Chapter 10

A solution's transmittance is \(35.0 \%\). What is the transmittance if you dilute \(25.0 \mathrm{~mL}\) of the solution to \(50.0 \mathrm{~mL}\) ?

A chemical deviation to Beer's law may occur if the concentration of an absorbing species is affected by the position of an equilibrium reaction. Consider a weak acid, HA, for which \(K_{\mathrm{a}}\) is \(2 \times 10^{-5}\). Construct Beer's law calibration curves of absorbance versus the total concentration of weak acid \(\left(C_{\text {total }}=[\mathrm{HA}]+\left[\mathrm{A}^{-}\right]\right),\) using values for \(C_{\text {total }}\) of \(1.0 \times 10^{-5}, 3.0 \times 10^{-5}, 5.0 \times 10^{-5}, 7.0 \times 10^{-5}, 9.0 \times 10^{-5}, 11 \times 10^{-5}\), and \(13 \times 10^{-5} \mathrm{M}\) for the following sets of conditions and comment on your results: (a) \(\varepsilon_{\mathrm{HA}}=\varepsilon_{\mathrm{A}^{-}}=2000 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ;\) unbuffered solution. (b) \(\varepsilon_{\mathrm{HA}}=2000 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ; \varepsilon_{\mathrm{A}^{-}}=500 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ;\) unbuffered solution. (c) \(\varepsilon_{\mathrm{HA}}=2000 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ; \varepsilon_{\mathrm{A}^{-}}=500 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ;\) solution buffered to a \(\mathrm{pH}\) of 4.5 Assume a constant pathlength of \(1.00 \mathrm{~cm}\) for all samples.

One instrumental limitation to Beer's law is the effect of polychromatic radiation. Consider a line source that emits radiation at two wavelengths, \(\lambda^{\prime}\) and \(\lambda^{\prime \prime}\). When treated separately, the absorbances at these wavelengths, \(A^{\prime}\) and \(A^{\prime \prime}\), are $$ A^{\prime}=-\log \frac{P_{\mathrm{T}}^{\prime}}{P_{0}^{\prime}}=\varepsilon^{\prime} b C \quad A^{\prime \prime}=-\log \frac{P_{\mathrm{T}}^{\prime \prime}}{P_{0}^{\prime \prime}}=\varepsilon^{\prime \prime} b C $$ If both wavelengths are measured simultaneously the absorbance is $$ A=-\log \frac{\left(P_{\mathrm{T}}^{\prime}+P_{\mathrm{T}}^{\prime \prime}\right)}{\left(P_{0}^{\prime}+P_{0}^{\prime \prime}\right)} $$ (a) Show that if the molar absorptivities at \(\lambda^{\prime}\) and \(\lambda^{\prime \prime}\) are the same \(\left(\varepsilon^{\prime}=\varepsilon^{\prime \prime}=\varepsilon\right),\) then the absorbance is equivalent to $$ A=\varepsilon b C $$ (b) Construct Beer's law calibration curves over the concentration range of zero to \(1 \times 10^{-4} \mathrm{M}\) using \(\varepsilon^{\prime}=1000 \mathrm{M}^{-1} \mathrm{~cm}^{-1}\) and \(\varepsilon^{\prime \prime}=1000\) \(\mathrm{M}^{-1} \mathrm{~cm}^{-1},\) and \(\varepsilon^{\prime}=1000 \mathrm{M}^{-1} \mathrm{~cm}^{-1}\) and \(\varepsilon^{\prime \prime}=100 \mathrm{M}^{-1} \mathrm{~cm}^{-1} .\) As- sume a value of \(1.00 \mathrm{~cm}\) for the pathlength and that \(P_{0}^{\prime}=P_{0}^{\prime \prime}=1\). Explain the difference between the two curves.

A second instrumental limitation to Beer's law is stray radiation. The following data were obtained using a cell with a pathlength of \(1.00 \mathrm{~cm}\) when stray light is insignificant \(\left(P_{\text {strav }}=0\right)\). $$ \begin{array}{cc} \text { [analyte] }(\mathrm{mM}) & \text { absorbance } \\ \hline 0.00 & 0.00 \\ 2.00 & 0.40 \\ 4.00 & 0.80 \\ 6.00 & 1.20 \\ 8.00 & 1.60 \\ 10.00 & 2.00 \end{array} $$ Calculate the absorbance of each solution when \(P_{\text {stray }}\) is \(5 \%\) of \(P_{0},\) and plot Beer's law calibration curves for both sets of data. Explain any differences between the two curves. (Hint: Assume \(P_{0}\) is \(\left.100\right)\).

One method for the analysis of \(\mathrm{Fe}^{3+}\), which is used with a variety of sample matrices, is to form the highly colored \(\mathrm{Fe}^{3+}\) -thioglycolic acid complex. The complex absorbs strongly at \(535 \mathrm{nm}\). Standardizing the method is accomplished using external standards. A 10.00 -ppm \(\mathrm{Fe}^{3+}\) working standard is prepared by transferring a 10 -mL aliquot of a 100.0 ppm stock solution of \(\mathrm{Fe}^{3+}\) 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 working solution into separate 50 -mL volumetric flasks, each of which contains \(5 \mathrm{~mL}\) of thioglycolic acid, \(2 \mathrm{~mL}\) of \(20 \% \mathrm{w} / \mathrm{v}\) ammonium citrate, and \(5 \mathrm{~mL}\) of \(0.22 \mathrm{M} \mathrm{NH}_{3}\). After diluting to volume and mixing, the absorbances of the external standards are measured against an appropriate blank. Samples are prepared for analysis by taking a portion known to contain approximately \(0.1 \mathrm{~g}\) of \(\mathrm{Fe}^{3+},\) dissolving it in a minimum amount of \(\mathrm{HNO}_{3}\), and diluting to volume in a \(1-\mathrm{L}\) volumetric flask. A 1.00 -mL aliquot of this solution is transferred to a \(50-\mathrm{mL}\) volumetric flask, along with \(5 \mathrm{~mL}\) of thioglycolic acid, \(2 \mathrm{~mL}\) of \(20 \% \mathrm{w} / \mathrm{v}\) ammonium citrate, and \(5 \mathrm{~mL}\) of \(0.22 \mathrm{M} \mathrm{NH}_{3}\) and diluted to volume. The absorbance of this solution is used to determine the concentration of \(\mathrm{Fe}^{3+}\) in the sample. (a) What is an appropriate blank for this procedure? (b) Ammonium citrate is added to prevent the precipitation of \(\mathrm{Al}^{3+}\). What is the effect on the reported concentration of iron in the sample if there is a trace impurity of \(\mathrm{Fe}^{3+}\) in the ammonium citrate? (c) Why does the procedure specify that the sample contain approximately \(0.1 \mathrm{~g}\) of \(\mathrm{Fe}^{3+}\) ? (d) Unbeknownst to the analyst, the \(100-\mathrm{mL}\) volumetric flask used to prepare the 10.00 ppm working standard of \(\mathrm{Fe}^{3+}\) has a volume that is significantly smaller than \(100.0 \mathrm{~mL}\). What effect will this have on the reported concentration of iron in the sample?

A spectrophotometric method for the analysis of iron has a linear calibration curve for standards of \(0.00,5.00,10.00,15.00,\) and 20.00 \(\mathrm{mg} \mathrm{Fe} / \mathrm{L}\). An iron ore sample that is \(40-60 \% \mathrm{w} / \mathrm{w}\) is analyzed by this method. An approximately \(0.5-\mathrm{g}\) sample is taken, dissolved in a minimum of concentrated HCl, and diluted to \(1 \mathrm{~L}\) in a volumetric flask using distilled water. A \(5.00 \mathrm{~mL}\) aliquot is removed with a pipet. To what volume- \(10,25,50,100,250,500,\) or \(1000 \mathrm{~mL}\) - should it be diluted to minimize the uncertainty in the analysis? Explain.

Lozano-Calero and colleagues developed a method for the quantitative analysis of phosphorous in cola beverages based on the formation of the blue-colored phosphomolybdate complex, \(\left(\mathrm{NH}_{4}\right)_{3}\left[\mathrm{PO}_{4}\left(\mathrm{MoO}_{3}\right)_{12}\right] .^{21}\) The complex is formed by adding \(\left(\mathrm{NH}_{4}\right)_{6} \mathrm{Mo}_{7} \mathrm{O}_{24}\) to the sample in the presence of a reducing agent, such as ascorbic acid. The concentration of the complex is determined spectrophotometrically at a wavelength of \(830 \mathrm{nm}\), using an external standards calibration curve. In a typical analysis, a set of standard solutions that contain known amounts of phosphorous is prepared by placing appropriate volumes of a 4.00 ppm solution of \(\mathrm{P}_{2} \mathrm{O}_{5}\) in a \(5-\mathrm{mL}\) volumetric flask, adding \(2 \mathrm{~mL}\) of an ascorbic acid reducing solution, and diluting to volume with distilled water. Cola beverages are prepared for analysis by pouring a sample into a beaker and allowing it to stand for \(24 \mathrm{~h}\) to expel the dissolved \(\mathrm{CO}_{2}\). A \(2.50-\mathrm{mL}\) sample of the degassed sample is transferred to a 50 -mL volumetric flask and diluted to volume. A \(250-\mu \mathrm{L}\) aliquot of the diluted sample is then transferred to a \(5-\mathrm{mL}\) volumetric flask, treated with \(2 \mathrm{~mL}\) of the ascorbic acid reducing solution, and diluted to volume with distilled water. (a) The authors note that this method can be applied only to noncolored cola beverages. Explain why this is true. (b) How might you modify this method so that you can apply it to any cola beverage? (c) Why is it necessary to remove the dissolved gases? (d) Suggest an appropriate blank for this method? (e) The author's report a calibration curve of $$ A=-0.02+\left(0.72 \mathrm{ppm}^{-1}\right) \times C_{\mathrm{P}_{2} \mathrm{O}_{5}} $$ A sample of Crystal Pepsi, analyzed as described above, yields an absorbance of \(0.565 .\) What is the concentration of phosphorous, reported as ppm \(\mathrm{P}\), in the original sample of Crystal Pepsi?

EDTA forms colored complexes with a variety of metal ions that may serve as the basis for a quantitative spectrophotometric method of analysis. The molar absorptivities of the EDTA complexes of \(\mathrm{Cu}^{2+}, \mathrm{Co}^{2+}\), and \(\mathrm{Ni}^{2+}\) at three wavelengths are summarized in the following table (all values of \(\varepsilon\) are in \(\left.\mathrm{M}^{-1} \mathrm{~cm}^{-1}\right).\) $$ \begin{array}{cccc} \text { metal } & \varepsilon_{462.9} & \varepsilon_{732.0} & \varepsilon_{378.7} \\ \hline \mathrm{Co}^{2+} & 15.8 & 2.11 & 3.11 \\ \mathrm{Cu}^{2+} & 2.32 & 95.2 & 7.73 \\ \mathrm{Ni}^{2+} & 1.79 & 3.03 & 13.5 \end{array} $$ Using this information determine the following: (a) The concentration of \(\mathrm{Cu}^{2+}\) in a solution that has an absorbance of 0.338 at a wavelength of \(732.0 \mathrm{nm}\). (b) The concentrations of \(\mathrm{Cu}^{2+}\) and \(\mathrm{Co}^{2+}\) in a solution that has an absorbance of 0.453 at a wavelength of \(732.0 \mathrm{nm}\) and 0.107 at a wavelength of \(462.9 \mathrm{nm}\) (c) The concentrations of \(\mathrm{Cu}^{2+}, \mathrm{Co}^{2+},\) and \(\mathrm{Ni}^{2+}\) in a sample that has an absorbance of 0.423 at a wavelength of \(732.0 \mathrm{nm}, 0.184\) at a wavelength of \(462.9 \mathrm{nm}\), and 0.291 at a wavelength of \(378.7 \mathrm{nm}\). The pathlength, \(b\), is \(1.00 \mathrm{~cm}\) for all measurements.

The concentration of phenol in a water sample is determined by using steam distillation to separate the phenol from non-volatile impurities, followed by reacting the phenol in the distillate with 4 -aminoantipyrine and \(\mathrm{K}_{3} \mathrm{Fe}(\mathrm{CN})_{6}\) at \(\mathrm{pH} 7.9\) to form a colored antipyrine dye. A phenol standard with a concentration of 4.00 ppm has an absorbance of 0.424 at a wavelength of \(460 \mathrm{nm}\) using a \(1.00 \mathrm{~cm}\) cell. A water sample is steam distilled and a \(50.00-\mathrm{mL}\) aliquot of the distillate is placed in a 100 -mL volumetric flask and diluted to volume with distilled water. The absorbance of this solution is 0.394 . What is the concentration of phenol (in parts per million) in the water sample?

Saito describes a quantitative spectrophotometric procedure for iron based on a solid-phase extraction using bathophenanthroline in a poly(vinyl chloride) membrane. \({ }^{22}\) In the absence of \(\mathrm{Fe}^{2+}\) the membrane is colorless, but when immersed in a solution of \(\mathrm{Fe}^{2+}\) and \(\mathrm{I}^{-},\) the membrane develops a red color as a result of the formation of an \(\mathrm{Fe}^{2+}\) -bathophenanthroline complex. A calibration curve determined using a set of external standards with known concentrations of \(\mathrm{Fe}^{2+}\) gave a standardization relationship of $$ A=\left(8.60 \times 10^{3} \mathrm{M}^{-1}\right) \times\left[\mathrm{Fe}^{2+}\right] $$ What is the concentration of iron, in \(\mathrm{mg} \mathrm{Fe} / \mathrm{L},\) for a sample with an absorbance of 0.100 ?

In the DPD colorimetric method for the free chlorine residual, which is reported as \(\mathrm{mg} \mathrm{Cl}_{2} / \mathrm{L},\) the oxidizing power of free chlorine converts the colorless amine \(\mathrm{N}, \mathrm{N}\) -diethyl- \(p\) -phenylenediamine to a colored dye that absorbs strongly over the wavelength range of \(440-580 \mathrm{nm}\). Analysis of a set of calibration standards gave the following results. $$ \begin{array}{cc} \mathrm{mg} \mathrm{Cl}_{2} / \mathrm{L} & \text { absorbance } \\ \hline 0.00 & 0.000 \\ 0.50 & 0.270 \\ 1.00 & 0.543 \\ 1.50 & 0.813 \\ 2.00 & 1.084 \end{array} $$ A sample from a public water supply is analyzed to determine the free chlorine residual, giving an absorbance of \(0.113 .\) What is the free chlorine residual for the sample in \(\mathrm{mg} \mathrm{Cl}_{2} / \mathrm{L}\) ?

Lin and Brown described a quantitative method for methanol based on its effect on the visible spectrum of methylene blue. \({ }^{23}\) In the absence of methanol, methylene blue has two prominent absorption bands at 610 \(\mathrm{nm}\) and \(663 \mathrm{nm}\), which correspond to the monomer and the dimer, respectively. In the presence of methanol, the intensity of the dimer's absorption band decreases, while that for the monomer increases. For concentrations of methanol between 0 and \(30 \% \mathrm{v} / \mathrm{v},\) the ratio of the two absorbance, \(A_{663} / A_{610}\), is a linear function of the amount of methanol. Use the following standardization data to determine the \(\% \mathrm{v} / \mathrm{v}\) methanol in a sample if \(A_{610}\) is 0.75 and \(A_{663}\) is 1.07 . $$ \begin{array}{cccc} \% \mathrm{v} / \mathrm{v} \text { methanol } & A_{663} / A_{610} & \% \mathrm{v} / \mathrm{v} \text { methanol } & A_{663} / A_{610} \\ \hline 0.0 & 1.21 & 20.0 & 1.62 \\ 5.0 & 1.29 & 25.0 & 1.74 \\ 10.0 & 1.42 & 30.0 & 1.84 \\ 15.0 & 1.52 & & \end{array} $$

The concentration of the barbiturate barbital in a blood sample is determined by extracting \(3.00 \mathrm{~mL}\) of blood with \(15 \mathrm{~mL}\) of \(\mathrm{CHCl}_{3}\). The chloroform, which now contains the barbital, is extracted with \(10.0 \mathrm{~mL}\) of \(0.45 \mathrm{M} \mathrm{NaOH}(\mathrm{pH} \approx 13)\). A 3.00-mL sample of the aqueous extract is placed in a 1.00 -cm cell and an absorbance of 0.115 is measured. The \(\mathrm{pH}\) of the sample in the absorption cell is then adjusted to approximately 10 by adding \(0.50 \mathrm{~mL}\) of \(16 \% \mathrm{w} / \mathrm{v} \mathrm{NH}_{4} \mathrm{Cl}\), giving an absorbance of 0.023 . When \(3.00 \mathrm{~mL}\) of a standard barbital solution with a concentration of \(3 \mathrm{mg} / 100 \mathrm{~mL}\) is taken through the same procedure, the absorbance at \(\mathrm{pH} 13\) is 0.295 and the absorbance at a \(\mathrm{pH}\) of 10 is 0.002. Report the mg barbital/100 mL in the sample.

Jones and Thatcher developed a spectrophotometric method for analyzing analgesic tablets that contain aspirin, phenacetin, and caffeine. \(^{24}\) The sample is dissolved in \(\mathrm{CHCl}_{3}\) and extracted with an aqueous solution of \(\mathrm{NaHCO}_{3}\) to remove the aspirin. After the extraction is complete, the chloroform is transferred to a \(250-\mathrm{mL}\) volumetric flask and diluted to volume with \(\mathrm{CHCl}_{3} .\) A \(2.00-\mathrm{mL}\) portion of this solution is then diluted to volume in a \(200-\mathrm{mL}\) volumetric flask with \(\mathrm{CHCl}_{3}\). The absorbance of the final solution is measured at wavelengths of \(250 \mathrm{nm}\) and \(275 \mathrm{nm}\), at which the absorptivities, in \(\mathrm{ppm}^{-1} \mathrm{~cm}^{-1},\) for caffeine and phenacetin are $$ \begin{array}{lcc} & \mathrm{a}_{250} & \mathrm{a}_{275} \\ \hline \text { caffeine } & 0.0131 & 0.0485 \\ \text { phenacetin } & 0.0702 & 0.0159 \end{array} $$ Aspirin is determined by neutralizing the \(\mathrm{NaHCO}_{3}\) in the aqueous solution and extracting the aspirin into \(\mathrm{CHCl}_{3}\). The combined extracts are diluted to \(500 \mathrm{~mL}\) in a volumetric flask. A 20.00 -mL portion of the solution is placed in a 100 -mL volumetric flask and diluted to volume with \(\mathrm{CHCl}_{3}\). The absorbance of this solution is measured at \(277 \mathrm{nm}\), where the absorptivity of aspirin is \(0.00682 \mathrm{ppm}^{-1} \mathrm{~cm}^{-1}\). An analgesic tablet treated by this procedure is found to have absorbances of 0.466 at \(250 \mathrm{nm}, 0.164\) at \(275 \mathrm{nm}\), and 0.600 at \(277 \mathrm{nm}\) when using a cell with a \(1.00 \mathrm{~cm}\) pathlength. Report the milligrams of aspirin, caffeine, and phenacetin in the analgesic tablet.

The concentration of \(\mathrm{SO}_{2}\) in a sample of air is determined by the \(p\) -rosaniline method. The \(\mathrm{SO}_{2}\) is collected in a 10.00 -mL solution of \(\mathrm{HgCl}_{4}^{2-},\) where it reacts to form \(\mathrm{Hg}\left(\mathrm{SO}_{3}\right)_{2}^{2-},\) by pulling air through the solution for 75 min at a rate of \(1.6 \mathrm{~L} / \mathrm{min}\). After adding \(p\) -rosaniline and formaldehyde, the colored solution is diluted to \(25 \mathrm{~mL}\) in a volumetric flask. The absorbance is measured at \(569 \mathrm{nm}\) in a \(1-\mathrm{cm}\) cell, yielding a value of \(0.485 .\) A standard sample is prepared by substituting a 1.00 -mL sample of a standard solution that contains the equivalent of \(15.00 \mathrm{ppm} \mathrm{SO}_{2}\) for the air sample. The absorbance of the standard is found to be 0.181 . Report the concentration of \(\mathrm{SO}_{2}\) in the air in \(\mathrm{mg}\) \(\mathrm{SO}_{2} / \mathrm{L}\). The density of air is \(1.18 \mathrm{~g} /\) liter.

The following table lists molar absorptivities for the Arsenazo complexes of copper and barium. \({ }^{27}\) Suggest appropriate wavelengths for analyzing mixtures of copper and barium using their Arsenzao complexes. $$ \begin{array}{ccc} \text { wavelength }(\mathrm{nm}) & \varepsilon_{\mathrm{Cu}}\left(\mathrm{M}^{-1} \mathrm{~cm}^{-1}\right) & \varepsilon_{\mathrm{Ba}}\left(\mathrm{M}^{-1} \mathrm{~cm}^{-1}\right) \\ \hline 595 & 11900 & 7100 \\ 600 & 15500 & 7200 \\ 607 & 18300 & 7400 \\ 611 & 19300 & 6900 \\ 614 & 19300 & 7000 \\ 620 & 17800 & 7100 \\ 626 & 16300 & 8400 \\ 635 & 10900 & 9900 \\ 641 & 7500 & 10500 \\ 645 & 5300 & 10000 \\ 650 & 3500 & 8600 \\ 655 & 2200 & 6600 \\ 658 & 1900 & 6500 \\ 665 & 1500 & 3900 \\ 670 & 1500 & 2800 \\ 680 & 1800 & 1500 \end{array} $$

The stoichiometry of a metal-ligand complex, \(\mathrm{ML}_{n}\), is determined by the method of continuous variations. A series of solutions is prepared in which the combined concentrations of \(\mathrm{M}\) and \(\mathrm{L}\) are held constant at \(5.15 \times 10^{-4} \mathrm{M}\). The absorbances of these solutions are measured at a wavelength where only the metal-ligand complex absorbs. Using the following data, determine the formula of the metal-ligand complex. $$ \begin{array}{ccc} \text { mole fraction } \mathrm{M} & \text { mole fraction } \mathrm{L} & \text { absorbance } \\ \hline 1.0 & 0.0 & 0.001 \\ 0.9 & 0.1 & 0.126 \\ 0.8 & 0.2 & 0.260 \\ 0.7 & 0.3 & 0.389 \\ 0.6 & 0.4 & 0.515 \\ 0.5 & 0.5 & 0.642 \\ 0.4 & 0.6 & 0.775 \\ 0.3 & 0.7 & 0.771 \\ 0.2 & 0.8 & 0.513 \\ 0.1 & 0.9 & 0.253 \\ 0.0 & 1.0 & 0.000 \end{array} $$

The stoichiometry of a metal-ligand complex, \(\mathrm{ML}_{n}\), is determined by the mole-ratio method. A series of solutions are prepared in which the metal's concentration is held constant at \(3.65 \times 10^{-4} \mathrm{M}\) and the ligand's concentration is varied from \(1 \times 10^{-4} \mathrm{M}\) to \(1 \times 10^{-3} \mathrm{M}\). Using the following data, determine the stoichiometry of the metal-ligand complex. $$ \begin{array}{cccc} \text { [ligand] (M) } & \text { absorbance } & \text { [ligand] (M) } & \text { absorbance } \\ \hline 1.0 \times 10^{-4} & 0.122 & 6.0 \times 10^{-4} & 0.752 \\ 2.0 \times 10^{-4} & 0.251 & 7.0 \times 10^{-4} & 0.873 \\ 3.0 \times 10^{-4} & 0.376 & 8.0 \times 10^{-4} & 0.937 \\ 4.0 \times 10^{-4} & 0.496 & 9.0 \times 10^{-4} & 0.962 \\ 5.0 \times 10^{-4} & 0.625 & 1.0 \times 10^{-3} & 1.002 \end{array} $$

Kawakami and Igarashi developed a spectrophotometric method for nitrite based on its reaction with 5,10,15,20 -tetrakis( 4 -aminophenyl) porphrine (TAPP). As part of their study they investigated the stoichiometry of the reaction between TAPP and \(\mathrm{NO}_{2}^{-}\). The following data are derived from a figure in their paper. \({ }^{29}\) $$ \begin{array}{ccc} {[\mathrm{TAPP}](\mathrm{M})} & {\left[\mathrm{NO}_{2}^{-}\right](\mathrm{M})} & \text { absorbance } \\ \hline 8.0 \times 10^{-7} & 0 & 0.227 \\ 8.0 \times 10^{-7} & 4.0 \times 10^{-8} & 0.223 \\ 8.0 \times 10^{-7} & 8.0 \times 10^{-8} & 0.211 \\ 8.0 \times 10^{-7} & 1.6 \times 10^{-7} & 0.191 \\ 8.0 \times 10^{-7} & 3.2 \times 10^{-7} & 0.152 \\ 8.0 \times 10^{-7} & 4.8 \times 10^{-7} & 0.127 \\ 8.0 \times 10^{-7} & 6.4 \times 10^{-7} & 0.107 \\ 8.0 \times 10^{-7} & 8.0 \times 10^{-7} & 0.092 \\ 8.0 \times 10^{-7} & 1.6 \times 10^{-6} & 0.058 \\ 8.0 \times 10^{-7} & 2.4 \times 10^{-6} & 0.045 \\ 8.0 \times 10^{-7} & 3.2 \times 10^{-6} & 0.037 \\ 8.0 \times 10^{-7} & 4.0 \times 10^{-6} & 0.034 \end{array} $$ What is the stoichiometry of the reaction?

The equilibrium constant for an acid-base indicator is determined by preparing three solutions, each of which has a total indicator concentration of \(1.35 \times 10^{-5} \mathrm{M}\). The \(\mathrm{pH}\) of the first solution is adjusted until it is acidic enough to ensure that only the acid form of the indicator is present, yielding an absorbance of \(0.673 .\) The absorbance of the second solution, whose \(\mathrm{pH}\) is adjusted to give only the base form of the indicator, is 0.118 . The \(\mathrm{pH}\) of the third solution is adjusted to 4.17 and has an absorbance of 0.439 . What is the acidity constant for the acid-base indicator?

Suppose you need to prepare a set of calibration standards for the spectrophotometric analysis of an analyte that has a molar absorptivity of \(1138 \mathrm{M}^{-1} \mathrm{~cm}^{-1}\) at a wavelength of \(625 \mathrm{nm}\). To maintain an acceptable precision for the analysis, the \(\% \mathrm{~T}\) for the standards should be between \(15 \%\) and \(85 \%\) (a) What is the concentration for the most concentrated and for the least concentrated standard you should prepare, assuming a 1.00 \(\mathrm{cm}\) sample cell. (b) Explain how you will analyze samples with concentrations that are \(10 \mu \mathrm{M}, 0.1 \mathrm{mM}\), and \(1.0 \mathrm{mM}\) in the analyte.

Hobbins reported the following calibration data for the flame atomic absorption analysis for phosphorous. \({ }^{30}\) $$ \begin{array}{cc} \text { mg P/L } & \text { absorbance } \\ \hline 2130 & 0.048 \\ 4260 & 0.110 \\ 6400 & 0.173 \\ 8530 & 0.230 \end{array} $$ To determine the purity of a sample of \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\), a 2.469 -g sample is dissolved and diluted to volume in a 100 -mL volumetric flask. Analysis of the resulting solution gives an absorbance of \(0.135 .\) What is the purity of the \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) ?

Bonert and Pohl reported results for the atomic absorption analysis of several metals in the caustic suspensions produced during the manufacture of soda by the ammonia-soda process. \(^{31}\) (a) The concentration of Cu is determined by acidifying a \(200.0-\mathrm{mL}\) sample of the caustic solution with \(20 \mathrm{~mL}\) of concentrated \(\mathrm{HNO}_{3}\), adding \(1 \mathrm{~mL}\) of \(27 \% \mathrm{w} / \mathrm{v} \mathrm{H}_{2} \mathrm{O}_{2},\) and boiling for \(30 \mathrm{~min} .\) The resulting solution is diluted to \(500 \mathrm{~mL}\) in a volumetric flask, filtered, and analyzed by flame atomic absorption using matrix matched standards. The results for a typical analysis are shown in the following table. $$ \begin{array}{ccc} \text { solution } & \mathrm{mg} \mathrm{Cu} / \mathrm{L} & \text { absorbance } \\ \hline \text { blank } & 0.000 & 0.007 \\ \text { standard } 1 & 0.200 & 0.014 \\ \text { standard } 2 & 0.500 & 0.036 \\ \text { standard } 3 & 1.000 & 0.072 \\ \text { standard } 4 & 2.000 & 0.146 \\ \text { sample } & & 0.027 \end{array} $$ Determine the concentration of \(\mathrm{Cu}\) in the caustic suspension. (b) The determination of \(\mathrm{Cr}\) is accomplished by acidifying a \(200.0-\mathrm{mL}\) sample of the caustic solution with \(20 \mathrm{~mL}\) of concentrated \(\mathrm{HNO}_{3}\), adding \(0.2 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) and boiling for \(30 \mathrm{~min}\). The Cr is isolated from the sample by adding \(20 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\), producing a precipitate that includes the chromium as well as other oxides. The precipitate is isolated by filtration, washed, and transferred to a beaker. After acidifying with \(10 \mathrm{~mL}\) of \(\mathrm{HNO}_{3}\), the solution is evaporated to dryness. The residue is redissolved in a combination of \(\mathrm{HNO}_{3}\) and \(\mathrm{HCl}\) and evaporated to dryness. Finally, the residue is dissolved in \(5 \mathrm{~mL}\) of \(\mathrm{HCl}\), filtered, diluted to volume in a 50 -mL volumetric flask, and analyzed by atomic absorption using the method of standard additions. The atomic absorption results are summarized in the following table. $$ \begin{array}{lcc} {\text { sample }} & \mathrm{mg} \mathrm{Cr}_{\text {added }} / \mathrm{L} & \text { absorbance } \\ \hline \text { blank } & & 0.001 \\ \text { sample } & & 0.045 \\ \text { standard addition } 1 & 0.200 & 0.083 \\ \text { standard addition } 2 & 0.500 & 0.118 \\ \text { standard addition } 3 & 1.000 & 0.192 \end{array} $$ Report the concentration of \(\mathrm{Cr}\) in the caustic suspension.

The concentration of \(\mathrm{Na}\) in plant materials are determined by flame atomic emission. The material to be analyzed is prepared by grinding, homogenizing, and drying at \(103^{\circ} \mathrm{C}\). A sample of approximately \(4 \mathrm{~g}\) 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 \(550^{\circ} \mathrm{C}\) for several hours. After cooling to room temperature the residue is dissolved by adding \(2 \mathrm{~mL}\) of \(1: 1 \mathrm{HNO}_{3}\) and evaporated to dryness. The residue is redissolved in \(10 \mathrm{~mL}\) of \(1: 9 \mathrm{HNO}_{3},\) filtered and diluted to \(50 \mathrm{~mL}\) in a volumetric flask. The following data are obtained during a typical analysis for the concentration of \(\mathrm{Na}\) in a \(4.0264-\mathrm{g}\) sample of oat bran. $$ \begin{array}{lcc} {\text { sample }} & \mathrm{mg} \mathrm{Na} / \mathrm{L} & \text { emission (arbitrary units) } \\ \hline \text { blank } & 0.00 & 0.0 \\ \text { standard 1 } & 2.00 & 90.3 \\ \text { standard } 2 & 4.00 & 181 \\ \text { standard } 3 & 6.00 & 272 \\ \text { standard } 4 & 8.00 & 363 \\ \text { standard } 5 & 10.00 & 448 \\ \text { sample } & & 238 \end{array} $$ Report the concentration of sodium in the sample of oat bran as \mug Na/g sample.

Yan and colleagues developed a method for the analysis of iron based its formation of a fluorescent metal-ligand complex with the ligand 5-(4-methylphenylazo)-8-aminoquinoline. \({ }^{33}\) In the presence of the surfactant cetyltrimethyl ammonium bromide the analysis is carried out using an excitation wavelength of \(316 \mathrm{nm}\) with emission monitored at \(528 \mathrm{nm}\). Standardization with external standards gives the following calibration curve. $$ I_{f}=-0.03+\left(1.594 \mathrm{mg}^{-1} \mathrm{~L}\right) \times \frac{\mathrm{mg} \mathrm{Fe}^{3+}}{\mathrm{L}} $$ A 0.5113 -g sample of dry dog food is ashed to remove organic materials, and the residue dissolved in a small amount of \(\mathrm{HCl}\) and diluted to volume in a 50 -mL volumetric flask. Analysis of the resulting solution gives a fluorescent emission intensity of \(5.72 .\) Determine the \(\mathrm{mg} \mathrm{Fe} / \mathrm{L}\) in the sample of dog food.

A solution of \(5.00 \times 10^{-5} \mathrm{M} 1,3\) -dihydroxynaphthelene in \(2 \mathrm{M} \mathrm{NaOH}\) has a fluorescence intensity of 4.85 at a wavelength of \(459 \mathrm{nm}\). What is the concentration of 1,3 -dihydroxynaphthelene in a solution that has a fluorescence intensity of 3.74 under identical conditions?

The following data is recorded for the phosphorescent intensity of several standard solutions of benzo[a] pyrene. $$ \begin{array}{cc} \text { [benzo[a]pyrene] }(\mathrm{M}) & \text { emission intensity } \\ \hline 0 & 0.00 \\ 1.00 \times 10^{-5} & 0.98 \\ 3.00 \times 10^{-5} & 3.22 \\ 6.00 \times 10^{-5} & 6.25 \\ 1.00 \times 10^{-4} & 10.21 \end{array} $$ What is the concentration of benzo[a] pyrene in a sample that yields a phosphorescent emission intensity of \(4.97 ?\)

The concentration of acetylsalicylic acid, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4},\) in aspirin tablets is determined by hydrolyzing it to the salicylate ion, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{O}_{2}^{-},\) and determining its concentration spectrofluorometrically. A stock standard solution is prepared by weighing \(0.0774 \mathrm{~g}\) of salicylic acid, \(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\), into a 1-L volumetric flask and diluting to volume. A set of calibration standards is prepared by pipeting \(0,2.00,4.00,6.00,8.00,\) and 10.00 \(\mathrm{mL}\) of the stock solution into separate \(100-\mathrm{mL}\) volumetric flasks that contain \(2.00 \mathrm{~mL}\) of \(4 \mathrm{M} \mathrm{NaOH}\) and diluting to volume. Fluorescence is measured at an emission wavelength of \(400 \mathrm{nm}\) using an excitation wavelength of \(310 \mathrm{nm}\) with results shown in the following table. $$ \begin{array}{cc} \text { mL of stock solution } & \text { emission intensity } \\ \hline 0.00 & 0.00 \\ 2.00 & 3.02 \\ 4.00 & 5.98 \\ 6.00 & 9.18 \\ 8.00 & 12.13 \\ 10.00 & 14.96 \end{array} $$ Several aspirin tablets are ground to a fine powder in a mortar and pestle. A 0.1013 -g portion of the powder is placed in a 1-L volumetric flask and diluted to volume with distilled water. A portion of this solution is filtered to remove insoluble binders and a 10.00 -mL aliquot transferred to a 100 -mL volumetric flask that contains \(2.00 \mathrm{~mL}\) of \(4 \mathrm{M}\) \(\mathrm{NaOH}\). After diluting to volume the fluorescence of the resulting solution is 8.69 . What is the \(\% \mathrm{w} / \mathrm{w}\) acetylsalicylic acid in the aspirin tablets?

Selenium (IV) in natural waters is determined by complexing with ammonium pyrrolidine dithiocarbamate and extracting into \(\mathrm{CHCl}_{3}\). This step serves to concentrate the \(\mathrm{Se}(\mathrm{IV})\) and to separate it from \(\mathrm{Se}(\mathrm{VI})\). The \(\mathrm{Se}(\mathrm{IV})\) is then extracted back into an aqueous matrix using \(\mathrm{HNO}_{3} .\) After complexing with 2,3 -diaminonaphthalene, the complex is extracted into cyclohexane. Fluorescence is measured at \(520 \mathrm{nm}\) following its excitation at \(380 \mathrm{nm}\). Calibration is achieved by adding known amounts of \(\mathrm{Se}(\mathrm{IV})\) to the water sample before beginning the analysis. Given the following results what is the concentration of \(\mathrm{Se}(\mathrm{IV})\) in the sample. \begin{tabular}{cc} {\([\) Se (IV)] added (nM) } & emission intensity \\ \hline 0.00 & 323 \\ 2.00 & 597 \\ 4.00 & 862 \\ 6.00 & 1123 \end{tabular}