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Module 2: Characteristics of Gases - Ideal Gas Law - Practice Problems

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

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

Temperature Converter
Pressure Converter
Volume Calculator (Ideal Gas)

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Q icon #1
For each case given below what is the relationship between volumes A and B?

equation 1(i)

equation 1(ii)

equation 1(iii)

equation 1(iv)

equation 1(v)
A icon
equation 1(i)
Answer: i. Gas A volume equals Gas B volume.

See Figure 3.
Figure 3

Solution:
All inputs into the ideal gas law equation are the same for gases A and B: same number of moles, same temperature and pressure. Therefore their volumes are the same. The different types of gas contained in A and B do not affect volume.
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equation 1(ii)
Answer: ii. Gas A volume is larger than Gas B volume.

See Figure 4.
Figure 4

Solution:
All inputs into the ideal gas law equation are the same for gases A and B except for the number of moles. Gas A has twice the number of moles as gas B. Therefore the volume of A is twice that of B.
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equation 1(iii)
Answer: iii. Gas A volume is smaller than Gas B volume.

See Figure 5.
Figure 5

Solution:
All inputs into the ideal gas law equation are the same for gases A and B except for the pressure. Gas A has a higher pressure than gas B. Therefore, the volume of A is smaller than that of B.
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equation 1(iv)
Answer: iv. Gas A volume is smaller than Gas B volume.

See Figure 6.
Figure 6

Solution:
All inputs into the ideal gas law equation are the same for gases A and B except for the temperature. Gas B has a higher temperature than gas A. Therefore, the volume of A is smaller than that of B.
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equation 1(v)
Answer: v. Gas A volume equals Gas B volume.

See Figure 7.
Figure 7

Solution:
Gas A has twice the number of moles and twice the pressure of gas B. From the ideal gas law equation, these effects cancel each other out. Therefore, the volumes of Gases A and B are the same.

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Q icon #2
What is the volume of 1,500 lb moles of combustion gas at an absolute pressure of 14.7 psia and a temperature of 68°F?

A icon
Answer: 578,106 ft3

Solution:
Solve the problem using the ideal gas law equation:

equation 2

  1. Convert temperature to absolute scale (°R).
    equation 2(1)

  2. Calculate the gas volume.
    equation 2(2)

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Q icon #3
What is the volume of 1,500 lb moles of combustion gas at an absolute pressure of 14.4 psia and a temperature of 350°F?

A icon
Answer: 905,344 ft3

Solution:
Solve the problem using the ideal gas law equation:

equation 3
  1. Convert temperature to absolute scale (°R).
    equation 3(1)

  2. Calculate the gas volume.
    equation 3(2)

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Q icon #4
Calculate the number of pound moles of combustion gas in an electrostatic precipitator having a length of 45 ft, a width of 24 ft, and a height of 30 ft. Use the following data to solve the problem:

Combustion gas pressure = 14.25 psia
Combustion gas temperature = 450°F

A icon
Answer: 47.28 lb moles

Solution:
Solve the problem using the following rearranged version of the ideal gas law:

equation 4
  1. Convert temperature to an absolute scale, °R.
    equation 4(1)

  2. Calculate the volume of the electrostatic precipitator.
    equation 4(2)

  3. Calculate the number of moles using the rearranged version of the ideal gas law.
    equation 4(3)

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Q icon #5
Calculate the number of pound moles of combustion gas in the same electrostatic precipitator described in question 4. Use the following data to solve the problem:

Electrostatic precipitator dimensions:
Length = 45 ft
Width = 24 ft
Height = 30 ft

Combustion gas pressure = 14.25 psia
Combustion gas temperature = 300°F

Q icon
Answer: 56.62 lb moles

Solution:
Solve the problem using the following rearranged version of the ideal gas law:

equation 5
  1. Convert temperature to an absolute scale, °R.
    equation 5(1)

  2. Calculate the volume of the electrostatic precipitator.
    equation 5(2)

  3. Calculate the number of moles using the rearranged version of the ideal gas law.
    equation 5(3)

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Q icon #6
Calculate the number of pound moles of combustion gas in the same electrostatic precipitator described in question 4. Use the following data to solve the problem:

Combustion gas pressure = -20 in. W.C.
Barometric pressure = 29.5 in. Hg
Combustion gas temperature = 300°F

A icon
Answer: 54.71 lb moles

Solution:
Solve the problem using the following rearranged version of the ideal gas law:

equation 6
  1. Convert temperature to an absolute scale, °R.
    equation 6(1)

  2. Convert the relative pressure to an absolute pressure. First convert the barometric and relative pressures to consistent units. See Conversion Factors.
    equation 6(2)

  3. Calculate the volume of the electrostatic precipitator.
    equation 6(3)

  4. Calculate the number of moles using the rearranged version of the ideal gas law.
    equation 6(3)

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Ideal Gas Law
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Flow Rate

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