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Module 2: Characteristics of Gases - Review Exercises

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Instructions:
Work these problems on a sheet of paper and check your answers against those provided below.

Important:
This Page has several links back to lesson material covered in Module 2. To return to this page, please use your browser's "Back" button.

Helpful Calculators:
The following calculators may be useful in solving these problems. You can access them either from the "Calculators" link in the Features box or from the links below.

Temperature Converter
Pressure Converter
Gas Flow Rate Converter (Actual Standard Conditions)
Gas Flow Rate Converter (Wet Dry Basis)
Concentration Converter (Major Gas Constituents)
Concentration Converter (Minor Gas Constituents)
Correction of Concentration (Wet Dry Basis)
Correction of Concentration (Measured Standard O2 Basis)

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Q icon #1
There are 12,789 SCFM of flue gas flowing through an air pollution control system.

  1. How many pound moles per minute are passing through?

  1. 12,789 lb mole/min
  2. 33.18 lb mole/min
  3. 0.553 lb mole/min
  4. It cannot be determined due to the lack of gas temperature and pressure data.

  1. If the average molecular weight of the gas is 29, how many pounds of gas are passing through per minute?

  1. 16.04 lbm/min
  2. 12,789 lbm/min
  3. 962.2 lbm/min
  4. It cannot be determined due to the lack of gas temperature and pressure data.

A icon
Answer: i. b. 33.18 lb mole/min

Solution:
equation 1(i)

Half Break Line

Answer: ii. c. 962.2 lbm/min

Solution:
equation 1(ii)

To review material, see Module 1 lesson on Moles and Module 2 lesson on Flow Rate.

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Q icon #2
How many moles per minute of oxygen can react in a gas stream having a total gas flow rate of 400,000 SCFM and an oxygen concentration of 8% by volume?

  1. 83.03 lb moles/min
  2. 103.78 lb moles/min
  3. 1.73 lb moles/min
  4. It cannot be determined from this data.

A icon
Answer: a. 83.03 lb moles/min

Solution:
  1. Calculate the number of moles per minute (molar flow rate) for the total gas stream using a modified version of the ideal gas equation provided below.

    equation 2(1)

  2. Calculate the quantity of oxygen present in the gas stream.

    equation 2(2)

    To review material, see Module 1 lesson on Moles and Module 2 lessons on Flow Rate and Concentrations.

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Q icon #3
Calculate the stack exit velocity based on the emission data and information provided below. See Figure 1.

equation 3

  1. 1,646 ft/min
  2. 1,130 ft/min
  3. 1,870 ft/min
  4. It cannot be determined from the available information.

A icon
Answer: c. 1,870 ft/min (or 31.2 ft/sec)

Solution:
Calculate the gas velocity based on the following equation:

equation 3(a)
  1. Convert the gas flow rate from DSCFM (dry SCFM) to SCFM.

    equation 3(1)

  2. Convert the gas flow rate from SCFM to ACFM based on the temperature and pressure data supplied.

    equation 3(2)

  3. Calculate the cross-sectional area of stack (at exit).

    equation 3(3)

  4. Calculate the gas velocity.

    equation 3(4)

    To review material, see Module 1 lesson on Geometry and Module 2 lessons on Flow Rate, Dry Basis Conversions, and Velocity.

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Q icon #4
A gas contains 5,000 ppm SO2 and 10% water at 400°F and 14.5 psia (absolute pressure).

  1. What is the SO2 concentration at standard conditions of temperature and pressure?

  1. 5,000 ppm
  2. 5,555 ppm
  3. 4,500 ppm
  4. It cannot be determined from the available data.

  1. What is the concentration of SO2 (5,000 ppm) expressed on a dry basis? The moisture content is 10%.

  1. 5,000 ppmvd
  2. 5,555 ppmvd
  3. 4,500 ppmvd
  4. It cannot be determined from the available data.

  1. What is the SO2 concentration (5,000 ppm) expressed in volume %?

  1. 0.005%
  2. 0.5%
  3. 5.0%
  4. 50%

  1. What is the SO2 concentration (5,000 ppm) in the gas stream expressed in terms of µg/m3 at standard conditions?

  1. 5,000,000 µg/m3
  2. 11,452,000 µg/m3
  3. 13,330,000 µg/m3
  4. 114,521,600 µg/m3

  1. Is the concentration of SO2 expressed in µg/m3 (standard conditions) the same as the concentration expressed in µg/m3 (at actual conditions)?

  1. Yes
  2. No

A icon
Answer: i. a. 5,000 ppm

Solution:
Concentration expressed in ppm is in a volume ratio, i.e. the volume of the pollutant is divided by the volume of the total gas stream. When conditions change from actual to standard conditions, the volumes of both the pollutant and total gas stream change proportionally. Therefore, the ppm value does not change.

To review material, see Module 1 lessons on Temperature and Pressure and Module 2 lessons on Concentrations and Dry Basis Conversions.

Half Break Line

Answer: ii. b. 5,555 ppmvd

Solution:
equation 4(ii)

To review material, see Module 2 lessons on Concentrations and Dry Basis Conversions.

Half Break Line

Answer: iii. b. 0.5%

Solution:
equation 4(iii)

To review material, see Module 2 lesson on Concentrations.

Half Break Line

Answer: iv. c. 13,330,000 µg/m3

Solution:
equation 4(iv)

To review material, see Module 2 lesson on Concentrations.

Half Break Line

Answer: v. b. No

Solution:
The µg/m3 format for concentration data has the pollutant weight divided by the volume occupied. When the conditions change to an actual basis, the volume occupied changes. Therefore, the concentration in µg/m3 (actual conditions) changes.

To review material, see Module 2 lessons on Ideal Gas Law and Concentrations.

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Q icon #5
Convert a measured sulfur dioxide concentration of 123 ppmvd to ppmvd @ 7% O2. Use a measured oxygen concentration of 14.3% in the conversion.

A icon
Answer: 259.5 ppmvd @ 7% O2

Solution:
equation 5

To review material, see Module 2 lessons on Concentrations and Oxygen Basis Conversions.

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Q icon #6
The results from an emission test are summarized below. Based on this information answer the questions given below.

Emission Test Results

equation 6

Dioxin-furan isomer catch weights are provided below.

Table 1

  1. What is the concentration of dioxin-furan compounds on a TEQ basis corrected to 7% oxygen and dry conditions?

  1. 0.0751 ng/DNm3 TEQ @ 7% O2
  2. 0.12 ng/DNm3 TEQ @ 7% O2
  3. 0.963 ng/DNm3 TEQ @ 7% O2
  4. 14.1 ng/DNm3 TEQ @ 7% O2

  1. What is the concentration of dioxin-furan compounds on a total basis corrected to 7% oxygen and dry conditions?

  1. 0.209 ng/DNm3 @ 7% O2
  2. 2.09 ng/DNm3 @ 7% O2
  3. 20.9 ng/DNm3 @ 7% O2
  4. 209.0 ng/DNm3 @ 7% O2

  1. What is the emission rate (mass per hour) of dioxin-furan compounds on a TEQ basis?

  1. 9.41 10-1 gm/hr TEQ
  2. 5.32 10-2 gm/hr TEQ
  3. 5.32 10-8 gm/hr TEQ
  4. 9.41 10-6 gm/hr TEQ

A icon
Answer: i. a. 0.0751 ng/DNm3 TEQ @ 7% O2

Solution:

Part i
  1. Convert the gas flow rate and gas sample volume data to Nm3 (for convenience).
    equation 6i(1)

  2. Calculate the measured concentrations of each isomer and apply the weighting factors. (Note: it is convenient to perform both calculations using a table as shown below.)

    The TEQ concentrations for each isomer are calculated by dividing the catch weight reported by the analytical laboratory by the sample volume expressed in dry standard conditions. This measured concentration is then multiplied by the weighting factor to provide the TEQ concentration value. This calculation procedure is illustrated below for 2,3,7,8 TCDD.

    equation 6i(2)

    The total TEQ concentration is the sum of the TEQ concentrations for each of the 17 isomers.

Table 2
Emissions of dioxin-furan compounds on a TEQ basis = 0.06154 ng/DNm3 TEQ.

  1. Correct the dioxin-furan TEQ concentration to a 7% oxygen basis.

equation 6i(3)

Half Break Line

Answer: ii. c. 20.9 ng/DNm3 @ 7% O2

Solution:

Part ii

  1. Calculate the total dioxin-furan concentration on a 7% oxygen basis.

    equation 6ii(1)

Half Break Line

Answer: iii. d. 9.41 10-6 gm/hr TEQ

Solution:

Part iii

  1. Calculate the dioxin-furan TEQ emission rate in grams/hour.

    equation 6iii(1)

To review material, see Module 2 lessons on Flow Rate, Concentrations, Dry Basis Conversions, and Oxygen Basis Conversions.

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Q icon #7
What is the average gas velocity in the duct described below?

equation 7

  1. 2,266 ft/min
  2. 3,261 ft/min
  3. 55 ft/min
  4. It cannot be determined from this data.
A icon
Answer: b. 3,261 ft/min

Solution:
Calculate the gas velocity (v) using the following equation:

equation 7(a)

  1. Convert from SCFM to ACFM prior to calculating velocity.

    equation 7(1)

  2. Calculate the cross-sectional area of the duct.

    equation 7(2)

  3. Calculate the gas velocity, v.

    equation 7(3)

To review material, see Module 1 lesson on Geometry and Module 2 lessons on Flow Rate and Velocity.

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Q icon #8
What is the treatment time for the electrostatic precipitator (ESP) described below?

equation 8

  1. 16.4 sec
  2. 1.64 sec
  3. 1.13 sec
  4. 11.3 sec
A icon
Answer: d. 11.3 sec

Solution:

  1. Convert the gas temperature and pressure data to absolute scales.

    equation 8(1)

  2. Convert the gas flow rate to actual conditions.

    equation 8(2)

  3. Calculate the treatment time.

    equation 8(3)

To review material, see Module 1 lessons on Geometry, Temperature, and Pressure and Module 2 lessons on Flow Rate and Treatment Time.

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Q icon #9
What is the space velocity for a catalytic incinerator having a catalyst volume of 10 ft3 and a inlet gas stream of 4,500 SCFM?

  1. 7.5 sec-1
  2. 0.75 sec-1
  3. 10.5 sec
  4. 1.05 sec
A icon
Answer: a. 7.5 sec-1

Solution:
The space velocity can be calculated based on either standard or actual conditions. Because no data is available to convert the gas stream temperature and pressure to actual conditions, the space velocity will be calculated based on standard conditions.

equation 9

To review material, see Module 2 lesson on Treatment Time.

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Q icon #10
Calculate the gas density of 1 lb mole of pure carbon dioxide gas (CO2) at an absolute pressure of 343 in. W.C. and an absolute temperature of 373°K. Link to periodic table of elements.

  1. 0.145 lbm/ft3
  2. 1.45 lbm/ft3
  3. 0.0076 lbm/ft3
  4. 0.076 lbm/ft3
A icon
Answer: d. 0.076 lbm/ft3

Solution:
Calculate the gas density by using the equation:

equation 10
  1. Calculate the mass of 1 lb mole of CO2 gas.

    equation 10(1)

  2. Calculate the volume of 1 lb mole of CO2 gas at absolute pressure of 343 in. W.C. and 373°K using the equation:

    equation 10(2)

  3. Calculate the density of the CO2 gas.

    equation 10(3)

To review material, see Module 1 lesson on Moles and Module 2 lessons on Ideal Gas Law and Desity.

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Q icon #11
How much heat must be added to a VOC-laden gas stream to achieve a temperature of 700°F?

equation 11

The following enthalpy data should be used.
Table 3
  1. 21,500 Btu/min
  2. 11,065 Btu/min
  3. 5,605 Btu/min
  4. It cannot be calculated from the available data
A icon
Answer: b. 11,065 Btu/min

Solution:
  1. Convert the gas flow rate to a standard basis.

    equation 11(1)

  2. Calculate the mass flow rates (lbm/min) each major constituent in the gas stream.

    equation 11(2)

  3. Calculate the enthalpy change for each major constituent using the general equation provided below.

    equation 11(3)

  4. Calculate the total enthalpy change for the gas stream.

    equation 11(4)

To review material, see Module 1 lesson on Moles and Module 2 lessons on Flow Rate, Concentrations, and Heat Capacity and Enthalpy.

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Q icon #12
Calculate the absolute viscosity of air at 350°F. Use an oxygen concentration of 10% and a moisture content of 9.63% in solving the problem.

  1. 237.9 micropoise
  2. 143.1 micropoise
  3. 4.78 micropoise
  4. None of the above

A icon
Answer: a. 237.9 micropoise

Solution:
The equation for estimating the absolute gas viscosity is provided below. It is important to remember that the gas temperature data must be in degrees Kelvin for this equation.

equation 12

  1. Convert the gas temperature from degrees Fahrenheit to degrees Kelvin.

    equation 12(1)

  2. Calculate the absolute gas viscosity.

    equation 12(2)

To review material, see Module 1 lesson on Temperature and Module 2 lesson on Viscosity.

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Q icon #13
What is the gas stream Reynolds number for boiler flue gas flowing in an 8-ft diameter duct at a velocity of 3,000 ft/min? Is the gas stream laminar or turbulent? Use the data provided below.

equation 13

  1. 1,940,645 (turbulent)
  2. 450,562 (turbulent)
  3. 1,322 (laminar)
  4. 12.8 (laminar)

A icon
Answer: a. 1,940,645 (turbulent)

Solution:
equation 13(a)
  1. Convert viscosity units.

    equation 13(1)

  2. Calculate the Reynolds number.

    equation 13(2)

    Reynolds numbers above 10,000 are associated with turbulent flow.

To review material, see Module 2 lessons on Viscosity and Flow Characteristics.

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