
**Figure 14.13** The relationship between the coded factor levels and the uncoded factor levels for Example 14.2. The numbers in red are the values defined in the $2^2$ fact... | {
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$$\beta_c \approx b_c = \frac{1}{n} \sum_{i=1}^n C_i R_i$$
14.12
$$\beta_{ac} \approx b_{ac} = \frac{1}{n} \sum_{i=1}^{n} A_i^* C_i R_i$$
14.13
$$\beta_{bc} \approx b_{bc} = \frac{1}{n} \sum_{i=1}^{n} B_i^* C_i^* R_i$$
14.14
$$\beta_{abc} \approx b_{abc} = \frac{1}{n} \sum_{i=1}^{n} A_{i}^{*} B_{i}^{*} C_{i}^{*... | {
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We can fit the 3<sup>1</sup> factorial design in Figure 14.15b to an empirical model that includes second-order factor effects.
$$R = \beta_0 + \beta_a A + \beta_{aa} A^2$$
In general, an n-level factorial design can model single-factor and interaction terms up to the (n-1)th order.
We can judge the effectiveness... | {
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This is not particularly surprising because a method typically is optimized by a single analyst using the same reagents, equipment, and instrumentation for each trial. Any variability introduced by different analysts, reagents, equipment, and instrumentation is not included in the single-operator characteristics. Other... | {
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For example, $E_A$ is
$$E_A = \frac{98.9 + 99.0 + 97.5 + 97.7}{4} - \frac{97.4 + 97.3 + 98.6 + 98.6}{4} = 0.30$$
Youden, W. J. "Statistical Techniques for Collaborative Tests," in *Statistical Manual of the Association of Official Analytical Chemists*, Association of Official Analytical Chemists: Washington, D. C... | {
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$$D_i = X_i - Y_i$$
To estimate the total contribution from random error we use the standard deviation of these differences, $s_D$ , for all analysts
$$s_D = \sqrt{\frac{\sum_{i=1}^{n} (D_i - \overline{D})^2}{2(n-1)}} = s_{\text{rand}} \approx \sigma_{\text{rand}}$$
14.18
**Figu... | {
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We include the $\sqrt{2}$ in the denominator because $s_T$ (see equation 14.20) underestimates the standard deviation when comparing $\overline{T}$ to $\mu_{\text{tot}}$ .
#### Example 14.7
The two samples analyzed in Example 14.6 are known to contain the following concentrations of cholesterol: $\mu_{\text... | {
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The variance of the individual mean values about the global mean, which we call the BETWEEN-SAMPLE VARIANCE, $s_b^2$ , is
$$s_b^2 = \frac{\sum_{i=1}^b n_i (\overline{X}_i - \overline{\overline{X}})^2}{h-1}$$
14.25
The between-sample variance includes contributions from both indeterminate errors and systematic erro... | {
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Our best estimate of the within sample variance is
$$\sigma_{rand}^2 \approx s_w^2 = 0.631$$
and our best estimate of the between sample variance is
$$\sigma_{\text{syst}}^2 \approx \frac{s_b^2 - s_w^2}{n} = \frac{34.76 - 0.631}{22/4} = 6.205$$
In this example the variance due to systematic differences between ... | {
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1997, 69, 789–790, (d) "The Amazing Horwitz Function," <a href="MMC Technical Brief 17">AMC Technical Brief 17</a>, July 2004; (e) Lingser, T. P. J. Trends Anal. Chem. 2006, 25, 1125
$$R = 2^{(1-0.5\log 0.001)} = 5.7\%$$
and we expect that approximately two-thirds of the analysts will report the analyte's concentra... | {
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In creating this object, I choose to list the results for analyst *A*, followed by the results for analyst *B*, *C*, and *D*.
The command **rep** (for repeat) has two variables: the item to repeat and the number of times it is repeated. The object analyst is the vector ("a","a","a","a","a","a", "b","b","b","b","b", "... | {
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Use a fixed-sized simplex searching algorithm to find the optimum response for the equation in Problem 1c. For the first simplex, set one vertex at (0,0) with step sizes of one. Compare your optimum response to the true optimum.
- 3. Show that [equation 14.3](#page-936-0) and [equation 14.4](#page-936-1) are correct.
-... | {
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7 –1 +1 +1 8 8 +1 +1 +1 12
- (c) Three runs at the center of the factorial design—a temperature of 150 <sup>o</sup> C, a pressure of 0.4 MPa, and a residence time of 15 min give percent yields of 8%, 9%, and 8.8%. Determine if a first-order empirical model is appropriate for this system at *a*=0.05.
- 9. Duarte and... | {
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The same model, however, may yield an inaccurate prediction for the response at other factor levels. For this reason, an empirical model, is tested before it is extrapolated to conditions other than those used in determining the model. For example, Palasota and Deming studied the effect of the relative amounts of H2SO4... | {
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| lab A | lab B | lab C | lab D | lab E | lab F | lab G |
|-------|-------|-------|-------|-------|-------|-------|
| 1.6 | 4.6 | 1.2 | 1.5 | 6.0 | 6.2 | 3.3 |
| 2.9 | 2.8 | 1.9 | 2.7 | 3.9 | 3.8 | 3.8 |
| 3.5 | 3.0 | 2.9 | 3.4 | 4.3 | 5.5 | 5.5 |
| 1.8 | 4.5 | 1.1 | 2.... | {
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- 15A [The Analytical Perspective—Revisited](#page-977-0)
- 15B [Quality Control](#page-978-0)
- 15C [Quality Assessment](#page-980-0)
- 15D [Evaluating Quality Assurance Data](#page-985-0)
- 15E [Key Terms](#page-995-0)
- 15F [Chapter Summary](#page-995-1)
- 15G [Problem](#page-996-0)s
- 15H [Solutions to Practice Exe... | {
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By identifying those samples, measurements, and results subject to gross systematic errors, inspection helps control the quality of an analysis.
Figure 7.7 in Chapter 7 shows an example of a bottom grab sampler.
The second additional consideration is the certification of an analyst's competence to perform the analy... | {
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A field blank helps identify systematic errors due to sampling, transport, and analysis. A trip blank is an analytefree sample carried from the laboratory to the sampling site and back to the laboratory without being opened. A trip blank helps to identify systematic errors due to cross-contamination of volatile organic... | {
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If the result for sample B is above the method's detection limit, or if it is within the range of 0.1 to 10 times the amount of analyte spiked into $B_{SF}$ , then a
spike recovery for *BSF* is determined. An unacceptable spike recovery for *BSF* indicates the presence of a systematic error that involves the sample.... | {
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| day: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| result: | 248.1 | 246.0 | 247.9 | 249.4 | 250.9 | 249.7 | 250.2 | 250.3 | 247.3 | 245.6 |
| day: | 11 | 12 | 13 | 14 ... | {
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For example, <u>Table 15.3</u> shows the
| Table 15.3<br>Average Range for the Concentration of Chromium<br>in Duplicate Water Samples | | | |
|---------------------------------------------------------------------------------------------|-------------------|------|--|
| ... | {
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Explain the rationale for each item on your list.
- 2. Write directives outlining good measurement practices for (a) a buret, for (b) a pH meter, and for (c) a spectrophotometer.
- 3. A atomic absorption method for the analysis of lead in an industrial wastewater has a method detection limit of 10 ppb. The relationship... | {
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| sample | $X_1$ (ppm) | $X_2$ (ppm) | sample | $X_1$ (ppm) | $X_2$ (ppm) |
|--------|-------------|-------------|--------|-------------|-------------|
| 3 | 22 | 19 | 16 | 16 | 20 |
| 4 | 17 | 20 | 17 | 18 | 21 |
| 5 | 32 ... | {
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Chapter 1: [Introduction to Analytical Chemistry](#page-1003-1)
Chapter 2: [Basic Tools of Analytical Chemistry](#page-1005-1)
Chapter 3: [The Vocabulary of Analytical Chemistry](#page-1006-1)
Chapter 4: [Evaluating Analytical Data](#page-1007-1)
Chapter 5: [Standardizing Analytical Methods](#page-1012-1)
Cha... | {
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"A Multiple of 12 for Avogadro," [arXiv:1201.5537 \[physics.gen-ph\]](http://arxiv.org/abs/1201.5537v3).
- Kemsley, J. "Rethinking the Mole and Kilogram," *C&E News*, August 25, 2014, p. 25.
The following are useful resources for maintaining a laboratory notebook and for preparing laboratory reports.
- Coghill, A. ... | {
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Educ.* **2005**, *82*, 1079–1081.
- Quintar, S. E.; Santagata, J. P.; Villegas, O. I.; Cortinez, V. A. "Detection of Method Effects on Quality of Analytical Data," *J. Chem. Educ.* **2003**, *80*, 326–329.
- Richardson, T. H. "Reproducible Bad Data for Instruction in Statistical Methods," *J. Chem. Educ.* **1991**, *68... | {
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"Header 3": "Resource Overview",
"token_count": 2056,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
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Chem. Educ.* **1993**, *70*, 838–841.
- Heydorn, K. "Detecting Errors in Micro and Trace Analysis by Using Statistics," *Anal. Chim. Acta* **1993**, *283*, 494–499.
- Hund, E.; Massart, D. L.; Smeyers-Verbeke, J. "Operational definitions of uncertainty," *Trends Anal. Chem.* **2001**, *20*, 394–406.
- Kragten, J. "Calc... | {
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"Header 3": "Resource Overview",
"token_count": 2029,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
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"Evaluation of analytical calibration based on least-squares linear regression for instrumental techniques: A tutorial review," *Trends Anal. Chem.* **2016**, *77*, 167–185.
- Renman, L., Jagner, D. "Asymmetric Distribution of Results in Calibration Curve and Standard Addition Evaluations," *Anal. Chim. Acta* **1997**,... | {
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"Header 3": "Resource Overview",
"token_count": 2053,
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An additional discussion on method blanks, including the use of the total Youden blank, is found in the following papers.
- Cardone, M. J. "Detection and Determination of Error in Analytical Methodology. Part II. Correction for Corrigible Systematic Error in the Course of Real Sample Analysis," *J. Assoc. Off. Anal... | {
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"Header 3": "Resource Overview",
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Educ. 1995, 72, 508–511.
Collected here are a papers that discuss a variety of approaches to solving equilibrium problems.
- Ault, A. "Do pH in Your Head," *J. Chem. Educ.* **1999**, *76*, 936–938.
- Chaston, S. "Calculating Complex Equilibrium Concentrations by a Next Guess Factor Method," *J. Chem. Educ.* **1993*... | {
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Educ.* **2000**, *77*, 1015–1016.
- Settle, F. A.; Pleva, M. "The Weakest Link Exercise," *Anal. Chem.* **1999**, *71*, 538A–540A.
- • Vitt, J. E.; Engstrom, R. C. "Effect of Sample Size on Sampling Error," *J. Chem. Educ.* **1999**, *76*, 99–100.
The following experiments describe homemade sampling devices for colle... | {
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J., eds.; American Chemical Society: Washington, D.C., 1997.
- Anderson, R. *Sample Pretreatment and Separation*, Wiley: Chichester, 1987.
- Bettiol, C.; Stievano, L.; Bertelle, M.; Delfino, F.; Argese, E. "Evaluation of microwave-assisted acid extraction procedures for the determination of metal content and potential ... | {
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"Header 3": "Resource Overview",
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"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
Chem. Educ.* **1990**, *67*, 67–68
- Graham. R.C.; DePew, S. "Determination of Ammonia in Household Cleaners," *J. Chem. Educ.* **1983**, *60*, 765–766.
- Kalbus, L. H.; Petrucci, R. H.; Forman, J. E.; Kalbus, G. E. "Titration of Chromate-Dichromate Mixtures," *J. Chem. Educ.* **1991**, *68*, 677–678.
- Kooser, A. S.; ... | {
"Header 1": "Additional Resources",
"Header 3": "Resource Overview",
"token_count": 2057,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
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