page_content stringlengths 12 2.63M | metadata unknown |
|---|---|
| alternative hypothesis<br>(p. 83) |
|---------------------------------------|
| binomial distribution<br>(p. 72) |
| central limit theorem<br>(p. 79) |
| confidence interval<br>(p. 75) |
| constant determinate error<br>(p. 60) |
| degrees of freedom<br>(p. 80) |
| detection limit<br>(p. 9... | {
"Header 1": "**4H KEY TERMS**",
"token_count": 580,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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limit of identification (*p. 95*)
The data we collect are characterized by their central tendency (where the values are clustered), and their spread (the variation of individual values around the central value). Central tendency is reported by stating the mean or median. The range, standard deviation, or variance may... | {
"Header 1": "**4I SUMMARY**",
"token_count": 391,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The following experiments may be used to introduce the statistical analysis of data in the analytical chemistry laboratory. Each experiment is annotated with a brief description of the data collected and the type of statistical analysis used in evaluating the data.
Cunningham, C. C.; B... | {
"Header 1": "**4I SUMMARY**",
"Header 3": "Suggested EXPERIMENTS",
"token_count": 960,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Continued from page 97
Spencer, R. D. "The Dependence of Strength in Plastics upon Polymer Chain Length and Chain Orientation," *J. Chem. Educ.* **1984**, *61*, 555–563.
The stretching properties of polymers are investigated by examining the effect of polymer orientation, polymer chain length, stretching rate, and ... | {
"Header 1": "**Experiments**",
"token_count": 1985,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Limiting yourself to glassware listed in Table 4.2, determine the proper combination of glassware to accomplish each dilution, and rank them in order of their most probable uncertainties.
- **12.** Explain why changing all values in a data set by a constant amount will change $\overline{X}$ but will have no effect on... | {
"Header 1": "**Experiments**",
"token_count": 1993,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Standard
method: 21.62 22.20 24.27 23.54 24.25 23.09 21.02 New method: 21.54 20.51 22.31 21.30 24.62 25.72 21.54
Using an appropriate statistical test, determine whether there is any significant difference between the standard and new methods at α = 0.05.
**24.** The accuracy of a spectrophotometer can be check... | {
"Header 1": "**Experiments**",
"token_count": 1788,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Following are the results, in parts per million.30
| Laboratory | Sample 1 | Sample 2 | Sample 3 |
|------------|----------|----------|----------|
| 1 | 22.6 | 13.6 | 16.0 |
| 2 | 23.0 | 14.2 | 15.9 |
| 3 | 21.5 | 13.9 | 16.3 |
| 4 | 21.9 | 1... | {
"Header 1": "**Experiments**",
"token_count": 1038,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A more comprehensive discussion of the analysis of data, covering all topics considered in this chapter as well as additional material, can be found in any textbook on statistics or data analysis; following are several such texts.
- Anderson, R. L. *Practical Statistics for Analytical Chemists.* Van Nostrand Reinhold... | {
"Header 1": "**4L SUGGESTED READINGS**",
"token_count": 970,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- 1. Goedhart, M. J.; Verdonk, A. H. *J. Chem. Educ.* **1991,** *68,* 1005–1009.
- 2. Rousseeuw, P. J. *J. Chemom.* **1991,** *5,* 1–20.
- 3. Ellison, S.; Wegscheider, W.; Williams, A. *Anal. Chem.* **1997,** *69,* 607A–613A.
- 4. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. *Experiments in Physical Chemistry,* 5th ... | {
"Header 1": "**4M REFERENCES**",
"token_count": 1670,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**I**n Chapter 3 we introduced a relationship between the measured signal, *S*meas, and the absolute amount of analyte
$$S_{\text{meas}} = kn_{\text{A}} + S_{\text{reag}}$$
5.1
or the relative amount of analyte in a sample
$$S_{\text{meas}} = kC_{\text{A}} + S_{\text{reag}}$$
5.2
where *n*<sup>A</sup> is the mo... | {
"Header 1": "Calibrations, Standardizations, and Blank Corrections",
"token_count": 246,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Signals are measured using equipment or instruments that must be properly calibrated if $S_{\rm meas}$ is to be free of determinate errors. Calibration is accomplished against a standard, adjusting $S_{\rm meas}$ until it agrees with the standard's known signal. Several common examples of calibration are discussed ... | {
"Header 1": "5A Calibrating Signals",
"token_count": 1156,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The American Chemical Society's Committee on Environmental Improvement defines standardization as the process of determining the relationship between the measured signal and the amount of analyte.<sup>3</sup> A method is considered standardized when the value of k in equation 5.1 or 5.2 is known.
In principle, it sho... | {
"Header 1": "5B Standardizing Methods",
"token_count": 223,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The accuracy of a standardization depends on the quality of the reagents and glass-ware used to prepare standards. For example, in an acid—base titration, the amount of analyte is related to the absolute amount of titrant used in the analysis by the stoichiometry of the chemical reaction between the analyte and the tit... | {
"Header 1": "**5B.** I Reagents Used as Standards",
"token_count": 1517,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Any standardization using a single standard containing a known amount of analyte.
**Figure 5.2**Example showing how an improper use of a single-point standardization can lead to a determinate error in the reported concentration of analyte.
<sup>\*</sup>The following discussion of sta... | {
"Header 1": "single-point standardization",
"token_count": 204,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The most commonly employed standardization method uses one or more **external standards** containing known concentrations of analyte. These standards are identified as external standards because they are prepared and analyzed separately from the samples.
A quantitative determination using a single external standard w... | {
"Header 1": "5B.3 External Standards",
"token_count": 2026,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Solving both equations for k and equating gives
$$\frac{S_{\text{samp}}}{C_{\text{A}}(V_{\text{o}}/V_{\text{f}})} = \frac{S_{\text{spike}}}{C_{\text{A}}(V_{\text{o}}/V_{\text{f}}) + C_{\text{S}}(V_{\text{s}}/V_{\text{f}})}$$
5.7
Equation 5.7 can be solved for the concentration of analyte in the original sample.
a... | {
"Header 1": "5B.3 External Standards",
"token_count": 1740,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 5.6
Starting with equation 5.6, show that the equations for the slope, y-intercept, and x-intercept in Figure 5.7(a) are correct.
#### SOLUTION
We begin by rewriting equation 5.6 as
$$S_{\text{spike}} = \frac{kC_{\text{A}}V_{\text{o}}}{V_{\text{c}}} + \frac{kC_{\text{S}}}{V_{\text{c}}} \times V_{\t... | {
"Header 1": "a",
"token_count": 499,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
<sup>8</sup>A fifth spectrophotometric method for the quantitative determination of the concentration of $Pb^{2+}$ in blood uses a multiple-point standard addition based on equation 5.6. The original blood sample has a volume of 1.00 mL, and the standard used for spiking the sample has a concentration of 1560 ppb $P... | {
"Header 1": "EXAMPLE 5.7",
"token_count": 1974,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### OF
#### EXAMPLE 5.9
A seventh spectrophotometric method for the quantitative determination of Pb<sup>2+</sup> levels in blood gives a linear internal standards calibration curve for which
$$\left(\frac{S_{\rm A}}{S_{\rm IS}}\right)_{\rm stand} = (2.11 \, \rm ppb^{-1}) \times C_{\rm A} - 0.006$$
What is t... | {
"Header 1": "EXAMPLE 5.7",
"token_count": 377,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In a single-point external standardization, we first determine the value of k by measuring the signal for a single standard containing a known concentration of analyte. This value of k and the signal for the sample are then used to calculate the concentration of analyte in the sample (see Example 5.2). With only a sing... | {
"Header 1": "5C Linear Regression and Calibration Curves",
"token_count": 1039,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A calibration curve shows us the relationship between the measured signal and the analyte's concentration in a series of standards. The most useful calibration curve is a straight line since the method's sensitivity is the same for all concentrations of analyte. The equation for a linear calibration curve is
$$y = \b... | {
"Header 1": "**5C.1 Linear Regression of Straight-Line Calibration Curves**",
"token_count": 792,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 5.10
Using the data from Table 5.1, determine the relationship between $S_{\text{meas}}$ and $C_{\text{S}}$ by an unweighted linear regression.
#### SOLUTION
Equations 5.13 and 5.14 are written in terms of the general variables x and y. As you work through this example, remember that x represents... | {
"Header 1": "0",
"token_count": 1795,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
|
|-----------------------|---------------------|----|------------|
| X; | V: | ŷ; | (v: -i |
| Xi | <b>y</b> i | ŷi | $(y_i - \hat{y}_i)^2$ |
|-------|------------|--------|-----------------------|
| 0.000 | 0.00 | 0.209 | 0.0437 |
| 0.100 | 12.36 ... | {
"Header 1": "0",
"token_count": 1379,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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#### EXAMPLE 5.12
Three replicate determinations are made of the signal for a sample containing an unknown concentration of analyte, yielding values of 29.32, 29.16, and 29.51. Using the regression line from Examples 5.10 and 5.11, determine the analyte's concentration, $C_A$ , and its 95% confidence interval.
###... | {
"Header 1": "6",
"token_count": 1162,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Equations 5.13 for the slope, $b_1$ , and 5.14 for the *y*-intercept, $b_0$ , assume that indeterminate errors equally affect each value of *y*. When this assumption is false, as shown in Figure 5.11b, the variance associated with each value of *y* must be included when estimating $\beta_0$ and $\beta_1$ . In this... | {
"Header 1": "5C.3 Weighted Linear Regression with Errors in y",
"token_count": 2015,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The confidence interval for the concentration of an analyte, however, will be at its optimum value when the analyte's signal is near the weighted centroid, $\overline{y}$ , of the calibration curve
$$\bar{y} = \frac{1}{n} \sum w_i y_i$$
#### 5C.4 Weighted Linear Regression with Errors in Both x and y
If we remov... | {
"Header 1": "5C.3 Weighted Linear Regression with Errors in y",
"token_count": 704,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In discussing ways to standardize a method, we assumed that an appropriate reagent blank had been used to correct *S*meas for signals originating from sources other than the analyte. At that time we did not ask an important question— "What constitutes an appropriate reagent blank?" Surprisingly, the answer is not intui... | {
"Header 1": "**5D Blank Corrections**",
"token_count": 1879,
"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.
$$S_{\text{meas}} = kn_{\text{A}} + S_{\text{reag}}$$
$$S_{\text{meas}} = kC_{\text{A}} + S_{\text{reag}}$$
To obtain accurate results we must eliminate determinate errors affecting the measur... | {
"Header 1": "**5F SUMMARY**",
"token_count": 467,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
*The following exercises and experiments help connect the material in this chapter to the analytical laboratory.*
Calibration—Volumetric glassware (burets, pipets, and volumetric flasks) can be calibrated in the manner described in Example 5.1. Most instruments have a calibration samp... | {
"Header 1": "**5G** *Suggested* **EXPERIMENTS**",
"token_count": 340,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **1.** In calibrating a 10-mL pipet, a measured volume of water was transferred to a tared flask and weighed, yielding a mass of 9.9814 g. (a) Calculate, with and without correcting for buoyancy, the volume of water delivered by the pipet. Assume that the density of water is 0.99707 g/cm3 and that the density of the ... | {
"Header 1": "**5H PROBLEMS**",
"token_count": 2044,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
If the two methods yield identical results, then the plot should have a true slope ( $\beta_1$ ) of 1.00 and a true y-intercept ( $\beta_0$ ) of 0.0. A t-test can be used to compare the actual slope and y-intercept with these ideal values. The appropriate test statistic for the y-intercept is found by rearranging equat... | {
"Header 1": "**5H PROBLEMS**",
"token_count": 601,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In addition to the texts listed as suggested readings in Chapter 4, the following text provides additional details on regression
Draper, N. R.; Smith, H. *Applied Regression Analysis*, 2nd. ed. Wiley: New York, 1981.
Several articles providing more details about linear regression follow.
Boqué, R.; Rius, F. X.; M... | {
"Header 1": "51 SUGGESTED READINGS",
"token_count": 1518,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- 1. Battino, R.; Williamson, A. G. *J. Chem. Educ.* **1984,** *61,* 51–52.
- 2. Ebel, S. *Fresenius J. Anal. Chem.* **1992,** *342,* 769.
- 3. ACS Committee on Environmental Improvement "Guidelines for Data Acquisition and Data Quality Evaluation in Environmental Chemistry," *Anal. Chem.* **1980,** *52,* 2242–2249.
- ... | {
"Header 1": "**5J REFERENCES**",
"token_count": 784,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
**R**egardless of the problem on which an analytical chemist is working, its solution ultimately requires a knowledge of chemistry and the ability to reason with that knowledge. For example, an analytical chemist developing a method for studying the effect of pollution on spruce trees needs to know, or know where to fi... | {
"Header 1": "Equilibrium Chemistry",
"token_count": 310,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In 1798, the chemist Claude Berthollet (1748–1822) accompanied a French military expedition to Egypt. While visiting the Natron Lakes, a series of salt water lakes carved from limestone, Berthollet made an observation that contributed to an important discovery. Upon analyzing water from the Natron Lakes, Berthollet fou... | {
"Header 1": "**6A Reversible Reactions and Chemical Equilibria**",
"token_count": 684,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Thermodynamics is the study of thermal, electrical, chemical, and mechanical forms of energy. The study of thermodynamics crosses many disciplines, including physics, engineering, and chemistry. Of the various branches of thermodynamics, the most important to chemistry is the study of the changes in energy occurring du... | {
"Header 1": "**6B Thermodynamics and Equilibrium Chemistry**",
"token_count": 1386,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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We will use two useful relationships when working with equilibrium constants. First, if we reverse a reaction's direction, the equilibrium constant for the new reaction is simply the inverse of that for the original reaction. For example, the equilibrium constant for the reaction
$$A + 2B \rightleftharpoons AB_2$$
$K... | {
"Header 1": "6C Manipulating Equilibrium Constants",
"token_count": 728,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A precipitation reaction occurs when two or more soluble species combine to form an insoluble product that we call a **precipitate**. The most common precipitation reaction is a metathesis reaction, in which two soluble ionic compounds exchange parts. When a solution of lead nitrate is added to a solution of potassium ... | {
"Header 1": "**6D.1** Precipitation Reactions",
"token_count": 2019,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The most common example of a strong base is an alkali metal hydroxide, such as sodium hydroxide, which completely dissociates to produce the hydroxide ion.
$$NaOH(aq) \rightarrow Na^{+}(aq) + OH^{-}(aq)$$
Weak bases only partially accept protons from the solvent and are characterized by a **base dissociation consta... | {
"Header 1": "**6D.1** Precipitation Reactions",
"token_count": 1043,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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What is the [OH<sup>-</sup>] if the [H<sub>3</sub>O<sup>+</sup>] is $6.12 \times 10^{-5}$ M?
SOLUTION
$$[OH^{-}] = \frac{K_{\rm w}}{[H_3O^{+}]} = \frac{1.00 \times 10^{-14}}{6.12 \times 10^{-5}} = 1.63 \times 10^{-10}$$
**pH** Defined as $pH = -log[H_3O^+]$ .
Equation 6.10 also allows us to develop a **pH** ... | {
"Header 1": "EXAMPLE 6.2",
"token_count": 1835,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
For example, the reaction between Cd<sup>2+</sup> and NH<sub>3</sub> involves four successive reactions
$$Cd^{2+}(aq) + NH_3(aq) \rightleftharpoons Cd(NH_3)^{2+}(aq)$$
**6.17**
$$Cd(NH_3)^{2+}(aq) + NH_3(aq) \rightleftharpoons Cd(NH_3)^{2+}(aq)$$
6.18
$$Cd(NH_3)_2^{2+}(aq) + NH_3(aq) \rightleftharpoons Cd(NH_3)_3... | {
"Header 1": "EXAMPLE 6.2",
"token_count": 2025,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The relationship between electrochemical potential and the concentrations of reactants and products can be determined by substituting equation 6.23 into equation 6.3
$$-nFE = -nFE^{\circ} + RT \ln Q$$
where *E°* is the electrochemical potential under standard-state conditions. Dividing through by –*nF* leads to t... | {
"Header 1": "EXAMPLE 6.2",
"token_count": 1195,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The equilibrium position for any reaction is defined by a fixed equilibrium constant, not by a fixed combination of concentrations for the reactants and products. This is easily appreciated by examining the equilibrium constant expression for the dissociation of acetic acid.
$$K_{\mathbf{a}} = \frac{[H_3O^+][CH_3COO^... | {
"Header 1": "6E Le Châtelier's Principle",
"token_count": 899,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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#### EXAMPLE 6.6
What is the effect on the solubility of AgCl if $HNO_3$ is added to the equilibrium solution defined by reaction 6.29?
#### SOLUTION
Nitric acid is a strong acid that reacts with ammonia as shown here
$$HNO_3(aq) + NH_3(aq) \rightleftharpoons NH_4^+(aq) + NO_3^-(aq)$$
Adding nitric acid low... | {
"Header 1": "0",
"token_count": 857,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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When developing or evaluating an analytical method, we often need to understand how the chemistry taking place affects our results. We have already seen, for example, that adding NH<sub>3</sub> to a solution of Ag<sup>+</sup> is a poor idea if we intend to isolate the Ag<sup>+</sup> as a precipitate of AgCl (reaction 6... | {
"Header 1": "6F Ladder Diagrams",
"token_count": 2042,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Because $F^-$ and NH<sub>4</sub><sup>+</sup> can coexist over a range of pHs we cannot be more specific in estimating the solution's pH.
The ladder diagram for HF/F<sup>-</sup> also can be used to evaluate the effect of pH on other equilibria that include either HF or F<sup>-</sup>. For example, the solubility of C... | {
"Header 1": "6F Ladder Diagrams",
"token_count": 798,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 6.8
Using the ladder diagram in Figure 6.7, predict the result of adding 0.080 mol of Ca<sup>2+</sup> to 0.060 mol of Mg(EDTA)<sup>2-</sup>. EDTA is an abbreviation for the ligand ethylenediaminetetraacetic acid.
#### SOLUTION
The predominance regions for Ca<sup>2+</sup> and Mg(EDTA)<sup>2-</sup> do ... | {
"Header 1": "9",
"token_count": 1983,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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When an insoluble compound such as Pb(IO3)2 is added to a solution a small portion of the solid dissolves. Equilibrium is achieved when the concentrations of Pb2+ and IO3 – are sufficient to satisfy the solubility product for Pb(IO3)2. At equilibrium the solution is saturated with Pb(IO3)2. How can we determine the con... | {
"Header 1": "**6G.1 A Simple Problem: Solubility of Pb(IO3)2 in Water**",
"token_count": 610,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Calculating the solubility of Pb(IO3)2 in distilled water is a straightforward problem since the dissolution of the solid is the only source of Pb2+ or IO3 –. How is the solubility of Pb(IO3)2 affected if we add Pb(IO3)2 to a solution of 0.10 M Pb(NO3)2? Before we set up and solve the problem algebraically, think about... | {
"Header 1": "**6G.2 A More Complex Problem: The Common Ion Effect**",
"token_count": 946,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Calculate the solubility of Pb(IO3)2 in 1.0 × 10–4 M Pb(NO3)2.
#### *SOLUTION*
Letting *x* equal the change in the concentration of Pb2+, the equilibrium concentrations are
$$[Pb^{2+}] = 1.0 \times 10^{-4} + x$$
$[IO_3^-] = 2x$
and
$$(1.0 \times 10^{-4} + x)(2x)^2 = 2.5 \times 10^{-13}$$
We start by assumin... | {
"Header 1": "**EXAMPLE 6.9**",
"token_count": 1784,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
These reactions are the dissolution of a soluble salt
$$NaHCO_3(s) \rightarrow Na^+(aq) + HCO_3^-(aq)$$
and the acid-base dissociation reactions of HCO<sub>3</sub><sup>-</sup> and H<sub>2</sub>O
$$HCO_3^-(aq) + H_2O(\ell) \rightleftharpoons H_3O^+(aq) + CO_3^{2-}(aq)$$
$$HCO_3^-(aq) + H_2O(\ell) \rightleftharpo... | {
"Header 1": "**EXAMPLE 6.9**",
"token_count": 302,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
To illustrate the systematic approach, let us calculate the pH of 1.0 M HF. Two equilbria affect the pH of this system. The first, and most obvious, is the acid dissociation reaction for HF
$$HF(aq) + H_2O(\ell) \rightleftharpoons H_3O^+(aq) + F^-(aq)$$
for which the equilibrium constant expression is
$$K_{\rm a}... | {
"Header 1": "6G.4 pH of a Monoprotic Weak Acid",
"token_count": 1646,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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#### EXAMPLE 6.11
Calculate the pH of 0.050 M NH<sub>3</sub>. State any assumptions made in simplifying the calculation, and verify that the error is less than 5%.
#### SOLUTION
Since NH<sub>3</sub> is a weak base ( $K_b = 1.75 \times 10^{-5}$ ), we assume that
$$[OH^-] >> [H_3O^+]$$
and $C_{NH_3} = 0.050 \tex... | {
"Header 1": "9",
"token_count": 2006,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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Alanine is an amphiprotic species, behaving as an acid
$$HL(aq) + H_2O(\ell) \rightleftharpoons H_3O^+(aq) + L^-(aq)$$
and a base
$$HL(aq) + H_2O(\ell) \rightleftharpoons OH^-(aq) + H_2L^+(aq)$$
As always, we must also consider the dissociation of water
$$2H_2O(\ell) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$$... | {
"Header 1": "9",
"token_count": 1565,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
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The solubility of a precipitate can be improved by adding a ligand capable of forming a soluble complex with one of the precipitate's ions. For example, the solubility of AgI increases in the presence of NH<sub>3</sub> due to the formation of the soluble $Ag(NH_3)_2^+$ complex. As a final illustration of the systemat... | {
"Header 1": "**6G.6** Effect of Complexation on Solubility",
"token_count": 1839,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Adding as little as 0.1 mL of concentrated HCl to a liter of $H_2O$ shifts the pH from 7.0 to 3.0. The same addition of HCl to a liter solution that is 0.1 M in both a weak acid and its conjugate weak base, however, results in only a negligible change in pH. Such solutions are called **buffers**, and their buffering ... | {
"Header 1": "**6H** Buffer Solutions",
"token_count": 1388,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Calculate the pH of a buffer that is 0.020 M in NH<sub>3</sub> and 0.030 M in NH<sub>4</sub>Cl. What is the pH after adding 1.00 mL of 0.10 M NaOH to 0.10 L of this buffer?
#### SOLUTION
The acid dissociation constant for $NH_4^+$ is $5.70 \times 10^{-10}$ ; thus the initial pH of the buffer is
pH =
$$9.24 + \... | {
"Header 1": "**6H** Buffer Solutions",
"Header 3": "**EXAMPLE** 6.13",
"token_count": 1743,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Suppose you need to prepare a buffer with a pH of 9.36. Using the Henderson–Hasselbalch equation, you calculate the amounts of acetic acid and sodium acetate needed and prepare the buffer. When you measure the pH, however, you find that it is 9.25. If you have been careful in your calculations and measurements, what ca... | {
"Header 1": "**61 Activity Effects**",
"token_count": 1719,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated
Table 6.1
Effective Diameters (α) for Selected Inorganic
Cations and Anions
| lon ... | {
"Header 1": "**61 Activity Effects**",
"token_count": 1756,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In this chapter we have reviewed and extended our understanding of equilibrium chemistry. We also have developed several tools for evaluating the composition of a system at equilibrium. These tools differ in how accurately they allow us to answer questions involving equilibrium chemistry. They also differ in their ease... | {
"Header 1": "**6J Two Final Thoughts About Equilibrium Chemistry**",
"token_count": 220,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
acid (*p. 140*) acid dissociation constant (*p. 140*) activity (*p. 172*) activity coefficient (*p. 172*) amphiprotic (*p. 142*) base (*p. 140*) base dissociation constant (*p. 141*) buffer (*p. 167*) charge balance equation (*p. 159*) common ion effect (*p. 158*) cumulative formation constant (*p. 144*) dissociation c... | {
"Header 1": "**6K KEY TERMS**",
"token_count": 392,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Analytical chemistry is more than a collection of techniques; it is the application of chemistry to the analysis of samples. As you will see in later chapters, almost all analytical methods use chemical reactivity to accomplish one or more of the following—dissolve the sample, separate analytes and interferents, transf... | {
"Header 1": "**6L SUMMARY**",
"token_count": 830,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The following experiments involve the experimental determination of equilibrium constants and, in some cases, demonstrate the importance of activity effects.
789-792.
"The Effect of Ionic Strength on an Equilibrium Constant (A Class Study)." In J. A. Bell, ed. *Chemical Principles in... | {
"Header 1": "Suggested EXPERIMENTS",
"token_count": 429,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- **1.** Write equilibrium constant expressions for the following reactions. Determine the value for the equilibrium constant for each reaction using appropriate equilibrium constants from Appendix 3.
- a. $NH_3(aq) + HCl(aq) \rightleftharpoons NH_4^+(aq) + Cl^-(aq)$
- b. $PbI_2(s) + S^{2-}(aq) \rightleftharpoons PbS... | {
"Header 1": "3",
"Header 3": "**6N PROBLEMS**",
"token_count": 2020,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The relevant reaction is
$$Fe^{3+}(aq) + SCN^{-}(aq) \rightleftharpoons Fe(SCN)^{2+}(aq)$$
- **17.** Over what pH range do you expect Ca<sub>3</sub>(PO<sub>4</sub>)<sub>2</sub> to have its minimum solubility?
- **18.** Construct ladder diagrams for the following systems, and describe the information that can be obt... | {
"Header 1": "3",
"Header 3": "**6N PROBLEMS**",
"token_count": 639,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A lucid discussion of Berthollet's discovery of the reversibility of reactions is found in
Roots-Bernstein, R. S. *Discovering.* Harvard University Press: Cambridge, MA, 1989.
The following texts and articles provide additional coverage of equilibrium chemistry and the systematic approach to solving equilibrium pro... | {
"Header 1": "**6O SUGGESTED READINGS**",
"token_count": 1008,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
- 1. (a) Runo, J. R.; Peters, D. G. *J. Chem. Educ.* **1993,** *70,* 708–713; (b) Vale, J.; Fernandez-Pereira, C.; Alcalde, M. *J. Chem. Educ.* **1993,** *70,* 790–795.
- 2. Van Slyke, D. D. *J. Biol. Chem.* **1922,** *52,* 525–570.
- 3. (a) Bower, V. E.; Bates, R. G. *J. Res. Natl. Bur. Stand. (U. S.)* **1955,** *55,*... | {
"Header 1": "**6P REFERENCES**",
"token_count": 373,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
When a manufacturer produces a chemical they wish to list as ACS Reagent Grade, they must demonstrate that it conforms to specifications established by the American Chemical Society (ACS). For example, ACS specifications for NaHCO<sub>3</sub> require that the concentration of iron be less than or equal to 0.001% w/w. T... | {
"Header 1": "The Importance of Sampling",
"token_count": 765,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 7.1
A quantitative analysis for an analyte gives a mean concentration of 12.6 ppm. The standard deviation for the method is found to be 1.1 ppm, and that due to sampling is 2.1 ppm. (a) What is the overall variance for the analysis? (b) By how much does the overall variance change if $s_m$ is improved ... | {
"Header 1": "dmi",
"token_count": 474,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 7.2
The following data were collected as part of a study to determine the effect of sampling variance on the analysis of drug animal-feed formulations.<sup>2</sup>
| % Drug (w/w) | | | % | Drug (w/v | v) |
|--------------|--------|--------|--------|-----------|--------|
| 0.0114 ... | {
"Header 1": "0",
"token_count": 502,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A sampling plan must support the goals of an analysis. In characterization studies a sample's purity is often the most important parameter. For example, a material scientist interested in the surface chemistry of a metal is more likely to select a freshly exposed surface, created by fracturing the sample under vacuum, ... | {
"Header 1": "7B Designing A Sampling Plan",
"token_count": 268,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Sampling errors occur when a sample's composition is not identical to that of the population from which it is drawn. When the material being sampled is homogeneous, individual samples can be taken without regard to possible sampling errors. Unfortunately, in most situations the target population is heterogeneous in eit... | {
"Header 1": "7B.1 Where to Sample the Target Population",
"token_count": 449,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
To analyze the properties of a 100 cm × 100 cm polymer sheet, ten 1 cm × 1 cm samples are to be selected at random and removed for analysis. Explain how a random number table can be used to ensure that samples are drawn at random.
#### *SOLUTION*
As shown in the following grid, we divide the polymer sheet into 10,0... | {
"Header 1": "**EXAMPLE 7.3**",
"token_count": 1737,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
After determining where to collect samples, the next step in designing a sampling plan is to decide what type of sample to collect. Three methods are commonly used to obtain samples: grab sampling, composite sampling, and in situ sampling. The most common type of sample is a **grab sample,** in which a portion of the t... | {
"Header 1": "**7B.2 What Type of Sample to Collect**",
"token_count": 1619,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Assume that the sample of $10^{13}$ particles from Example 7.4 weighs 80 g. By how much must you reduce the radius of the particles if you wish to work with a sample of 0.6 g?
#### SOLUTION
To reduce the sample from 80 g to 0.6 g you must change its mass by a factor of
$$\frac{80}{0.6} = 133 \text{ times}$$
T... | {
"Header 1": "EXAMPLE 7.5",
"token_count": 2004,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
How many samples are needed to obtain a relative sampling error of no more than 0.80% at the 95% confidence level?
#### SOLUTION
Because the value of t depends on $n_s$ , and the value of $n_s$ is not yet known, we begin by letting $n_s = \infty$ and use the associated value of t. From Appendix 1B, the value f... | {
"Header 1": "EXAMPLE 7.5",
"token_count": 1299,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
After a sampling plan has been developed, it is put into action. Implementing a sampling plan normally involves three steps: physically removing the sample from its target population, preserving the sample, and preparing the sample for analysis. Except for in situ sampling, the analysis of a sample occurs after removin... | {
"Header 1": "7C Implementing the Sampling Plan",
"token_count": 1698,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Typical examples of gaseous samples include automobile exhaust, emissions from industrial smokestacks, atmospheric gases, and compressed gases. Also included with gaseous samples are solid aerosol particulates.
**Sample Collection** The simplest approach for collecting a gas sample is to fill a container, such as a s... | {
"Header 1": "**7C.2 Gases**",
"token_count": 1013,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Typical examples of solid samples include large particulates, such as those found in ores; smaller particulates, such as soils and sediments; tablets, pellets, and capsules used in dispensing pharmaceutical products and animal feeds; sheet materials, such as polymers and rolled metals; and tissue samples from biologica... | {
"Header 1": "**7C.3 Solids**",
"token_count": 2045,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
| Table 7.2 | Acids and Bases Used for Sample Digestion | | |
|------------... | {
"Header 1": "**7C.3 Solids**",
"token_count": 1423,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
When a method shows a high degree of selectivity for the analyte, the task of performing a quantitative, qualitative, or characterization analysis is simplified. For example, a quantitative analysis for glucose in honey is easier to accomplish if the method is selective for glucose, even in the presence of other reduci... | {
"Header 1": "**7D Separating the Analyte from Interferents**",
"token_count": 591,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The goal of an analytical separation is to remove either the analyte or the interferent from the sample matrix. To achieve a separation there must be at least one significant difference between the chemical or physical properties of the analyte and interferent. Relying on chemical or physical properties, however, prese... | {
"Header 1": "7E General Theory of Separation Efficiency",
"token_count": 535,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
An analysis to determine the concentration of Cu in an industrial plating bath uses a procedure for which Zn is an interferent. When a sample containing 128.6 ppm Cu is carried through a separation to remove Zn, the concentration of Cu remaining is 127.2 ppm. When a 134.9-ppm solution of Zn is carried through the separ... | {
"Header 1": "7E General Theory of Separation Efficiency",
"Header 3": "EXAMPLE 7.10",
"token_count": 951,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Following the separation outlined in Example 7.10, an analysis is to be carried out for the concentration of Cu in an industrial plating bath. The concentration ratio of Cu to Zn in the plating bath is 7:1. Analysis of standard solutions containing only Cu or Zn give the following standardization equations
$$S_{\text... | {
"Header 1": "7E General Theory of Separation Efficiency",
"Header 3": "EXAMPLE 7.11",
"token_count": 728,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
An analyte and an interferent can be separated if there is a significant difference in at least one of their chemical or physical properties. Table 7.4 provides a partial list of several separation techniques, classified by the chemical or physical property that is exploited.
#### 7F.I Separations Based on Size
The... | {
"Header 1": "7F Classifying Separation Techniques",
"token_count": 970,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
If there is a difference in the mass or density of the analyte and interferent, then a separation using centrifugation may be possible. The sample, as a suspension, is placed in a centrifuge tube and spun at a high angular velocity (high numbers of revolutions per minute, rpm). Particles experiencing a greater centrifu... | {
"Header 1": "**7F.2 Separations Based on Mass or Density**",
"token_count": 833,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
One of the most widely used techniques for preventing an interference is to bind the interferent as a soluble complex, preventing it from interfering in the analyte's determination. This process is known as **masking.** Technically, masking is not a separation
**Figure 7.12**
Illustr... | {
"Header 1": "**7F.3 Separations Based on Complexation Reactions (Masking)**",
"token_count": 543,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Show that CN– is an appropriate masking agent for Ni2+ in a method in which nickel's complexation with EDTA is an interference.
#### *SOLUTION*
The relevant reactions and equilibrium constants from Appendix 3C are
$$Ni^{2+} + Y^{4-} \rightarrow NiY^{2-}$$
$K_f = 4.2 \times 10^{18}$ $Ni^{2+} + 4CN^- \rightarrow ... | {
"Header 1": "**EXAMPLE 7.13**",
"token_count": 2023,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
After filtering, the filtrate is acidified to recover the aluminum as a precipitate of $Al(OH)_3$ .
The pH of an NH<sub>3</sub>/NH<sub>4</sub>Cl buffer (p $K_a$ = 9.24) is sufficient to ensure the precipitation of most metals as the hydroxide. The alkaline earths and alkaline metals, however, will not precipitate a... | {
"Header 1": "**EXAMPLE 7.13**",
"token_count": 424,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The most important class of separation techniques is based on the selective partitioning of the analyte or interferent between two immiscible phases. When a phase containing a solute, *S*, is brought into contact with a second phase, the solute partitions itself between the two phases.
$$S_{\text{phase 1}} \rightleft... | {
"Header 1": "7F.5 Separations Based on a Partitioning Between Phases",
"token_count": 2036,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
For example, when acetone is the solvent, a Soxhlet extraction is limited to 56 °C. With a microwave-assisted extraction, however, a temperature of over 150 °C can be obtained when using acetone as the solvent.
Two other examples of a continuous extraction deserve mention. Volatile organic compounds (VOCs) can be qua... | {
"Header 1": "7F.5 Separations Based on a Partitioning Between Phases",
"token_count": 674,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
A liquid–liquid extraction is one of the most important separation techniques used in environmental, clinical, and industrial laboratories. Two examples from environmental analysis serve to illustrate its importance. Public drinking water supplies are routinely monitored for trihalomethanes (CHCl3, CHBrCl2, CHBr2Cl, an... | {
"Header 1": "**7G Liquid–Liquid Extractions**",
"token_count": 351,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Earlier we learned that the partitioning of a solute between two phases is described by a partition coefficient. If the solute is initially in an aqueous phase and is extracted into an organic phase\*
$$S_{aq} \rightleftharpoons S_{org}$$
the partition coefficient is
$$K_{\rm D} = \frac{[S_{\rm org}]}{[S_{\rm ad}... | {
"Header 1": "**7G Liquid–Liquid Extractions**",
"Header 3": "7G.1 Partition Coefficients and Distribution Ratios",
"token_count": 475,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In the simplest form of liquid–liquid extraction, the only reaction affecting extraction efficiency, is the partitioning of the solute between the two phases (Figure 7.20). In this case the distribution ratio and the partition coefficient are equal.
$$D = \frac{[S_{\text{org}}]_{\text{tot}}}{[S_{\text{ad}}]_{\text{to... | {
"Header 1": "7G.2 Liquid-Liquid Extraction with No Secondary Reactions",
"token_count": 1846,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
If a second extraction is carried out, the fraction of solute remaining in the aqueous phase, $(q_{aq})_2$ , is given by
$$(q_{\text{aq}})_2 = \frac{(\text{moles aq})_2}{(\text{moles aq})_1} = \frac{V_{\text{aq}}}{DV_{\text{org}} + V_{\text{aq}}}$$
If the volumes of the aqueous and organic layers are the same for ... | {
"Header 1": "7G.2 Liquid-Liquid Extraction with No Secondary Reactions",
"token_count": 322,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
#### EXAMPLE 7.15
For the extraction described in Example 7.14, determine (a) the extraction efficiency for two extractions and for three extractions; and (b) the number of extractions required to ensure that 99.9% of the solute is extracted.
#### SOLUTION
(a) The fraction of solute remaining in the aqueous phase... | {
"Header 1": "Colorplate 4 shows an example of a liquid-liquid extraction.",
"token_count": 610,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
In a simple liquid–liquid extraction the distribution ratio and the partition coefficient are identical. As a result, the distribution ratio is unaffected by any change in the composition of the aqueous or organic phase. If the solute also participates in a single-phase equilibrium reaction, then the distribution ratio... | {
"Header 1": "7G.3 Liquid-Liquid Extractions Involving Acid-Base Equilibria",
"token_count": 737,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
An acidic solute, HA, has an acid dissociation constant of $1.00 \times 10^{-5}$ , and a partition coefficient between water and benzene of 3.00. Calculate the extraction efficiency when 50.00 mL of a 0.025 M aqueous solution of HA buffered to a pH of 3.00, is extracted with 50.00 mL of benzene. Repeat for cases in wh... | {
"Header 1": "EXAMPLE 7.16",
"token_count": 234,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
The fraction of solute remaining in the aqueous phase is
$$(Q_{\rm aq})_1 = \frac{50.00 \text{ mL}}{(2.97)(50.00 \text{ mL}) + 50.00 \text{ mL}} = 0.252$$
The extraction efficiency, therefore, is almost 75%. When the same calculation is carried out at a pH of 5.00, the extraction efficiency is 60%, but the extracti... | {
"Header 1": "0",
"token_count": 1696,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
Two frequently encountered analytical problems are: (1) the presence of matrix components interfering with the analysis of the analyte; and (2) the presence of analytes at concentrations too small to analyze accurately. We have seen how a separation can be used to solve the former problem. Interestingly, separation tec... | {
"Header 1": "**7H Separation Versus Preconcentration**",
"token_count": 429,
"source_pdf": "datasets/websources/biochem/Modern analytical chemistry by David Harvey.pdf"
} |
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