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Chapter 10: Problem 15

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?

Short Answer

Expert verified
The concentration of phenol in the water sample is 7.434 ppm.

Step by step solution

01

Understanding Beer's Law

Beer's Law, or Beer-Lambert Law, states that the absorbance of a solution is directly proportional to the concentration of the absorbing species and the path length of the cell. Mathematically, it can be expressed as \( A = \, \varepsilon \cdot c \cdot l \), where \( A \) is the absorbance, \( \varepsilon \) is the molar absorptivity, \( c \) is the concentration, and \( l \) is the path length.
02

Determine the Molar Absorptivity \(\varepsilon\)

Using the standard phenol solution, we calculate the molar absorptivity. For the standard solution with a concentration of 4.00 ppm, \( A = 0.424 \) and \( l = 1.00 \, \mathrm{cm} \). So, \( \varepsilon = \frac{A}{c \cdot l} = \frac{0.424}{4.00 \, \text{ppm} \cdot 1.00 \, \mathrm{cm}} = 0.106 \, \mathrm{ppm}^{-1} \cdot \mathrm{cm}^{-1} \).
03

Calculate Concentration of the Diluted Sample

For the diluted water sample, \( A = 0.394 \) and \( l = 1.00 \mathrm{~cm} \). Using the molar absorptivity from Step 2, the concentration \( c \) of the diluted solution can be calculated as \( c = \frac{A}{\varepsilon \cdot l} = \frac{0.394}{0.106 \cdot 1.00} = 3.717 \text{ ppm} \).
04

Account for Dilution

The 50.00 mL aliquot of the distillate was diluted to 100 mL in the volumetric flask. Therefore, the concentration in the original distillate (\( c_{\text{original}} \)) is twice that of the diluted solution: \( c_{\text{original}} = 2 \times 3.717 = 7.434 \text{ ppm} \).
05

Calculate Phenol Concentration in the Water Sample

Since only part of the water sample was distilled, the calculated concentration in the distillate represents the concentration of phenol in the original water sample. Thus, the phenol concentration in the water sample is 7.434 ppm.

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Key Concepts

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

Beer-Lambert Law
The Beer-Lambert Law is a fundamental principle in analytical chemistry that relates to how light absorbs as it passes through a solution. It's a simple yet powerful equation:
  • Absorbance (A): This is a measure of the amount of light absorbed by the sample. Absorbance itself does not have units.

  • Molar Absorptivity (\( \varepsilon \)): This is a constant that indicates how well a substance absorbs light at a particular wavelength. It is specific to each compound and is measured in \( \, \text{L mol}^{-1} \text{cm}^{-1} \).

  • Concentration (c): Refers to the amount of solute dissolved in a unit volume of solution, usually expressed in molarity. In this exercise, concentration is given in parts per million (ppm).

  • Path length (l): The distance that light travels through the solution, usually measured in centimeters (cm).

The Beer-Lambert Law can be expressed mathematically as:\[A = \varepsilon \cdot c \cdot l\] This equation shows that the absorbance is directly proportional to the concentration of the absorbing species and the path length, making it a useful tool for determining unknown concentrations. In practice, by measuring the absorbance and knowing the path length and molar absorptivity, one can solve for the concentration, which is precisely what is done in the given exercise.
Molar Absorptivity
Molar absorptivity, also known as the molar extinction coefficient, is a key concept for understanding how different substances interact with light. It's a measure that reflects how strongly a substance absorbs light at a specific wavelength.
  • The unit for molar absorptivity is usually \( \text{L mol}^{-1} \text{cm}^{-1} \), but in this exercise, it is calculated per parts per million (ppm) for convenience.

  • It is unique to each compound and wavelength. This means different substances will have different molar absorptivity values at different wavelengths.

In the exercise, the molar absorptivity for phenol was found using a standard phenol solution with known concentration and absorbance. By rearranging the Beer-Lambert Law, we have:\[\varepsilon = \frac{A}{c \cdot l}\]For the standard phenol solution, absorbance \(A\) of 0.424, concentration \(c\) of 4.00 ppm, and path length \(l\) of 1.00 cm, the molar absorptivity was calculated as:\[\varepsilon = \frac{0.424}{4.00 \, \text{ppm} \times 1.00 \, \text{cm}} = 0.106 \, \text{ppm}^{-1} \cdot \text{cm}^{-1}\]Understanding molar absorptivity is essential for calculating unknown concentrations when using spectrophotometry.
Spectrophotometry
Spectrophotometry is an analytical method used to measure the amount of light absorbed by a solution, which in turn relates to the concentration of a solute within it. It is based on the Beer-Lambert Law, and it helps researchers and scientists make quantitative measurements of chemical concentrations. Here are some essential points about spectrophotometry:
  • It uses an apparatus known as a spectrophotometer, which passes a beam of light through a solution and measures the intensity of light passing through.

  • The spectrophotometer compares the intensity of light before and after passing through the sample to determine absorbance.

  • This technique is valuable in many fields, including chemistry, physics, biology, and biochemical analysis, as it provides accurate data on the concentration of solutes in a solution.

In the context of the exercise, spectrophotometry was employed to determine the absorbance of a phenol solution at 460 nm wavelength. By knowing the absorbance, molar absorptivity, and path length, we used spectrophotometry to calculate the phenol concentration in the water sample. This approach proves to be precise and efficient, especially when dealing with solutions of known characteristics and properties.

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Most popular questions from this chapter

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.

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. $$ \begin{array}{cccc} \text { [ligand] (M) } & \text { absorbance } & \text { [ligand] (M) } & \text { absorbance } \\ \hline 1.0 \times 10^{-4} & 0.122 & 6.0 \times 10^{-4} & 0.752 \\ 2.0 \times 10^{-4} & 0.251 & 7.0 \times 10^{-4} & 0.873 \\ 3.0 \times 10^{-4} & 0.376 & 8.0 \times 10^{-4} & 0.937 \\ 4.0 \times 10^{-4} & 0.496 & 9.0 \times 10^{-4} & 0.962 \\ 5.0 \times 10^{-4} & 0.625 & 1.0 \times 10^{-3} & 1.002 \end{array} $$

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?
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