/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 21 The concentration of \(\mathrm{S... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 21

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.

Short Answer

Expert verified
The concentration of SO2 in air is approximately 0.838 mg/L.

Step by step solution

01

Calculate Volume of Air Sample

First, determine the total volume of air that was passed through the solution in 75 minutes. Given that the air flow rate is \(1.6 \text{ L/minute}\), we multiply this by the number of minutes: \[1.6 \text{ L/minute} \times 75 \text{ minutes} = 120 \text{ L}.\]Thus, the total volume of air is \(120 \text{ L}\).
02

Determine Concentration of SO2 in Solution

Use the absorbance values to find the concentration of \(\text{SO}_2\) in solution using the relationship of the standard solution. The concentration of \(\text{SO}_2\) in the standard solution is given by the absorbance ratio: \[\frac{C_x}{C_s} = \frac{A_x}{A_s},\]where \(C_x\) is the concentration of the unknown, \(C_s\) is the concentration of the standard equivalent (15 ppm), \(A_x\) is the absorbance of the unknown sample (0.485), and \(A_s\) is the absorbance of the standard (0.181). Solving for \(C_x\):\[C_x = \frac{0.485}{0.181} \times 15 \text{ ppm} \approx 40.165 \text{ ppm}.\]
03

Convert Concentration to mg/L in Air

Since 1 ppm is equivalent to 1 mg/L, \(C_x = 40.165 \text{ mg/L in the final solution}\). To find \(\text{mg/L}\) in air, account for the dilutions: the solution was diluted from 10.00 mL to 25 mL. This means the concentration of \(\text{SO}_2\) in the original 10 mL solution was \[C_{original} = \frac{25}{10} \times 40.165 \text{ mg/L} = 100.4125 \text{ mg/L}. \]Thus, the \(\text{mg SO}_2\) per \(\text{L}\) of air sample is \[\frac{100.4125 \text{ mg}}{120 \text{ L}} \approx 0.8376 \text{ mg SO}_2/ \text{L air}\].

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Key Concepts

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

SO2 concentration
Measuring the concentration of sulfur dioxide ( SO_2 ) in the air is crucial for understanding air quality and its potential impact on human health and the environment. SO_2 is a colorless gas that can cause respiratory problems, and its levels need to be monitored accurately in various environments. SO_2 concentration indicates the amount of this gas present in a given volume of air. In analytical chemistry, this is often expressed in terms like parts per million (ppm) or milligrams per liter (mg/L). To find SO_2 concentration, air samples are typically collected and analyzed using different chemical methods. One popular technique involves collecting the SO_2 in a reactive solution that forms a measurable compound, which can then be quantified.
p-rosaniline method
The p-rosaniline method is a well-established procedure for determining SO_2 levels. It's a colorimetric technique, meaning it relies on measuring the color intensity of a solution. In this method, SO_2 from an air sample reacts with a solution containing mercury chloride ( HgCl_4^{2-} ) to form mercury(II) sulfite ( Hg(SO_3)_2^{2-} ). Subsequently, this compound reacts with formal aldehyde and p-rosaniline, forming a colored complex. The intensity of the color relates to the concentration of SO_2. This is then compared to a standard solution to calculate the concentration of SO_2 in the original air sample. This method is popular due to its sensitivity, allowing detection of small changes in SO_2 levels.
It involves simple laboratory equipment, making it accessible for routine air quality monitoring.
absorbance measurement
Absorbance measurement is a central element in analytical chemistry, particularly in colorimetric assays like the p-rosaniline method. Absorbance refers to how much light at a specific wavelength is absorbed by a solution. This technique utilizes a spectrophotometer, which directs light through the sample. As the light passes through the solution containing the colored complex, part of it is absorbed by the sample. The spectrophotometer measures the absorbance, which is directly related to the concentration of the absorbing substance.The Beer-Lambert law formalizes this relationship: \[ A = \, \varepsilon c l \]where A is the absorbance, \varepsilon (epsilon) is the molar absorptivity, c is the concentration of the solution, and l is the path length of the cell (typically 1 cm).By knowing the absorbance of the unknown solution and comparing it to a standard, the concentration of SO_2 is determined. This approach is reliable and provides a quantitative measure of SO_2 concentration.
air sample analysis
Air sample analysis involves a series of steps to ensure the accurate determination of SO_2 concentration in a large volume of air. Initially, air is drawn through an absorbing solution at a controlled rate and time duration. This allows the SO_2 to chemically react and get retained in the solution. For the p-rosaniline method, the collection phase occurs over 75 minutes at a flow rate of 1.6 L/min, leading to efficient capture of SO_2 over time. After collection, the change in reaction mixture is analyzed through color development by adding reagents like formaldehyde and p -rosaniline. Subsequent absorbance measurement further gives the quantitative concentration of SO_2 in the air.
  • The analysis considers dilution factors.
  • Ensures quality control by using known standards. By comparing results with standards and correcting for air volume, analysts can accurately report SO_2 levels in mg/L, providing crucial air quality data.

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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?

    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?

    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.

    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?
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