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Figure 9.42 shows an example of the titration curve for a mixture of Fe<sup>2+</sup> and Sn<sup>2+</sup>
The balanced reactions for this analysis are: $C_6H_8O_6(aq) + I_3^-(aq) \longrightarrow$ $3I^-(aq) + C_6H_6O_6(aq) + 2H^+(aq)$ $I_3^-(aq) + 2S_2O_3^{2-}(aq) \longrightarrow$
$S_4 O_6^{2-}(aa) + 3I^{-}(aa)$ ... | {
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For example, after adding 35.0 mL of titrant
$$\begin{split} [\mathrm{Ag^{+}}] &= \frac{(\mathrm{mol}\ \mathrm{Ag^{+}})_{\mathrm{added}} - (\mathrm{mol}\ \mathrm{Cl^{-}})_{\mathrm{initial}}}{\mathrm{total}\ \mathrm{volume}} = \frac{M_{\mathrm{Ag}}\ V_{\mathrm{Ag}} - M_{\mathrm{Cl}}\ V_{\mathrm{Cl}}}{V_{\mathrm{Ag}} +... | {
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In the Volhard Method for $Ag^+$ using KSCN as the titrant, for example, a small amount of $Fe^{3+}$ is added to the titrand's solution. The titration's end point is the formation of the reddish-colored $Fe(SCN)^{2+}$ complex. The titration is carried out in an acidic solution to prevent the precipitation of $Fe... | {
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After adding 50.00 mL of 0.05619 M AgNO<sub>3</sub> and allowing the precipitate to form, the remaining silver is back titrated with 0.05322 M KSCN, requiring 35.14 mL to reach the end point. Report the %w/w I<sup>-</sup> in the sample.
#### SOLUTION
There are two precipitates in this analysis: AgNO<sub>3</sub> and... | {
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For your convenience, here are hyperlinks to the appendices containing these constants
[Appendix 10: Solubility Products](#page-1077-1)
[Appendix 11: Acid Dissociation Constants](#page-1081-1)
[Appendix 12: Metal-Ligand Formation Constants](#page-1089-1)
[Appendix 13: Standard State Reduction Potentials](#page-... | {
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For your convenience, here are hyperlinks to the appendices containing these constants [Appendix 10: Solubility Products](#page-1077-1) [Appendix 11: Acid Dissociation Constants](#page-1081-1)
- [Appendix 12: Metal-Ligand Formation Constants](#page-1089-1) [Appendix 13: Standard State Reduction Potentials](#page-1094-1... | {
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| Volume of | | Volume of | | Volume of | |
|-----------|------|-----------|-------|-----------|-------|
| NaOH (ml) | pН | NaOH (mL) | pН | NaOH (ml) | pН |
| 1.00 | 1.83 | 24.00 | 4.45 | 47.00 | 12.14 |
| 2.00 | 1.86 | 25.00 | 4.53 | 48.00 | 12.17 |
| 3.00 |... | {
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Given that the proteins in grains average 17.54% w/w N, report the %w/w protein in the sample.
- 19. The concentration of $SO_2$ in air is determined by bubbling a sample of air through a trap that contains $H_2O_2$ . Oxidation of $SO_2$ by $H_2O_2$ results in the formation of $H_2SO_4$ , which is then determin... | {
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If the error is systematic, then indicate whether the experimentally determined molarity for NaOH is too high or too low. The standardization reaction is
$$C_8 H_5 O_4^-(\it{aq}) \, + \, OH^-(\it{aq}) \longrightarrow C_8 H_4 O_4^-(\it{aq}) \, + \, H_2 O(\it{b})$$
- (a) The balance used to weigh KHP is not properly ... | {
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In a typical analysis a 5.00-mL sample from an electroplating bath is transferred to a 250-mL Erlenmeyer flask, and treated with 100 mL of H<sub>2</sub>O, 5 mL of 20% w/v NaOH and 5 mL of 10% w/v KI. The sample is titrated with 0.1012 M AgNO<sub>3</sub>, requiring 27.36 mL to reach the end point as signaled by the form... | {
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For your convenience, here are hyperlinks to the appendices containing these constants
Appendix 10: Solubility Products
Appendix 11: Acid Dissociation Constants
Appendix 12: Metal-Ligand Formation Constants
Appendix 13: Standard State Reduction Potentials
$$C_{\text{EDTA}} = [H_6 Y^{2^+}] + [H_5 Y^+] + [H_4 Y... | {
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A 25-mL aliquot of the sample is transferred to a 250-mL volumetric flask and diluted to volume with distilled water. A 25-mL aliquot of the diluted sample is added to an Erlenmeyer flask, diluted with 200 mL of distilled water, and acidified with 20 mL of 25% v/v $H_2SO_4$ . The resulting solution is titrated with a ... | {
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There is a complication, however, because AgCl is more soluble than AgSCN.
- (a) Why do the relative solubilities of AgCl and AgSCN lead to a titration error?
- (b) Is the resulting titration error a positive or a negative determinate error?
- (c) How might you modify the procedure to eliminate this source of determina... | {
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For example, after adding 10.0 mL of HCl
$$[NH_3] = \frac{(0.125 \text{ M}) (25.0 \text{ mL}) - (0.0625 \text{ M}) (10.0 \text{ mL})}{25.0 \text{ mL} + 10.0 \text{ mL}} = 0.0714 \text{ M}$$
$$[NH_4^+] = \frac{(0.0625 \text{ M}) (10.0 \text{ mL})}{25.0 \text{ mL} + 10.0 \text{ mL}} = 0.0179 \text{ M}$$
$$pH = 9.244 + ... | {
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The titration, therefore, is to the first equivalence point for which the moles of NaOH equal the moles of salicylic acid; thus
$$\begin{array}{c} (0.1354~\text{M})\,(0.02192~\text{L}) \,=\, 2.968\times 10^{-3}~\text{mol NaOH} \\ \\ 2.968\times 10^{-3}~\text{mol NaOH}\times \frac{1~\text{mol }C_7H_6O_3}{\text{mol NaO... | {
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To evaluate the titration curve, therefore, we need the conditional formation constant for CdY<sup>2-</sup>, which, from <u>Table 9.11</u> is $K_f' = 1.1 \times 10^{16}$ . Note that the conditional formation constant is larger in the absence of an auxiliary complexing agent.
The titration's equivalence point require... | {
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The two points after the equivalence point for a pH of 7 ( $V_{\rm EDTA}$ =27.5 mL, pCd=12.2 and $V_{\rm EDTA}$ =50 mL, pCd=13.2) are plotted using the log $K_{\rm f}$ ′ of 13.2 for CdY<sup>2-</sup>. The two points after the equivalence point for a pH of 10 ( $V_{\rm EDTA}$ =27.5 mL, pCd=15.0 and $V_{\rm EDTA}$ =50 m... | {
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For example, after adding 40.0 mL of titrant, the concentrations of $Tl^+$ and $Tl^{3+}$ are
$$[Tl^{+}] = \frac{(0.0500 \text{ M}) (50.0 \text{ mL})}{50.0 \text{ mL} + 40.0 \text{ mL}} = 0.0278 \text{ M}$$
$$[Tl^{3+}] = \frac{(0.100 \text{ M}) (40.0 \text{ mL}) - (0.050 \text{ M}) (50.0 \text{ mL})}{50.0 \text{ m... | {
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A conservation of electrons for the titration, therefore, requires that two
moles of KMnO<sub>4</sub> (10 moles of $e^{-}$ ) react with five moles of Na<sub>2</sub>C<sub>2</sub>O<sub>4</sub> (10 moles of $e^{-}$ ).
The moles of KMnO<sub>4</sub> used to reach the end point is
$(0.0400~M~KMnO_4)\,(0.03562~L)=1.42... | {
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For example, after adding 35.0 mL of titrant
$$[Cl^{-}] = \frac{(0.100 \,\mathrm{M}) (35.0 \,\mathrm{mL}) - (0.0500 \,\mathrm{M}) (50.0 \,\mathrm{mL})}{50.0 \,\mathrm{mL} + 35.0 \,\mathrm{mL}}$$
$$= 1.18 \times 10^{-2} \,\mathrm{M}$$
or a pCl of 1.93. To find the concentration of $Ag^+$ we use the $K_{sp}$ for ... | {
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- 10A [Overview of Spectroscopy](#page-541-1)
- [10B Spectroscopy Based on Absorption](#page-553-1)
- 10C [UV/Vis and IR Spectroscopy](#page-563-1)
- 10D [Atomic Absorption Spectroscopy](#page-595-1)
- 10E [Emission Spectroscopy](#page-608-1)
- 10F [Photoluminescent Spectroscopy](#page-608-2)
- 10G [Atomic Emission Spe... | {
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What are the frequency and the wavenumber for this line?
#### SOLUTION
The frequency and wavenumber of the sodium D line are
$$\nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \text{ m/s}}{589 \times 10^{-9} \text{m}} = 5.09 \times 10^{14} \text{s}^{-1}$$
$$\overline{\nu} = \frac{1}{\lambda} = \frac{1}{589 \tim... | {
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Several representative spectroscopic techniques are listed in [Table 10.2.](#page-547-0)
#### **10A.3 Basic Components of Spectroscopic Instruments**
The spectroscopic techniques in [Table 10.1](#page-545-0) and [Table 10.2](#page-547-0) use instruments that share several common basic components, including a source... | {
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A purple filter, for example, removes the complementary color green from 500–560 nm.
**Figure 10.11** Example showing the effect of the wavelength selector's effective bandwidth on resolution and noise. The spectrum with the smaller effective bandwidth (on the right) has a better resolu... | {
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One advantage of the Si photodiode is that it is easy to miniaturize. Groups of photodiodes are gathered together in a linear array that contains 64--4096 individual photodiodes. With a width of 25 $\mu$ m per diode, a linear array of 2048 photodiodes requires only 51.2 mm of linear space. By placing a **Photodiode** ... | {
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The bonds and functional groups that give rise to the absorption of ultraviolet and visible radiation are called chromophores.
Many transition metal ions, such as Cu2<sup>+</sup> and Co2<sup>+</sup>, form colorful solutions because the metal ion absorbs visible light. The transitions that give rise to this absorption... | {
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As we learned from Figure 10.20, atomic absorption lines are very narrow. Even with a high quality monochromator, the effective bandwidth for a continuum source is $100{-}1000\times$ greater than the width of an atomic absorption line. As a result, little radiation from a continuum source is absorbed when it passes t... | {
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If $\varepsilon_{\rm HA}$ and $\varepsilon_{\rm A}$ — have the same value at the selected wavelength, then equation 10.10 simplifies to
$$A = \varepsilon_{\text{A}^-}bC_{\text{total}} = \varepsilon_{\text{HA}}bC_{\text{total}}$$
Alternatively, if $\alpha_{\rm HA}$ has the same value for all standard solutions,... | {
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Fixed wavelength single-beam spectrophotometers are not practical for recording spectra because manually adjusting the wavelength and recalibrating the spectrophotometer is awkward and time-consuming. The accuracy of a single-beam spectrophotometer is limited by the stability of its source and detector over time.
**D... | {
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*Double-beam spectrophotometer.* Infrared instruments using a monochromator for wavelength selection use double-beam optics similar to that shown in [Figure 10.27](#page-566-0). Double-beam optics are preferred over single-beam optics because the sources and detectors for infrared radiation are less stable than those... | {
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When chlorine is added to water the portion available for disinfection is called the chlorine residual. There are two forms of chlorine residual. The free chlorine residual includes $Cl_2$ , HOCl, and OCl<sup>-</sup>. The combined chlorine residual, which forms from the reaction of NH<sub>3</sub> with HOCl, consists... | {
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4-aminoantipyrene
$$H_2NO_3S$$
$N=N$ $NH_2^+$ $C_2H_4NH_3^+$ red azo dye
| Table 10.7 Examples of the Molecular UV/Vis Analysis of Clinical Samples | | ... | {
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A strong oxidizing agent will oxidize some $Fe^{2+}$ to $Fe^{3+}$ . Because $Fe(phen)_3^{3+}$ does not absorb as strongly as $Fe(phen)_3^{2+}$ , the absorbance is smaller than expected, which produces a negative determinate error. The excess hydroxylamine reacts with the oxidizing agents, removing them from the... | {
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#### SOLUTION
Substituting known values into equation 10.11 and equation 10.12 gives
$$A_{550} = 0.183 = 9970C_{Fe} + 34C_{Cu}$$
$A_{396} = 0.109 = 84C_{Fe} + 856C_{Cu}$
To determine $C_{\text{Fe}}$ and $C_{\text{Cu}}$ we solve the first equation for $C_{\text{Cu}}$
$$C_{\text{Cu}} = \frac{0.183 - 9970... | {
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#### Example 10.7
Figure 10.35 shows visible absorbance spectra for a standard solution of 0.0250 M ${\rm Cr}^{3+}$ , a standard solution of 0.0750 M ${\rm Co}^{2+}$ , and a mixture that contains unknown concentrations of each ion. The data for these spectra are shown here.<sup>10</sup>
| $\lambda$ (nm) | $A_{\rm... | {
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The interpretation of UV/ Vis and IR spectra receives adequate coverage elsewhere in the chemistry curriculum, notably in organic chemistry, and is not considered further in this text.
With the availability of computerized data acquisition and storage it is possible to build digital libraries of standard reference sp... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
The data for this problem is adapted from Meloun, M.; Havel, J.; Högfeldt, E. *Computation of Solution Equilibria*, Ellis Horwood: Chichester, England, 1988, p. 236.
| XL | absorbance | XL | absorbance | XL | absorbance | XL | absorbance |
|--------|------------|--------|------------|--------|--------... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
The indicator's total concentration, C, is given by a mass balance equation
$$C = [HIn] + [In^{-}]$$
10.16
Solving equation 10.16 for [HIn] and substituting into equation 10.15 gives
$$A = \varepsilon_{\text{HIn}}b(C - [\text{In}^{-}]) + \varepsilon_{\text{In}^{-}}b[\text{In}^{-}]$$
which we simplify to
$$A =... | {
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Examples of the type of problems that are encountered include the presence of particulates in the sample that scatter radiation, and the presence of interferents that react with analytical reagents. In the latter case the interferent may react to form an absorbing species, which leads to a positive determinate error. I... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
See <u>Figure 10.24</u> for an example of how the choice of wavelength affects a calibration curve's sensitivity.
beam instrument equipped with variable slit widths, and operating over an extended range of wavelengths. Fourier transform infrared spectrometers can be obtained for as little as \$15,000–\$20,000, alth... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
Flame microsampling is accomplished using a micropipet to place 50–250 μL of sample in a Teflon funnel connected to the nebulizer, or by
| Table 10.9 | Fuels and Oxidants Used for Flame Combustion | | |
|-------------|----------------------------------------------|------------------------|--|... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
| Table 10.10 Concentration of Analyte That Yields an Absorbance of 0.20 | | | | | |
|------------------------------------------------------------------------|-----------------------------------|----------------------------|--|--|--|
| ... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
One of the most common methods for BACKGROUND CORRECTION is to use a continuum source, such as a $D_2$ lamp. Because a $D_2$ lamp is a continuum source, absorbance of its radiation by the analyte's narrow absorption line is negligible. Only the background, therefore, absorbs radiation from the $D_2$ lamp. Both ... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
| wavelength | slit width | mg Cu/L for | |
|------------|------------|-------------|---------------|
| (nm) | (nm) | A=0.20 | P0 (relative) |
| 217.9 | 0.2 | 15 | 3 |
| 218.2 | 0.2 | 15 | 3 |
| 222.6 | 0.2 | ... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
Spectroscopic methods based on photoluminescence are the subject of the next section and atomic emission is covered in Section 10G.
#### 10F Photoluminescence Spectroscopy
Photoluminescence is divided into two categories: fluorescence and phosphorescence. A pair of electrons that occupy the same electronic ground s... | {
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A decrease in the solvent's viscosity decreases U*<sup>f</sup>* for similar reasons. For an analyte with acidic or basic functional groups, a change in pH may change the analyte's structure and its fluorescent properties.
As shown in [Figure 10.48,](#page-610-0) fluorescence may return the molecule to any of several ... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
One approach is to place a drop of a solution that contains the analyte on a small disc of filter paper. After drying the sample under a heat lamp, the sample is placed in the spectrofluorometer for analysis. Other solid substrates include silica gel, alumina, sodium acetate, and sucrose. This approach is particularly ... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
The concentration of chloride in urine typically ranges from 4600–6700 ppm Cl– . Explain how this procedure prevents an interference from chloride.
The procedure uses two extractions. In the first of these extractions, quinine is separated from urine by extracting it into a mixture of The best way to appreciate the t... | {
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#### **SELECTIVITY**
The selectivity of fluorescence and phosphorescence is superior to that of absorption spectrophotometry for two reasons: first, not every compound that absorbs radiation is fluorescent or phosphorescent; and, second, selectivity between an analyte and an interferent is possible if there is a di... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
#### **Selecting the Wavelength and Slit Width**
The choice of wavelength is dictated by the need for sensitivity and the need to avoid interferences from the emission lines of other constituents in the sample. Because an analyte's atomic emission spectrum has an abundance of emission lines—particularly when using ... | {
"Header 1": "The approach outlined here for a multi-wavelength linear regression uses a single standard solution for each analyte. A more rigorous approach uses multiple standards for each analyte. The math behind the analysis of such data—which we call a multiple linear regression—is beyond the level of this text.... |
and the practical details discussed in this section is to carefully examine a typical analytical method. Although each method is unique, the following description of the determination of sodium in salt substitutes provides an instructive example of a typical procedure. The description here is based on Goodney, D. E. *J... | {
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#### ACCURACY
When spectral and chemical interferences are insignificant, atomic emission can achieve quantitative results with accuracies of 1–5%. For flame emission, accuracy frequently is limited by chemical interferences. Because the higher temperature of a plasma source gives rise to more emission lines, accur... | {
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#### **Selecting <sup>a</sup> Wavelength for the Incident Radiation**
The choice of wavelength is based primarily on the need to minimize potential interferences. For turbidimetry, where the incident radiation is transmitted through the sample, a monochromator or filter allow us to avoid wavelengths that are absorb... | {
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Although each method is unique, the following description of the determination of sulfate in water provides an instructive example of a typical procedure. The description here is based on Method 4500–SO<sub>4</sub><sup>2-</sup>–C in Standard Methods for the Analysis of Water and Wastewater, American Public Health Assoc... | {
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| | | | molar | |
|-----------------------|------------|------|--------------------|------------|
| [analyte] | | | absorptivity | pathlength |
| (M) | absorbance | %T | $(M^{-1} cm^{-1})$ | (cm) ... | {
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A 10.00-ppm Fe<sup>3+</sup> working standard is prepared by transferring a 10-mL aliquot of a 100.0 ppm stock solution of Fe<sup>3+</sup> to a 100-mL volumetric flask and diluting to volume. Calibration standards of 1.00, 2.00, 3.00, 4.00, and 5.00 ppm are prepared by transferring appropriate amounts of the 10.0 ppm wo... | {
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<sup>22</sup> In the absence of $Fe^{2+}$ the membrane is colorless, but when immersed in a solution of $Fe^{2+}$ and $I^-$ , the membrane develops a red color as a result of the formation of an $Fe^{2+}$ -bathophenanthroline complex. A calibration curve determined using a set of external standards with known con... | {
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A calibration curve is prepared by filling a 10-cm IR gas cell with a known pressure of CO and measuring the absorbance using an FT-IR, giving a calibration equation of
$$A = -1.1 \times 10^{-4} + (9.9 \times 10^{-4}) \times P_{\text{CO}}$$
Samples are prepared by using a vacuum manifold to fill the gas cell. After... | {
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absorbance
absorbance
| wavelength (nm) | PAR | Cu standard | Zn standard | mixture |
|-----------------|-------|-------------|-------------|---------|
| 480 | 0.211 | 0.698 | 0.971 | 0.656 |
| 496 | 0.137 | 0.732 | 1.018 | 0.668 |
| 510 | 0.100 | ... | {
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| pH | absorbance | pH | absorbance |
|------|------------|------|------------|
| 1.53 | 0.010 | 4.88 | 0.193 |
| 2.20 | 0.010 | 5.09 | 0.227 |
| 3.66 | 0.035 | 5.69 | 0.288 |
| 4.11 | 0.072 | 7.20 | 0.317 |
| 4.35 | 0.103 | 7.78 | 0.317 |
| 4.75 | 0.169 | ... | {
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The material to be analyzed is prepared by grinding, homogenizing, and drying at 103 <sup>o</sup> C. A sample of approximately 4 g is transferred to a quartz crucible and heated on a hot plate to char the organic material. The sample is heated in a muffle furnace at 550<sup>o</sup> C for several hours. After cooling to... | {
"Header 1": "The best way to appreciate the theoretical",
"token_count": 1959,
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#### 10L Solutions to Practice Exercises
#### **Practice Exercise 10.1**
The frequency and wavenumber for the line are
$$\nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8 \text{ m/s}}{656.3 \times 10^{-9} \text{ m}} = 4.57 \times 10^{14} \text{ s}^{-1}$$
$$\overline{\nu} = \frac{1}{\lambda} = \frac{1}{656.3 \t... | {
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Click here to return to the chapter.
The value of $K_a$ is
$$K_{\rm a} = (1.00 \times 10^{-6}) \times \frac{0.225 - 0.000}{0.680 - 0.225} = 4.95 \times 10^{-7}$$
Click here to return to the chapter.
#### **Practice Exercise 10.10**
To determine $K_a$ we use equation 10.21... | {
"Header 1": "The best way to appreciate the theoretical",
"token_count": 408,
"source_pdf": "datasets/websources/biochem/clairvoyance.ipynb.pdf"
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- 11A [Overview of Electrochemistry](#page-661-1)
- 11B [Potentiometric Methods](#page-667-1)
- 11C [Coulometric Methods](#page-704-1)
- 11D [Voltammetric and Amperometric Methods](#page-719-1)
- 11E [Key Terms](#page-750-1)
- 11F [Chapter Summary](#page-751-1)
- 11G [Problems](#page-752-1)
- 11H [Solutions to Practice... | {
"Header 1": "Electrochemical Methods",
"Header 3": "Chapter Overview",
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of a metal-ligand complex in bulk solution, such as $Fe(OH)^{2+}$ , also affects the concentration of $Fe^{3+}$ .
#### **CURRENT IS A MEASURE OF RATE**
The reduction of Fe<sup>3+</sup> to Fe<sup>2+</sup> consumes an electron, which is drawn from the electrode. The oxidation of another species, perhaps the solve... | {
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"Header 3": "Chapter Overview",
"token_count": 916,
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This point bears repeating: It is impor-
#### **POTENTIOMETERS**
To measure the potential of an electrochemical cell under a condition of zero current we use a **POTENTIOMETER**. Figure 11.3 shows a schematic diagram for a manual potentiometer that consists of a power supply, an electrochemical cell with a working ... | {
"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 this section we introduce the conventions for describing potentiometric electrochemical cells, and the relationship between the measured potential and the analyte's activity.
#### POTENTIOMETRIC ELECTROCHEMICAL CELLS
A schematic diagram of a typical potentiometric electrochemical cell is shown in Figure 11.7. Th... | {
"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... |
Using equation 11.4, the potential of the anode and cathode in <u>Figure 11.7</u> are
$$E_{ ext{anode}} = E_{ ext{Zn}^{2+}/ ext{Zn}}^{\circ} - rac{0.05916}{2} \log rac{1}{a_{ ext{Zn}^{2+}}}$$
$E_{ ext{cathode}} = E_{ ext{Ag}^{+}/ ext{Ag}}^{\circ} - rac{0.05916}{1} \log rac{1}{a_{ ext{Ao}^{+}}}$
Substituting $E_{... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
In writing the shorthand notation for an electrochemical cell we use a double slash (||) to indicate the salt bridge, suggesting a potential exists at the interface between each end of the salt bridge and the solution in which it is immersed. The origin of this potential is discussed in the following section.
#### **... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
$$AgCl(s) + e^{-} \rightleftharpoons Ag(s) + Cl^{-}(aq)$$
As is the case for the calomel electrode, the activity of Cl<sup>-</sup> determines the potential of the Ag/AgCl electrode; thus
$$E = E_{AgCI/Ag}^{\circ} - 0.05916 \log a_{CI} = +0.2223 \text{ V} - 0.05916 \log a_{CI}$$
When prepared using a saturated s... | {
"Header 1": "tant to understand that the experimental designs in Figure 11.3, Figure 11.4, and Figure 11.5 do not represent the electrochemical instruments you will find in today's analytical labs. For further information about modern electrochemical instrumentation, see this chapter's additional resources.",
"to... |
$$\operatorname{Zn}(s) + 2\operatorname{H}^{+}(aq) \Rightarrow$$
$\operatorname{H}_{2}(q) + \operatorname{Zn}^{2+}(aq)$
If we saturate the indicator electrode's half-cell with AgI, the solubility reaction
$$AgI(s) \Rightarrow Ag^{+}(aq) + I^{-}(aq)$$
determines the concentration of Ag<sup>+</sup>; thus
$$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... |
A membrane shows good selectivity for the analyte when $K_{A,I}$ is significantly less than 1.00.
Selectivity coefficients for most commercially available ion-selective electrodes are provided by the manufacturer. If the selectivity coefficient is not known, it is easy to determine its value experimentally by prepa... | {
"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... |
trodes have been developed for the analysis of Li<sup>+</sup>, K<sup>+</sup>, Rb<sup>+</sup>, Cs<sup>+</sup>, NH<sub>4</sub><sup>+</sup>, Ag<sup>+</sup>, and Tl<sup>+</sup>. Table 11.1 provides several examples.
Because an ion-selective electrode's glass membrane is very thin—it is only about 50 µm thick—they must ... | {
"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... |
As shown in <u>Figure 11.17</u>, the LaF<sub>3</sub> membrane is sealed into the end of a non-conducting plastic cylinder, which
| Table 11.2 Representative Examples of Polycrystalline Solid-<br>State Ion-Selective Electrodes | | ... | {
"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... |
One example of a liquid-based ion-selective electrode is that for Ca2<sup>+</sup>, which uses a porous plastic membrane saturated with the cation exchanger di-(*n*-decyl) phosphate. As shown in Figure 11.18, the membrane is placed at the end of a non-conducting cylindrical tube and is in contact with two reservoirs. ... | {
"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... |
Substituting equation 11.13 into equation 11.11 gives
$$E_{\text{cell}} = K' + 0.05916 \log a_{\text{CO}_2}$$
where K' is a constant that includes the constant for the pH electrode, the equilibrium constant for reaction 11.12 and the activity of $HCO_3^-$ in the inner solution.
<u>Table 11.4</u> lists the prope... | {
"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... |
| Table 11.5 Representative Examples of Potentiometric Biosensors <sup>a</sup> | | | | |
|------------------------------------------------------------------------------|-------------------------------------------------|-------------------------... | {
"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... |
If $V_{\text{std}}$ is significantly smaller than $V_{\text{samp}}$ , then we can safely ignore the change in the sample's matrix and assume that the analyte's activity coefficient is constant. Example 11.9 demonstrates how we can use a one-point standard addition to determine the concentration of analyte in a sampl... | {
"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... |
Measure the cell potential for the external standards and the samples using a F<sup>-</sup> ion-selective electrode and an appropriate reference electrode. When measuring the potential, stir the solution and allow two to three minutes to reach a stable potential. Report the concentration of F<sup>-</sup> in the toothpa... | {
"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... |
Swirl the pH electrode and allow it to equilibrate until you obtain a stable reading. Adjust the "Standardize" or "Calibrate" knob until the meter displays the correct pH. Rinse and dry the electrode, and place it in the second buffer. After the electrode equilibrates, adjust the "Slope" or "Temperature" knob until the... | {
"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... |
More details about potentiometric titrations are found in Chapter 9.
#### **11B.6 Evaluation**
#### **Scale of Operation**
The working range for most ion-selective electrodes is from a maximum concentration of 0.1–1 M to a minimum concentration of 10–5–10–11 M.10 This broad working range extends from major analyt... | {
"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... |
If the current varies with time, as it does in controlled-potential coulometry, then the total charge is
$$Q = \int_{0}^{t_{i}} i(t) dt$$
11.27
In coulometry, we monitor current as a function of time and use either equation 11.26 or equation 11.27 to calculate Q. Knowing the total charge, we then use equation 11.25... | {
"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... |
The reason we can use such a negative potential is that the reaction rate for the reduction of $H_3O^+$ to $H_2$ is very slow at a Pt electrode. This results in a significant **OVERPOTENTIAL**—the need to apply a potential more positive or a more negative than that predicted by thermodynamics—which shifts $E^0$ f... | {
"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... |
See <u>Figure 9.40</u> for the titration curve and for ferroin's color change.
Figure 11.4 shows an example of a manual galvanostat. Although a modern galvanostat uses very different circuitry, you can use Figure 11.4 and the accompanying discussion to understand how we can use the working electrode and the counter... | {
"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... |
If we apply a constant potential of +0.40 V versus the SCE, Ag(I) deposits on the electrode as Ag and the other metal ions remain in solution. When electrolysis is complete, we use the total charge to determine the amount of silver in the alloy. Next, we shift the working electrode's potential to –0.08 V versus the SCE... | {
"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... |
Second, because it is relatively easy to measure a
$3\mathbf{Z}\mathbf{n}^{2+}(aq) + K^{+}(aq) + 2\mathrm{Fe}(CN)_{6}^{4-}(aq)$
$\Rightarrow$ K<sub>2</sub>Zn<sub>3</sub>[Fe(CN)<sub>6</sub>]<sub>2</sub>(s)
Table 11.10 Representative Coulometric Titrations Using Acid-Base, Complexation, and **Precipitation Reactio... | {
"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... |
Prepare a mediator solution of approximately 0.3 M NH<sub>4</sub>Fe(SO<sub>4</sub>)<sub>2</sub>. Add 5.00 mL of sample, 2 mL of 9 M H<sub>2</sub>SO<sub>4</sub>, and 10–25 mL of the mediator solution to the working electrode's cell, and add distilled water as needed to cover the electrodes. Bubble pure N<sub>2</sub> thr... | {
"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... |
T.; Heineman, W. R., eds., Laboratory Techniques in Electroanalytical Chemistry, Marcel Dekker Inc.: New York, 1984, pp. 539–568.
a level where electrolysis of the analyte is feasible. The limiting factor in the accuracy of many controlled-potential coulometric methods of analysis is the determination of charge. With... | {
"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... |
**Figure 11.35** Approximate potential windows for mercury, platinum, and carbon (graphite) electrodes in acidic, neutral, and basic aqueous solvents. The useful potential windows are shown in **green**; potentials in **red** result in the oxidation or the reduction of the solvent or the electrode. Complied from Adam... | {
"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... |
Diffusion occurs whenever the concentration of an ion or a molecule at the surface of the electrode is different from that in bulk solution. If we apply a potential sufficient to completely reduce Fe(CN) <sup>3</sup> 6 - at the electrode surface, the result is a concentration gradient similar to that shown in [Figure 1... | {
"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... |
Let's also assume that only O initially is present in bulk solution and that we are stirring the solution. When we apply a potential that results in the reduction of O to R, the current depends on the rate at which O diffuses through the fixed diffusion layer shown in Figure 11.41. Using equation 11.36, the current, i,... | {
"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... |
**Figure 11.45** Potential-excitation signals and voltammograms for (a) normal pulse polarography, (b) differential pulse polarography, (c) staircase polarography, and (d) square-wave polarography. The current is sampled at the time intervals shown by the black rectangles. When measurin... | {
"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 adsorptive stripping voltammetry, the deposition step occurs without electrolysis. Instead, the analyte adsorbs to the electrode's surface. During deposition we maintain the electrode at a potential that enhances adsorption. For example, we can adsorb a neutral molecule on a Hg drop if we apply a potential of –0.4... | {
"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... |
For example, amperometry is ideally suited for detecting analytes in flow systems, including the *in vivo* analysis of a patient's blood or as a selective sensor for the rapid analysis of a single analyte. The portability of amperometric sensors, which are similar to potentiometric sensors, also make them ideal for fie... | {
"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... |
What is the concentration of indium and cadmium in a sample if $\Delta i_p$ is 167.0 at a potential of -0.557 V and 99.5 at a potential of -0.597V.
All potentials are relative to a saturated Ag/AgCl reference electrode.
#### SOLUTION
The change in current, $\Delta i_p$ , in differential pulse polarography is 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... |
For example, the dissolved O2 sensor described earlier is used to determine the level of dissolved oxygen and the biochemical oxygen demand, or BOD, of waters and wastewaters. The latter test—which is a measure of the amount of oxygen required by aquatic bacteria as they decompose organic matter—is important when evalu... | {
"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... |
How can we tell if a redox reaction is reversible by looking at its voltammogram? For a reversible redox reaction equation 11.43, which we repeat here, describes the relationship between potential and current for a voltammetric experiment with a limiting current.
$$E = E_{O/R}^{\circ} - \frac{0.05916}{n} \log \frac{K... | {
"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... |
SCE) |
|---------|---------------------------|
| 0.020 | -0.494 |
| 0.040 | -0.512 |
| 0.060 | -0.523 |
| 0.080 | -0.530 |
| 0.100 | -0.536 |
Determine the stoichiometry of the metal-ligand complex and its formati... | {
"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... |
The potential of a metallic electrode is the result of a redox reaction at the electrode's surface. An electrode of the first kind responds to the concentration of its cation in solution; thus, the potential of a Ag wire is determined by the activity of Ag<sup>+</sup> in solution. If another species is in equilibrium w... | {
"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... |
A potentiometric electrode for HCN uses a gas-permeable membrane, a buffered internal solution of 0.01 M KAg(CN)2, and a Ag2S ISE electrode that is immersed in the internal solution. Consider the equilibrium reactions that take place within the internal solution and derive an equation that relates the electrode's poten... | {
"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... |
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