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| 727 |
| 11F<br>Chapter Summary | 728 |
| 11G<br>Problems | 729 |
| 11H<br>Solutions to Practice Exercises ... | {
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- A [Organization](#page-17-1)
- B [Role of Equilibrium Chemistry](#page-17-2)
- C [Computational Software](#page-18-1)
- D [How to Use The Electronic Textbook's Features](#page-18-2)
- E [Acknowledgments](#page-20-1)
- F [Updates, Ancillary Materials, and Future Editions](#page-22-1)
- G [How To Contact the Author](#p... | {
"Header 1": "Preface",
"Header 3": "Overview",
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Choose the option for "Multimedia Trust" and check the option for "Allow multimedia operations." If the permission for QuickTime or Flash is set to "Never" you can change it to "Prompt," which will ask you to authorize the use of multimedia when you first try to play the movie, or change it to "Always" if you do not wi... | {
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- 1A [What is Analytical Chemistry?](#page-25-1)
- 1B [The Analytical Perspective](#page-28-1)
- 1C [Common Analytical Problems](#page-30-1)
- 1D [Key Terms](#page-31-1)
- 1E [Chapter Summary](#page-31-2)
- 1F [Problems](#page-32-1)
- 1G [Solutions to Practice Exercises](#page-33-1)
Chemistry is the study of matter, ... | {
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You will come across numerous examples of analytical methods in this textbook, most of which are routine examples of chemical analysis. It is important to remember, however, that nonroutine problems prompted analytical chemists to develop these methods.
#### **1B The Analytical Perspective**
Having noted that eac... | {
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Perhaps the most common analytical problem is a quantitative analysis, examples of which include the elemental analysis of a newly synthesized compound, measuring the concentration of glucose in blood, or determining the difference between the bulk and the surface concentrations of Cr in steel. Much of the analytical... | {
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- 2A [Measurements in Analytical Chemistry](#page-37-1)
- 2B [Concentration](#page-41-1)
- 2C [Stoichiometric Calculations](#page-46-1)
- 2D [Basic Equipment](#page-47-0)
- 2E [Preparing Solutions](#page-52-1)
- 2F [Spreadsheets and Computational Software](#page-55-1)
- 2G [The Laboratory Notebook](#page-56-1)
- 2H [Ke... | {
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For simplicity, we express these measurements using SCIENTIFIC NOTATION; thus, a mole contains $6.022\ 136\ 7\times 10^{23}$ particles, and the detected mass is $1\times 10^{-15}$ g. Sometimes we wish to express a measurement without the exponential term, replacing it with a prefix (Table 2.3). A mass of $1\times ... | {
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For example, when we divide the product of 22.91 and 0.152 by 16.302, we report the answer as 0.214 (three significant figures) because 0.152 has the fewest number of significant figures.
The log of $2.8 \times 10^2$ is 2.45. The log of 2.8 is 0.45 and the log of $10^2$ is 2. The 2 in 2.45, therefore, only indica... | {
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Since density is a temperature dependent property, a solution's volume, and thus its molar concentration, changes with temperature. By using the solvent's mass in place of the solution's volume, the resulting concentration becomes independent of temperature.
#### 2B.4 Weight, Volume, and Weight-to-Volume Percents
W... | {
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A more appropriate equation for pH is
$pH = -log(a_H +)$
where $a_{H^+}$ is the activity of the hydrogen
ion. See Chapter 6I for more details. For
now the approximate equation
is sufficient.
#### Example 2.4
What is pNa for a solution of $1.76 \times 10^{-3}$ M Na<sub>3</sub>PO<sub>4</sub>?
#### SOL... | {
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#### Example 2.7
An analysis for disulfiram, $C_{10}H_{20}N_2S_4$ , in Antabuse is carried out by oxidizing the sulfur to $H_2SO_4$ and titrating the $H_2SO_4$ with NaOH. If a 0.4613-g sample of Antabuse requires 34.85 mL of 0.02500 M NaOH to titrate the $H_2SO_4$ , what is the... | {
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For example, the 10 mL transfer pipet in Figure 2.5 will deliver 10.00 mL with an accuracy of ±0.02 mL.
To fill a transfer pipet, use a rubber suction bulb to pull the solution up past the calibration mark (*Never use your mouth to suck a solution into a pipet!*). After replacing the bulb with your finger, adjust the... | {
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To prepare a solution where the solute's concentration is a volume percent, you measure out an appropriate volume of solute and add sufficient solvent to obtain the desired total volume.
#### Example 2.8
Describe how to prepare the following three solutions: (a) 500 mL of approximately 0.20 M NaOH using solid NaOH;... | {
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org software package at <a href="https://www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffice.com/www.openoffic... | {
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An analyst wishes to add 256 mg of Cl– to a reaction mixture. How many mL of 0.217 M BaCl2 is this?
- 8. The concentration of lead in an industrial waste stream is 0.28 ppm. What is its molar concentration?
- 9. Commercially available concentrated hydrochloric acid is 37.0% w/w HCl. Its density is 1.18 g/mL. Using this... | {
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#### **Practice Exercise 2.3**
The concentrations of Na<sup>+</sup> and SO<sub>4</sub><sup>2-</sup> are
$$\begin{split} \frac{1.5 \text{ g Na}_2 \text{SO}_4}{0.500 \text{ L}} \times & \frac{1 \text{ mol Na}_2 \text{SO}_4}{142.0 \text{ g Na}_2 \text{SO}_4} \times \\ & \frac{2 \text{ mol Na}^+}{\text{mol Na}_2 \tex... | {
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- 3A [Analysis, Determination, and Measurement](#page-65-1)
- 3B [Techniques, Methods, Procedures, and Protocols](#page-66-1)
- 3C [Classifying Analytical Techniques](#page-67-1)
- [3D Selecting an Analytical Method](#page-68-1)
- 3E [Developing the Procedure](#page-76-1)
- 3F [Protocols](#page-78-1)
- 3G [The Importan... | {
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#### 3A Analysis, Determination and Measurement
The first important distinction we will make is among the terms analysis, determination, and measurement. An analysis provides chemical or physical information about a sample. The component in the sample of interest to us is called the ANALYTE, and the remainder of the ... | {
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Finally, lead's multiple oxidation states (Pb<sup>0</sup>, Pb<sup>2+</sup>, Pb<sup>4+</sup>) makes feasible a variety of electrochemical methods.
Ultimately, the requirements of the analysis determine the best method. In choosing among the available methods, we give consideration to some or all the following design c... | {
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When the concentration of $Ca^{2+}$ is 100 times greater than that of $Zn^{2+}$ , an analysis for $Ca^{2+}$ has a relative error of +0.5%. What is the selectivity coefficient for this method?
#### SOLUTION
Since only relative concentrations are reported, we can arbitrarily assign absolute concentrations. To ma... | {
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#### 3D.6 Scale of Operation
Another way to narrow the choice of methods is to consider three potential limitations: the amount of sample available for the analysis, the expected concentration of analyte in the samples, and the minimum amount of analyte that will produce a measurable signal. Collectively, these lim... | {
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If we happen to know the interferent's identity and concentration, then we can be add it to the method blank; however, this is not a common circumstance and we must, instead, find a method for separating the analyte and interferent before continuing the analysis.
A method blank also is known as a reagent blank.
Whe... | {
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<sup>11</sup> D'Elia, C. F.; Sanders, J. G.; Capone, D. G. *Envrion. Sci. Technol.* **1989**, *23*, 768–774.
In selecting an analytical method we consider criteria such as accuracy, precision, sensitivity, selectivity, robustness, ruggedness, the amount of available sample, the amount of analyte in the sample, time... | {
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#### 3K Solutions to Practice Exercises
#### **Practice Exercise 3.1**
Because the signal for $Ag^+$ in the presence of $Ni^{2+}$ is reported as a relative error, we will assign a value of 100 as the signal for $1\times10^{-9}$ M $Ag^+$ . With a relative error of +4.9%, the signal for the solution of $1\t... | {
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- 4A [Characterizing Measurements and Results](#page-87-1)
- 4B [Characterizing Experimental Errors](#page-91-1)
- 4C [Propagation of Uncertainty](#page-99-0)
- 4D [The Distribution of Measurements and Results](#page-105-1)
- 4E [Statistical Analysis of Data](#page-120-1)
- 4F [Statistical Methods for Normal Distributi... | {
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When n = 5, the median is the third value
#### Example 4.2
What is the median for the data in $\underline{\text{Table 4.1}}$ ?
#### SOLUTION
To determine the median we order the measurements from the smallest to the largest value
Because there are seven measurements, the median is the fourth value in the ord... | {
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#### Example 4.3
Report the standard deviation, the relative standard deviation, and the percent relative standard deviation for the data in <u>Table 4.1</u>?
#### SOLUTION
To calculate the standard deviation we first calculate the difference between each measurement and the data set's mean value (3.117), square ... | {
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Other types of volumetric glassware, such as beakers and graduated cylinders, are not used to measure volume accurately. [Table](#page-93-0) [4.2](#page-93-0) provides a summary of typical measurement errors for Class A volumetric glassware. Tolerances for digital pipets and for balances are provided in [Table 4.3](#p... | {
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The analyte's expected concentration of 50% w/w is shown by the dashed line.
mental concentration versus the sample's mass (Figure 4.3) is evidence of a constant determinate error.
A proportional determinate error, in which the error's magnitude depends on the amount of sample, is more difficult to detect because t... | {
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**Figure 4.5** Background noise in an instrument showing the random fluctuations in the signal.
| Table 4.8<br>Replicate Determinations of the Mass of a<br>Single Circulating U. S. Penny | | | |
|-------------------------------------------------------------... | {
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For example, if the result is given by the equation
$$R = A + B - C$$
then the absolute uncertainty in *R* is
$$u_R = \sqrt{u_A^2 + u_B^2 + u_C^2} 4.6$$
#### Example 4.5
If we dispense 20 mL using a 10-mL Class A pipet, what is the total volume dispensed and what is the uncertainty in this volume? First, comp... | {
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| Table 4.10 | <b>Propagation of Uncertainty for Selected</b> |
|------------|------------------------------------------------|
| | Mathematical Functions <sup>†</sup> |
| Function | $u_R$ |
|-----------... | {
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#### SOLUTION
The dilution calculations for case (a) and case (b) are
case (a): 1.0 M
$$\times \frac{1.000 \text{ mL}}{1000.0 \text{ mL}} = 0.0010 \text{ M}$$
case (b): 1.0 M
$$\times \frac{20.00 \text{ mL}}{1000.0 \text{ mL}} \times \frac{25.00 \text{ mL}}{500.0 \text{ mL}} = 0.0010 \text{ M}$$
Using toleran... | {
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(a) The mean number of <sup>13</sup>C atoms in a molecule of cholesterol is
$$\mu = N_p = 27 \times 0.0111 = 0.300$$
with a standard deviation of
$$\sigma = \sqrt{Np(1-p)} = \sqrt{27 \times 0.0111 \times (1-0.0111)} = 0.544$$
(b) The probability of finding a molecule of cholesterol without an atom of ${}^{13... | {
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#### **4D.3 Confidence Intervals for Populations**
If we select at random a single member from a population, what is its most likely value? This is an important question, and, in one form or another, it is at the heart of any analysis in which we wish to extrapolate from a sample to ... | {
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According to the central limit theorem, when a measurement is subject to a variety of indeterminate errors, the results for that measurement will approximate
| Table 4.13 | | | | | Masses for a Sample of 100 Circulating U. S. Pennies | | |
|------------|----------|-------|... | {
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The distribution of the means for samples of size n = 10, however, closely approximates a normal distribution.
#### **D**EGREES OF FREEDOM
Did you notice the differences between the equation for the variance of a population and the variance of a sample? If not, here are the two equations:
$$\sigma^2 = \frac{\sum_... | {
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Substituting into equation 4.12 gives
$$\mu = 3.117 \text{ g} \pm \frac{2.447 \times 0.051 \text{ g}}{\sqrt{7}} = 3.117 \text{ g} \pm 0.047 \text{ g}$$
For the second experiment the mean and the standard deviation are 3.081 g and 0.073 g, respectively, with four degrees of freedom. The 95% confidence interval is
... | {
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This is an important point and one that is easy to forget. To appreciate this point let's return to our sample of 100 pennies in [Table 4.13](#page-115-0). After looking at the data we might propose the following null and alternative hypotheses.
*H*0: The mass of a circulating U.S. penny is between 2.900 g–3.200 g. ... | {
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$$\mu = \overline{X} \pm \frac{t_{\exp}s}{\sqrt{n}}$$
4.14
Rearranging this equation and solving for $t_{exp}$
$$t_{\rm exp} = \frac{|\mu - \overline{X}|\sqrt{n}}{s} \tag{4.15}$$
gives the value of $t_{\rm exp}$ when $\mu$ is at either the right edge or the left edge of the sample's confidence interval (Fi... | {
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A critical value, $F(\alpha, \nu_{\rm num}, \nu_{\rm den})$ , is the largest value of $F_{\rm exp}$ that we can attribute to indeterminate error given the specified significance level, $\alpha$ , and the degrees of freedom for the variance in the numerator, $\nu_{\rm num}$ , and the variance in the denominator, $... | {
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$$\overline{X}_A \pm \frac{t_{\exp} s_A}{\sqrt{n_A}} = \overline{X}_B \pm \frac{t_{\exp} s_B}{\sqrt{n_B}}$$
Solving for $|\overline{X}_A - \overline{X}_B|$ and using a propagation of uncertainty, gives
$$|\overline{X}_A - \overline{X}_B| = t_{\text{exp}} \times \sqrt{\frac{s_A^2}{n_A} + \frac{s_B^2}{n_B}}$$
$... | {
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$$\nu = \frac{\left(\frac{(0.32)^2}{6} + \frac{(2.16)^2}{6}\right)^2}{\frac{\left(\frac{(0.32)^2}{6}\right)^2}{6+1} + \frac{\left(\frac{(2.16)^2}{6}\right)^2}{6+1} - 2 = 5.3 \approx 5$$
From Appendix 4, the critical value for t(0.05, 5) is 2.57. Because $t_{\rm exp}$ is greater than t(0.05, 5) we reject the null ... | {
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| Location | Air-Water<br>Interface | Sediment-Water<br>Interface |
|----------|------------------------|-----------------------------|
| 1 | 0.430 | 0.415 |
| 2 | 0.266 | 0.238 |
| 3 | 0.457 | 0.390 ... | {
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To calculate a potential outlier's probability we first calculate its standardized deviation, z
$$z = \frac{|X_{\text{out}} - \overline{X}|}{s}$$
where $X_{\text{out}}$ is the potential outlier, $\overline{X}$ is the sample's mean and s is the sample's standard deviation. Note that this equation is identical ... | {
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Consider, for example, the situation shown in Figure 4.16b where the signal for a sample that contains the analyte is exactly equal to $(S_A)_{DL}$ . In this case the probability of a type 2 error is 50% because half of the sample's possible signals are below the detection limit. We correctly detect the analyte at the... | {
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To solve [Example 4.11](#page-110-0) using Excel enter the following formulas into separate cells
=**norm.dist**(243, 250, 5, TRUE)
=**norm.dist**(262, 250, 5, TRUE)
obtaining results of 0.080 756659 and 0.991802464. Subtracting the smaller value from the larger value and adjusting to the correct number of signif... | {
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We obtained this result by calculating the deviation, *z*, of each limit from the population's expected mean, *n*, of 250 mg in terms of the population's expected standard deviation, *v*, of 5 mg. After we calculated values for *z*, we used the table in [Ap](#page-1066-1)[pendix 3](#page-1066-1) to find the area under ... | {
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The 95% confidence interval is the range of values for *F*exp that are explained by random error. If this range includes the expected value for *F*, in this case 1.00, then there is insufficient evidence to reject the null hypothesis. Note that R does not adjust for significant figures.
```
> t.test(penny1, penny2, v... | {
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A dot chart provides a simple visual display that allows us to examine the data for non-random trends. [Figure 4.25c](#page-149-0) shows the result of entering
> **dotchart**(penny, xlab="Mass of Pennies (g)", ylab="Penny Number", main="Dotchart of Data in Table 4.13")
In this plot the masses of the 100 pennies are... | {
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*Spectroscopy* **1993**, *8(6)*, 37–47.
these tables.
Many of the problems that follow require access to statistical tables. For your convenience, here are hyperlinks to the appendices containing
[Appendix 3: Single-Sided Normal Distribution](#page-1066-1) [Appendix 4: Critical Values for the](#page-1068-1) *t*-T... | {
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For your convenience, here are hyperlinks to the appendices containing
Appendix 3: Single-Sided Normal Distribution Appendix 4: Critical Values for the *t*-Test Appendix 5: Critical Values for the F-Test Appendix 6: Critical Values for Dixon's Q-Test Appendix 7: Critical Values for Grubb's Test
- 10. What is the sm... | {
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"token_count": 2020,
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A spectrophotometric determination of the concentration of Fe in this solution yields results of 5840, 5770, 5650, and 5660 ppm. Determine whether there is a significant difference between the experimental mean and the expected value at *a*=0.05.
- 22. Horvat and co-workers used atomic absorption spectroscopy to determ... | {
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[Appendix 3: Single-Sided Normal Distribution](#page-1066-1) [Appendix 4: Critical Values for the](#page-1068-1) *t*-Test [Appendix 5: Critical Values for the](#page-1069-1) *F*-Test [Appendix 6: Critical Values for Dixon's](#page-1071-1) *Q*-Test [Appendix 7: Critical Values for Grubb's Test](#page-1072-1)
| ... | {
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"Planning and Analysis of Results of Collaborative Tests," in *Statistical Manual of the Association of Official Analytical Chemists*, Association of Official Analytical Chemists: Washington, D. C., 1975.
Many of the problems that follow require access to statistical tables. For your convenience, here are hyperlinks ... | {
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[Appendix 3: Single-Sided Normal Distribution](#page-1066-1) [Appendix 4: Critical Values for the](#page-1068-1) *t*-Test [Appendix 5: Critical Values for the](#page-1069-1) *F*-Test [Appendix 6: Critical Values for Dixon's](#page-1071-1) *Q*-Test
[Appendix 7: Critical Values for Grubb's Test](#page-1072-1)
Many of... | {
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Although Table 4.15 does not include a value for t(0.05, 99), we can approximate its value by using the values for t(0.05, 60) and t(0.05, 100) and by assuming a linear change in its value.
$$t(0.05,99) = t(0.05,60) - \frac{39}{40} \{ t(0.05,60) - t(0.05,100) \}$$
$$t(0.05,99) = 2.000 - \frac{39}{40} \{ 2.000 - 1.9... | {
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Click [here](#page-134-0) to return to the chapter.
#### **Practice Exercise 4.12**
You will find small differences between the values you obtain using Excel's built in functions and the worked solutions in the chapter. These differences arise because Excel does not round off the results of intermediate calculati... | {
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```
> data = runif(100, min = 0, max = 0)
> data
[1] 18.928795 80.423589 39.399693 23.757624 30.088554
[6] 76.622174 36.487084 62.186771 81.115515 15.726404
[11] 85.765317 53.994179 7.919424 10.125832 93.153308
[16] 38.079322 70.268597 49.879331 73.115203 99.329723
[21] 48.203305 33.093579 73.410984 75.128703 98.6821... | {
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- 5A [Analytical Standards](#page-171-1)
- 5B [Calibrating the Signal \(](#page-173-1)*Stotal*)
- 5C [Determining the Sensitivity \(](#page-173-2)*kA*)
- 5D [Linear Regression and Calibration Curves](#page-186-1)
- 5E [Compensating for the Reagent Blank \(](#page-201-1)*Sreag*)
- 5F [Using Excel and R for a Regression ... | {
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In either case, the balance automatically adjusts $S_{total}$ to match $S_{std}$ .
We also must calibrate our instruments. For example, we can evaluate a spectrophotometer's accuracy by measuring the absorbance of a carefully prepared solution of 60.06 mg/L $K_2Cr_2O_7$ in 0.0050 M $H_2SO_4$ , using 0.0050 M $... | {
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In [Figure](#page-174-1) [5.2](#page-174-1), for example, the value of *kA* is greatest when the analyte's concentration is small and it decreases continuously for higher concentrations of analyte. The value of *kA* at any point along the calibration curve in [Figure 5.2](#page-174-1) is the slope at that point. In ei... | {
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The matrix for the external standards in Figure 5.3, for example, is dilute ammonia. Because the $Cu (NH_3)_4^{2+}$ complex absorbs more strongly than $Cu^{2+}$ , adding ammonia increases the signal's magnitude. If we fail to add the same amount of ammonia to our samples, then we will introduce a proportional determ... | {
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In this case the final volume after the standard addition is $V_o + V_{std}$ and equation 5.7, equation 5.8, and equation 5.9 become
$$S_{samp} = k_A C_A$$
$$S_{spike} = k_A \left( C_A \frac{V_o}{V_o + V_{std}} + C_{std} \frac{V_{std}}{V_o + V_{std}} \right)$$
$$\frac{S_{samp}}{C_A} = \frac{S_{spike}}{C_A \frac... | {
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The equation for the calibration curve in Figure 5.7a is
$$S_{std} = 0.0854 \times V_{std} + 0.1478$$
What is the concentration of Mn<sup>2+</sup> in this sample? Compare your answer to the data in <u>Figure 5.7b</u>, for which the calibration curve is
$$S_{std} = 0.0425 \times C_{std}(V_{std}/V_{f}) + 0.1478$$ ... | {
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#### 5D Linear Regression and Calibration Curves
In a single-point external standardization we determine the value of $k_A$ by measuring the signal for a single standard that contains a known concentration of analyte. Using this value of $k_A$ and our sample's signal, we then calculate the concentration of anal... | {
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where $b_0$ and $b_1$ are estimates for the *y*-intercept and the slope, and $\widehat{y}$ is the predicted value of *y* for any value of *x*. Because we assume that all uncertainty is the result of indeterminate errors in *y*, the difference between *y* and $\widehat{y}$ for each value of *x* is the **RESIDU... | {
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$$s_{b_1} = \sqrt{\frac{ns_r^2}{n\sum_{i=1}^n x_i^2 - \left(\sum_{i=1}^n x_i\right)^2}} = \sqrt{\frac{s_r^2}{\sum_{i=1}^n (x_i - \overline{x})^2}}$$
5.20
$$s_{b_0} = \sqrt{\frac{s_r^2 \sum_{i=1}^n x_i^2}{n \sum_{i=1}^n x_i^2 - \left(\sum_{i=1}^n x_i\right)^2}} = \sqrt{\frac{s_r^2 \sum_{i=1}^n x_i^2}{n \sum_{i=1}^n ... | {
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Knowing the value of $s_{CA}$ , the confidence interval for the analyte's concentration is
$$\mu_{C_A} = C_A \pm ts_{C_A}$$
where $\mu_{C_A}$ is the expected value of $C_A$ in the absence of determinate errors, and with the value of t is based on the desired level of confidence and n–2 degrees of freedom.
##... | {
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For example, a trend toward larger residual errors at higher concentrations, [Figure 5.13b,](#page-197-1) suggests that the indeterminate errors affecting the signal are not independent of the analyte's concentration. [In Figure 5.13c,](#page-197-1) the residual errors are not random, which suggests we cannot model the... | {
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| $x_i$ | $y_i$ | $w_{i}$ | $w_i x_i$ | $w_i y_i$ | $w_i x_i^2$ | $w_i x_i y_i$ |
|-------|-------|---------|-----------|-----------|-------------|---------------|
| 0.000 | 0.00 | 2.8339 | 0.0000 | 0.0000 | 0.0000 | 0.0000 |
| 0.100 | 12.36 | 2.8339 | 0.2834 | 35.0270 | 0.0283 | 3.5027... | {
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#### **5E Compensating for the Reagent Blank (***Sreag***)**
Thus far in our discussion of strategies for standardizing analytical methods, we have assumed that a suitable reagent blank is available to correct for signals arising from sources other than the analyte. We did not, however ask an important question: "W... | {
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#### **5F Using Excel and R for a Regression Analysis**
Although the calculations in this chapter are relatively straightforward consisting, as they do, mostly of summations—it is tedious to work through problems using nothing more than a calculator. Both Excel and R include functions for completing a linear regres... | {
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The take-home lesson here is simple: do not fall in love with the correlation coefficient!
The second table in Figure 5.16 is entitled *ANOVA*, which stands for analysis of variance. We will take a closer look at ANOVA in Chapter 14. For now, it is sufficient to understand that this part of Excel's summary provides i... | {
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To examine our data and the regression line, we use the **plot** command, which takes the following general form
plot(*x*, *y*, optional arguments to control style)
where *x* and *y* are the objects that contain our data, and the **abline** command
abline(*object*, optional arguments to control style)
where *ob... | {
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$$lm(y - x, weights = object)$$
Let's use this command to complete [Example 5.12.](#page-198-0) First, we need to create an object that contains the weights, which in R are the reciprocals of the standard deviations in *y*, (*syi* ) –2. Using the data from [Example 5.12,](#page-198-0) we enter
> syi=c(0.02, 0.02,... | {
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Analysis of the sample yields signals for the analyte and the internal standard of 0.274 and 0.198, respectively. Report the analyte's concentration in the sample.
- 7. For each of the pair of calibration curves shown in Figure 5.26, select the calibration curve that uses the more appropriate set of standards. Briefly ... | {
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Statis.* **1973**, *27*, 17-21.
- (a) An unweighted linear regression analysis for the three data sets gives nearly identical results. To three significant figures, each data set has a slope of 0.500 and a *y*-intercept of 3.00. The standard deviations in the slope and the *y*-intercept are 0.118 and 1.125 for each d... | {
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| $x_i$ | ${\cal Y}_i$ | $x_i y_i$ | $x_i^2$ |
|-----------------------|--------------|------------------------|------------------------|
| 0.000 | 0.00 | 0.000 | 0.000 |
| $1.55 \times 10^{-3}$ | 0.050 | $7.7... | {
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| $x_i$ | ${\cal Y}_i$ | $\widehat{\mathcal{Y}}_i$ | $y_i - \widehat{y}_i$ |
|-----------------------|--------------|---------------------------|-----------------------|
| 0.000 | 0.00 | 0.0015 | -0.0015 |
| $1.55 \times 10^{-3}$ | 0.050 ... | {
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0.1 ' ' 1
Residual standard error: 0.001996 on 4 degrees of freedom
Multiple R-Squared: 0.9996, Adjusted R-squared: 0.9995
F-statistic: 9690 on 1 and 4 DF, p-value: 6.386e-08
> samp=c(0.114, 0.114, 0.114)
> inverse.predict(model,samp,alpha=0.05)
$Prediction
[1] 0.003805234
$`Standard Error`
[1] 4.771723e-05
$Confidence... | {
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- 6A [Reversible Reactions and Chemical Equilibria](#page-225-1)
- 6B [Thermodynamics and Equilibrium Chemistry](#page-226-1)
- 6C [Manipulating Equilibrium Constants](#page-228-1)
- 6D [Equilibrium Constants for Chemical Reactions](#page-229-1)
- [6E Le Châtelier's Principle](#page-239-1)
- 6F [Ladder Diagrams](#page-... | {
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"Header 3": "Chapter Overview",
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Reactions that produce a large number of simple, gaseous products usually have a positive $\Delta S$ .
**Figure 6.1** Graph showing how the masses of Ca<sup>2+</sup> and CaCO<sub>3</sub> change as a function of time during the precipitation of CaCO<sub>3</sub>. The dashed line indicat... | {
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We usually write a precipitation reaction as a net ionic equation, which shows only the precipitate and those ions that form the precipitate; thus, the precipitation reaction for PbCl2 is
$$Pb^{2+}(aq) + 2Cl^{-}(aq) \Rightarrow PbCl_{2}(s)$$
When we write the equilibrium constant for a precipitation reaction, we fo... | {
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"Header 3": "Chapter Overview",
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$$HCO_3^-(aq) + H_2O(l) \Rightarrow H_3O^+(aq) + CO_3^{2-}(aq)$$
6.8
$$HCO_3^-(aq) + H_2O(l) \Rightarrow OH^-(aq) + H_2CO_3(aq)$$
6.9
A species that is both a proton donor and a proton acceptor is called AMPHIPROTIC. Whether an amphiprotic species behaves as an acid or as a base depends on the equilibrium constan... | {
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Remember that equation 6.14 applies to a conjugate acid—base pair only. The conjugate acid of $\rm H_2\,PO_4^-$ is $\rm H_3PO_4^-$ , not $\rm HPO_4^{2^-}$ .
#### **Practice Exercise 6.2**
Using Appendix 11, calculate $K_b$ values for hydrogen oxalate, $HC_2O_4^-$ , and oxalate, $C_2O_4^{2-}$ .
Click here ... | {
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We can divide a redox reaction, such as reaction 6.22, into separate HALF-REACTIONS that show the oxidation and the reduction processes.
$$H_2C_2O_4(aq) + 2H_2O(l) = 2CO_2(g) + 2H_3O^+(aq) + 2e^-$$
$Fe^{3+}(aq) + e^- = Fe^{2+}(aq)$
It is important to remember, however, that an oxidation reaction and a reduction... | {
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For the reaction in Practice Exercise 6.4, we could replace $H^+$ with $H_3O^+$ and increase the stoichiometric coefficient for $H_2O$ from 4
#### **Practice Exercise 6.4**
For the following reaction at 25 °C
$$5Fe^{2+}(aq) + MnO_4^-(aq) + 8H^+(aq) =$$
$5Fe^{3+}(aq) + Mn^{2+}(aq) + 4H_2O(l)$
calculate (... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
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If we concentrate the solution of $Ag(NH_3)^+_2$ by evaporating some of the solvent, equilibrium is reestablished in the opposite direction. This is a general conclusion that we can apply to any reaction. Increasing volume always favors the direction that produces the greatest number of particles, and decreasing volu... | {
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"Header 3": "Chapter Overview",
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The solution's final composition depends on which spe-
$$O_{2}N$$
$O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O_{-}$ $O... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 2005,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
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#### Practice Exercise 6.6
Using Figure 6.5, predict the approximate pH and the composition of the solution formed by mixing together 0.090 moles of *p*-nitrophenolate and 0.040 moles of acetic acid.
Click <u>here</u> to review your answer to this exercise.
Figure 6.6 Acid–base la... | {
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For example, the first three stepwise formation constants for the reaction of $\rm Zn^{2+}$ with $\rm NH_3$
$$Zn^{2+}(aq) + NH_3(aq) \Rightarrow Zn(NH_3)^{2+}(aq) \quad K_1 = 1.6 \times 10^2$$
$Zn(NH_3)^{2+}(aq) + NH_3(aq) \Rightarrow Zn(NH_3)^{2+}(aq) \quad K_2 = 1.95 \times 10^2$
$Zn(NH_3)^{2+}(aq) + NH_3(aq) ... | {
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"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
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At equilibrium the solution is saturated with Pb(IO<sub>3</sub>)<sub>2</sub>, which means simply that no more solid can dissolve. How do we determine the equilibrium concentrations of Pb<sup>2+</sup> and IO<sub>3</sub><sup>-</sup>, and what is the molar solubility of Pb(IO<sub>3</sub>)<sub>2</sub> in this saturated sol... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 2028,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
The molar solubility of $Pb(IO_3)_2$ is equal to the additional concentration of $Pb^{2+}$ in solution, or $7.9 \times 10^{-4}$ mol/L. As expected, we find that $Pb(IO_3)_2$ is less soluble in the presence of a solution that already contains one of its ions. This is known as the COMMON ION EFFECT.
As outlin... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 2015,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
#### Example 6.11
Write mass balance equations and a charge balance equation for a 0.10 M solution of NaHCO<sub>3</sub>.
#### SOLUTION
It is easier to keep track of the species in solution if we write down the reactions that define the solution's composition. These reactions are the dissolution of a soluble sal... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 1977,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
For our problem, the equation's roots are
$$x = \frac{-6.8 \times 10^{-4} \pm \sqrt{(6.8 \times 10^{-4})^2 - (4)(1)(-6.8 \times 10^{-4})}}{(2)(1)}$$
$$x = \frac{-6.8 \times 10^{-4} \pm 5.22 \times 10^{-2}}{2}$$
$$x = 2.57 \times 10^{-2}$$
or $-2.64 \times 10^{-2}$
Only the positive root is chemically significant... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 1285,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
These equations are $K_{a2}$ and $K_{b2}$ for alanine
$$K_{a2} = \frac{[H_3O^+][L^-]}{[HL]}$$
$$K_{b2} = \frac{K_{w}}{K_{a1}} = \frac{[OH^{-}][H_{2}L^{+}]}{[HL]}$$
the $K_{\rm w}$ equation
$$K_{\rm w} = [\mathrm{H}_3\mathrm{O}^+][\mathrm{OH}^-]$$
a mass balance equation for alanine
$$C_{\rm HL} = [{\r... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 2046,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
Because $NH_3$ is a weak base we may reasonably assume that most uncomplexed ammonia remains as $NH_3$ ; thus
$$[NH_4^+] << [NH_3]$$
**Assumption Three.** Because $K_{\rm sp}$ for AgI is significantly smaller than $\beta_2$ for Ag(NH<sub>3</sub>) $_2^+$ , the solubility of AgI probably is small enough that v... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 2036,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
$$K_{\rm a} = \frac{[{\rm H}_3{\rm O}^+][{\rm A}^-]}{[{\rm HA}]}$$
6.54
$$K_{\rm w} = [\mathrm{H}_3\mathrm{O}^+][\mathrm{OH}^-]$$
The remaining three equations are mass balance equations for HA and Na<sup>+</sup>
$$C_{\text{HA}} + C_{\text{NaA}} = [\text{HA}] + [\text{A}^{-}]$$
6.55
$$C_{\text{NaA}} = [\text{... | {
"Header 1": "Equilibrium Chemistry",
"Header 3": "Chapter Overview",
"token_count": 1975,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
} |
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