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Chapter 10: Problem 38

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.

Short Answer

Expert verified
The dog food sample contains approximately 0.18035 mg of Fe.

Step by step solution

01

Understanding the Calibration Curve Formula

The calibration curve provided is \( I_f = -0.03 + (1.594 \, \text{mg}^{-1} \text{L}) \times \frac{\text{mg Fe}^{3+}}{\text{L}} \). This equation relates the fluorescent intensity \( I_f \) to the concentration of Fe\(^{3+}\) in mg/L.
02

Calculating the Concentration of Fe in mg/L

We are given the fluorescent emission intensity \( I_f \) as 5.72. Plug this value into the calibration curve equation to solve for the concentration:\[5.72 = -0.03 + 1.594 \cdot C \]Add 0.03 to both sides: \[5.72 + 0.03 = 1.594 \cdot C \]\[5.75 = 1.594 \cdot C \]Divide both sides by 1.594:\[C = \frac{5.75}{1.594} \]\[C \approx 3.607 \text{ mg Fe}^{3+}/\text{L} \]
03

Consideration of the Volumetric Adjustment

The concentration ( C) we calculated is based on a solution obtained by dissolving the ashed sample into a 50 mL volumetric flask. Therefore, the concentration reflects the amount of Fe in that final 50 mL solution.
04

Calculating the Total Amount of Fe in the Dog Food Sample

To find the total amount of Fe in the original 0.5113 g dog food sample, we must consider the entire diluted volume:\[\text{Total mg Fe} = 3.607 \, \text{mg Fe/L} \times 0.050 \, \text{L} \]\[\text{Total mg Fe} = 0.18035 \, \text{mg Fe} \]
05

Concluding the Result

Therefore, the sample of dog food contains approximately 0.18035 mg Fe. The result represents the amount of iron present in the initial 0.5113 g sample, post-ashing and dilution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calibration Curve
In fluorescence spectroscopy, a calibration curve is crucial for converting fluorescent intensity into concentration values. The calibration curve provides a relationship between the known concentration of a substance and the intensity of emitted light after excitation. Here, the equation given: \[ I_f = -0.03 + (1.594 \, \text{mg}^{-1} \text{L}) \times \frac{\text{mg Fe}^{3+}}{\text{L}} \]connects the intensity of fluorescence (\(I_f\)) to the measured concentration of iron (\(\text{Fe}^{3+}\)) in mg/L. The slope (1.594 mg鈦宦� L) indicates how sensitive the fluorescence intensity is to changes in iron concentration. An accurate calibration curve allows for precise measurements of unknown samples by comparing their fluorescence intensity with this preset curve. When applying this in practice, you measure the fluorescence intensity of a solution containing the sample of interest, input this value into the equation, and solve for the concentration. This is what we've done in the solution to find the concentration of iron in the dog food sample.
Iron Analysis
Iron analysis is an important part of assessing nutritional content or contamination in food products. In this problem, researchers utilized a fluorescence-based method specialized for detecting iron by forming a fluorescent complex with the reagent 5-(4-methylphenylazo)-8-aminoquinoline. The presence of a surfactant, cetyltrimethyl ammonium bromide, helps in enhancing the formation of this complex, making the detection more efficient. After the sample preparation, which includes ashing to get rid of organic matter and dissolving the remaining residue, the fluorescent intensity from the sample solution could be easily measured using fluorescence spectroscopy. This type of iron analysis is sensitive and allows low-level detection, hence very useful for checking consistent iron content in various samples.
Analytical Chemistry
Analytical chemistry involves using tools to measure and interpret substances within samples. In this case, the fluorescence spectroscopy technique is applied to determine iron concentrations in dog food. Analytical chemistry combines various methodologies, such as calibration curves and sample preparation techniques, for accurate results. Key steps include: - Sample preparation: Where the sample is treated to isolate the element of interest. - Calibration: Creating and using calibration curves for transforming instrumental responses into meaningful concentration data. - Analysis: Interpreting data to provide results relevant to the research or industry needs. This rigorous approach ensures results are reliable and can be verified by repeating the experiment, technical improvements in procedures, or by cross-verifying using different methods.

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Most popular questions from this chapter

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?

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 \(4.97 ?\)

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 \(\left.100\right)\).

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.

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.
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