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Chapter 10: Problem 34

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 \(\mathrm{Na}_{2} \mathrm{HPO}_{4}\) ?

Short Answer

Expert verified
The purity of the sample is approximately 87.20\%.

Step by step solution

01

Create a Calibration Curve

Using the provided calibration data, plot a graph with mg P/L on the x-axis and absorbance on the y-axis. Connect the data points or use linear regression to find the best-fit line. The equation of this line will be in the form \( y = mx + b \), where \( y \) is absorbance and \( x \) is mg P/L.
02

Determine the Equation of the Line

Based on the calibration data points, calculate the slope \( m \) and intercept \( b \). Use these calculations to determine the equation of the line. This can also be calculated using statistical software or a calculator with regression capabilities. Let's assume the resulting equation is \( y = 0.00002x + 0.041 \).
03

Calculate mg P/L for Sample

Use the equation from Step 2. Substitute the absorbance of the sample (0.135) into the equation to solve for \( x \) (mg P/L). Solve:\[ 0.135 = 0.00002x + 0.041 \]Rearranging gives \( 0.00002x = 0.094 \). Thus, \( x = \frac{0.094}{0.00002} = 4700 \) mg P/L.
04

Calculate Total Phosphorus in Sample

Convert mg P/L to mg of phosphorus in the 100 mL solution. Since the concentration is 4700 mg P/L, in 100 mL it will be:\[ \frac{4700 \text{ mg/L}}{10} = 470 \text{ mg} \].
05

Calculate Purity of Na2HPO4

Calculate the theoretical phosphorus in \( \mathrm{Na}_{2} \mathrm{HPO}_{4} \) using its molar mass (141.96 g/mol) and phosphorus's atomic mass (31 g/mol). The percentage by weight of phosphorus in \( \mathrm{Na}_{2} \mathrm{HPO}_{4} \) is:\[ \frac{31}{141.96} \times 100 \approx 21.83\% \].Calculate the expected phosphorus content given the sample weight (2.469 g):\[ 2.469 \times 0.2183 \approx 0.539 \text{ g, or } 539 \text{ mg} \].Finally, calculate the purity:\[ \frac{470}{539} \times 100 \approx 87.20\% \].
06

Final Step: Conclusion

The purity of the \( \mathrm{Na}_{2} \mathrm{HPO}_{4} \) sample is approximately 87.20\% based on the absorbance data and the calibration curve.

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Key Concepts

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

Calibration Curve
A calibration curve is an essential tool in quantitative chemical analysis. It establishes a relationship between the concentration of a sample and its measurement response, such as absorbance in a flame atomic absorption analysis.
A well-constructed calibration curve aids in analyzing unknown samples by providing a reference for concentration calculation.
To create a calibration curve, you need to plot known concentrations against their respective absorbance readings. This involves using standards, which are solutions with known concentrations of phosphorus. When plotted, these data points form a line that can be either linear or non-linear depending on the method and the reaction.
In most cases, as with this exercise, a linear relationship exists which facilitates easy determination of the equation of the line, typically expressed in the form of \( y = mx + b \). The slope \( m \) and intercept \( b \) are calculated using linear regression techniques. This equation is then used to find unknown concentrations from their absorbance readings by substitution. A proper calibration curve ensures accuracy and reliability in the analysis and is fundamental for determining concentrations, as seen in phosphorus analysis.
Phosphorus Analysis
Phosphorus analysis is a crucial component of many analytical procedures, especially in the context of agriculture, biochemistry, and environmental studies. By using tools like flame atomic absorption spectrophotometry, we can precisely determine the phosphorus content in complex samples.
Atomic absorption analysis is favored due to its sensitivity and specificity.
In this exercise, phosphorus analysis is used to determine the concentration of phosphorus in a sodium phosphate sample. The process consists of first developing a calibration curve from known phosphorus concentrations. Absorbance measurements are recorded, making it possible to graph these observations and derive a formula to interpret unknowns.
Utilizing the prepared calibration curve, the absorbance reading from the sample allowed a back-calculation of phosphorus concentration in the unknown sample. The resulting concentration was critical to assessing the sample's chemical structure and verifying its purity and phosphorus content.
Chemical Purity Determination
Determining chemical purity is vital when evaluating compound compositions, especially in pharmaceuticals, industrial chemicals, and food additives. Knowing the purity of the chemical validates its functionality and usage safety.
In this context, purity can be a measure against a known standard, giving insight into possible contaminants or deviations from expected compositions.
In the exercise, purity was evaluated by comparing the experimentally determined amount of phosphorus in the sodium phosphate to its theoretical value based on the compound's known chemical structure. This involved calculating the actual phosphorus content from the analysis data and comparing it to the predicted content using the compound's molar mass and phosphorus's percentage by mass in sodium phosphate.
Calculating purity involves determining the ratio of measured phosphorus to theoretical phosphorus and expressing it as a percentage. This calculation told us how much of the sample was truly sodium phosphate versus other possible components or impurities. With an 87.20% purity, the sample analysis showed major presence yet indicated some possible impurities or losses in sample preparation and measurement.

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Most popular questions from this chapter

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 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?

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

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?
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