Question

A few decades ago benzene was thought to be a harmless chemical with a somewhat pleasant odor and was widely used as a cleaning solvent. It has since been found that chronic exposure to benzene can causc health problems such as anemia and possibly leukemia. Benzene has an OSHA permissible exposure level (PEL) of 1.0 ppm (part per million on a molar basis, equivalent to a mole fraction of $1.0 \times 10^{-6}$ ) averaged over an 8 -hour period. The safcty engincer in a plant wishes to determine whether the benzene concentration in a laboratory exceeds the PEL. One Monday at 9 a.m., 1 p.m., and 5 p.m., she collects samples of room air $\left(33^{\circ} \mathrm{C}, 99 \mathrm{kPa}\right)$ in evacuated 2 -liter stainless steel containers. To collect a sample she opens the container valve, allows room air to enter until the container pressure equals atmospheric pressure, and then charges clean dry helium into the container until the pressure reaches 500 kPa. Next, she takes the containers to an analytical laboratory in which the temperature is $23^{\circ} \mathrm{C}$, leaves them there for a day. and then feeds gas from each container to a gas chromatograph (GC) until the pressure in the container is reduced to $400 \mathrm{kPa}$. In the order in which they were collected, the samples that pass through the GC are found to contain $0.656 \mu \mathrm{g}$ (microgram), $0.788 \mu \mathrm{g},$ and $0.910 \mu \mathrm{g}$ of benzene, respectively. (a) What were the concentrations of benzene (ppm on a molar basis) in the original room air at the three collection times? (Assume ideal-gas behavior.) Is the average concentration below the PEL? (b) Why did the engineer add helium to the container after collecting the room air sample? Why did she wait a day before analyzing the container contents? (c) Why might a finding that the average benzene concentration is below the PEL not necessarily mean that the laboratory is safe insofar as exposure to benzene is concerned? Give several reasons, including possible sources of error in the sampling and analysis procedure. (Among other things, note the day on which the samples were taken.)

Name: Problem 30, Chapter 5: Elementary Principles of Chemical Processes
Uploaded: 2021-02-10T02:16:20-08:00
Duration: 17 min 6 s
Channel: Niamat Khuda

   A few decades ago benzene was thought to be a harmless chemical with a somewhat pleasant odor and was widely used as a cleaning solvent. It has since been found that chronic exposure to benzene can causc health problems such as anemia and possibly leukemia. Benzene has an OSHA permissible exposure level (PEL) of 1.0 ppm (part per million on a molar basis, equivalent to a mole fraction of
$1.0 \times 10^{-6}$ ) averaged over an 8 -hour period. The safcty engincer in a plant wishes to determine whether the benzene concentration in a laboratory exceeds the PEL. One Monday at 9 a.m., 1 p.m., and 5 p.m., she collects samples of room air $\left(33^{\circ} \mathrm{C}, 99 \mathrm{kPa}\right)$ in evacuated 2 -liter stainless steel containers. To collect a sample she opens the container valve, allows room air to enter until the container pressure equals atmospheric pressure, and then charges clean dry helium into the container until the pressure reaches 500 kPa. Next, she takes the containers to an analytical laboratory in which the temperature is $23^{\circ} \mathrm{C}$, leaves them there for a day. and then feeds gas from each container to a gas chromatograph (GC) until the pressure in the container is reduced to $400 \mathrm{kPa}$. In the order in which they were collected, the samples that pass through the GC are found to contain $0.656 \mu \mathrm{g}$ (microgram), $0.788 \mu \mathrm{g},$ and $0.910 \mu \mathrm{g}$ of benzene, respectively.
(a) What were the concentrations of benzene (ppm on a molar basis) in the original room air at the three collection times? (Assume ideal-gas behavior.) Is the average concentration below the PEL?
(b) Why did the engineer add helium to the container after collecting the room air sample? Why did she wait a day before analyzing the container contents?
(c) Why might a finding that the average benzene concentration is below the PEL not necessarily mean that the laboratory is safe insofar as exposure to benzene is concerned? Give several reasons, including possible sources of error in the sampling and analysis procedure. (Among other things, note the day on which the samples were taken.)

Elementary Principles of Chemical Processes

Richard M. Felder,… 4th Edition

Chapter 5, Problem 30

Instant Answer

Solved by Expert Niamat Khuda

02/10/2021

Step 1

We can use the ideal gas law for this, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. At condition 1 (when the sample is collected), the pressure P1 is 99 kPa, Show more…

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A few decades ago benzene was thought to be a harmless chemical with a somewhat pleasant odor and was widely used as a cleaning solvent. It has since been found that chronic exposure to benzene can causc health problems such as anemia and possibly leukemia. Benzene has an OSHA permissible exposure level (PEL) of 1.0 ppm (part per million on a molar basis, equivalent to a mole fraction of $1.0 \times 10^{-6}$ ) averaged over an 8 -hour period. The safcty engincer in a plant wishes to determine whether the benzene concentration in a laboratory exceeds the PEL. One Monday at 9 a.m., 1 p.m., and 5 p.m., she collects samples of room air $\left(33^{\circ} \mathrm{C}, 99 \mathrm{kPa}\right)$ in evacuated 2 -liter stainless steel containers. To collect a sample she opens the container valve, allows room air to enter until the container pressure equals atmospheric pressure, and then charges clean dry helium into the container until the pressure reaches 500 kPa. Next, she takes the containers to an analytical laboratory in which the temperature is $23^{\circ} \mathrm{C}$, leaves them there for a day. and then feeds gas from each container to a gas chromatograph (GC) until the pressure in the container is reduced to $400 \mathrm{kPa}$. In the order in which they were collected, the samples that pass through the GC are found to contain $0.656 \mu \mathrm{g}$ (microgram), $0.788 \mu \mathrm{g},$ and $0.910 \mu \mathrm{g}$ of benzene, respectively. (a) What were the concentrations of benzene (ppm on a molar basis) in the original room air at the three collection times? (Assume ideal-gas behavior.) Is the average concentration below the PEL? (b) Why did the engineer add helium to the container after collecting the room air sample? Why did she wait a day before analyzing the container contents? (c) Why might a finding that the average benzene concentration is below the PEL not necessarily mean that the laboratory is safe insofar as exposure to benzene is concerned? Give several reasons, including possible sources of error in the sampling and analysis procedure. (Among other things, note the day on which the samples were taken.)

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Key Concepts

Air Sampling Techniques

This concept involves methods to collect representative air samples for chemical analysis. It includes the use of containers or devices that reliably capture ambient air, ensuring that the sample reflects the actual environmental conditions at the time and place of collection, while minimizing contamination or loss of analytes.

Ideal Gas Law

The ideal gas law (PV = nRT) is used to relate the pressure, volume, and temperature of gases to calculate the number of moles of a substance present. In environmental sampling and analysis, it allows for the determination of gas concentrations by converting measured amounts under different conditions to a common basis.

Gas Chromatography

Gas chromatography is an analytical technique used to separate and quantify volatile components in a gas mixture. It plays a crucial role in identifying trace levels of chemicals in environmental samples, providing precise measurements of concentration after proper calibration and methodological control.

OSHA Permissible Exposure Limits

OSHA’s permissible exposure limits (PELs) define the maximum acceptable concentrations of hazardous substances, averaged over a specified period, to protect worker health. Understanding PELs is fundamental when assessing workplace safety and ensuring that measured contaminant levels do not exceed regulatory thresholds.

Dilution and Use of Inert Gas

This concept explains the practice of adding an inert gas—such as helium—to a collected sample to bring it to a desired pressure for analysis. This step is vital to ensure a controlled, reproducible environment that minimizes the chemical reactivity or degradation of the target analyte during storage and analysis.

Temporal Variability in Environmental Sampling

Environmental contaminant concentrations can vary throughout the day due to factors like operational activities and external conditions. Recognizing temporal variability is key in sampling design, as collecting samples at different times helps establish whether peak concentrations might exceed safe exposure limits even if average levels appear compliant.

Sampling and Analysis Uncertainties

Measurement uncertainties can arise from several sources including sampling errors, instrumental calibration, delays between collection and analysis, and environmental changes during storage. Understanding these potential sources of error is crucial for accurately interpreting results and ensuring the reliability of conclusions about safety and compliance.

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Transcript

00:03 Hey guys let's do problem 30 in this problem we need to calculate the concentration of benzene in the original room temperature at three collection times let's do that the condition one is when the sample is collected we need to calculate the concentration of benzin in the collection period from ideal gas law we know pv is equal to in r t or the number of moles is equal to pressure 1 divided by v or temperature 1.

00:42 Given the pressure is, pressure of the system is 99 kilo -pascal, let's convert it to atm, which is 0 .977 atm, and the temperature is 33 degrees celsius.

01:05 Let's convert it to kelvin scale, which is 300 ,000.

01:12 Kelvin therefore the number of moles is 0 .977 atmospheric pressure multiplied by 2 liter which is given gas constant is 0 .08 to 1 liter 80m mole inverse 1 kelvin inverse 1 and the temperature is 306 kelvin therefore the number of moons at condition 1 is 0 .078 moles and this is equal to the number equal to the sum of number of moles of air and the number of moles of benzene therefore 0 .078 is equal to in air plus in benzene now let's go to condition 2 when helium is added and in this case pressure is 500 kilo -pascal let's convert 8m.

02:33 Atmosphere pressure which is 4 .93 atmospheric pressure.

02:39 The temperature was 33 degrees celsius therefore it is 306 kelvin therefore the number of moles is 4 .9303m.

03:02 Multiplied 2 liter divided by 0 .081 liter 1 inverse 1, kelvin inverse 1 multiplied by 306 kelvin, which is equal to 0 .393 mole.

03:19 Therefore, the number of moles at condition 2 is 0 .0 .0 .393 mole.

03:31 And this number is the sum of the number of the number of mole of air, number of mole of benzene, and number of mole of helium.

03:41 Now we need to go to condition 3 when the gas is fed to gas chromatograph.

04:06 Let's go to condition 3 when gas is fed to gas chromatograph.

04:37 In this situation, pressure is 400 kilo -pascal.

04:43 Let's convert it to atmospheric pressure, which is 3 .94 atmospheric pressure.

04:52 The temperature is 23 degrees celsius which is 296 kelvin therefore the number of moles is 3 .93 atmospheric pressure multiplied by 2 liter divided by 0 .08 to 1 multiply by 296 kelvin and the number of moles we get is 0 .325 moles therefore the number of moles at condition 3 is 0 .325 moles which is equal to the entrance of number which is equal to the number of moles at condition 3 and number of months of gas injected therefore in 3 is the subtraction of number of moles of gas at condition 2 minus the number of moles of gas injected or 0 .325 mol is equal to n2 and we know n2 is in air number of months of air number of months of benzene and number of months of helium now if we subtract equation two equation three from equation two then what we will get is number of during injection number of months of gas injected is equal to 0 .393 minus 0 .325 moles which is 0 .068 mole therefore the number of months of benzene is equal to number of moles in the benzene gas chromatograph multiply by number of moons during condition 2 divided by number of months number of moons of gas injected or we can write or we can write that number of moons of benzene is equal to mass of benzene in the gas chromatograph divided by molar mass of benzene multiplied by number of moons during condition 2 divided by number of months in the injected gas the molar mass of benzene is 78 gram per moon and the number of moles during condition 2 is 0 .393 mole and number of moles of gas injected is 0 .068 moles...

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