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Module 2: Characteristics of Gases - Ideal Gas Law
Lesson Material-
Equivalent Values of R, the Universal Gas Constant
- Calculator:
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Volume Calculator (Ideal Gas)
Objectives
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Use the ideal gas law to determine gas volumes at different absolute temperatures and absolute pressures.
- Explain the effect that changing the pressure, number of moles, and temperature (individually) has on volume.
The ideal gas law is one of the fundamental principles used in calculations involving gas flow in air pollution-related work. This law is used to calculate actual gas flow rates based on the quantity of gas present at standard pressures and temperatures. It is also used to determine the total quantity of a contaminant in a gas that can participate in a chemical reaction.
The ideal gas law summarizes many of the concepts we have discussed in Module 1. It states that the volume occupied by a gas is a function of these three parameters:
- Number of moles of gas
- Absolute temperature
- Absolute pressure
The ideal gas law is expressed using this standard equation:
- Where:
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V = Volume
- n = Number of moles
- R = Universal gas constant
- T = Absolute temperature
- P = Absolute pressure
- n = Number of moles
Remember, moles is a measure of the number of molecules present.
The value of "R" depends on the units used for the other parameters. A number of equivalent forms of the universal gas constant are provided below.
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The ideal gas law is accurate as long as the pressures are relatively similar to normal ambient atmospheric pressures. This is almost always the case in air pollution-related work since the pressures usually range from -100 in. W.C. (absolute pressure of 307 in. W.C. at standard conditions) to approximately 50 in. W.C. (absolute pressure of 457 in. W.C. at standard conditions). This range of pressures is relatively small and does not extend to the pressures at which gases become compressible and the ideal gas no longer applies. The ideal gas law applies to mixtures of gases as well as to pure gases. Accordingly, it is very useful for evaluating gas stream properties.
Purpose: This Volume Calculator displays the volume of an ideal gas at a particular temperature, pressure, and molar quantity.
Restrictions on Use: Pressure must be ±10% of absolute atmospheric pressure and no vapors should be near their dew points.
Notes:
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This Java applet may take a few minutes to load.
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Sometimes calculator output is provided in an exponential format in base ten as shown below.
5.2e003 = 5.2
103
5.2e-003 = 5.2 10-3
- Inputting non-numeric characters such as commas and percent signs will result in erroneous output. (Decimal points are fine to use.)
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#1
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Do gases A, B, and C have the same or different volumes?
TIP: When the ideal gas law applies, a mole of any gas occupies the same volume under the same conditions of temperature and pressure.
The volume that gases occupy depends on the number of moles, the gas temperature, and pressure. The volume of a particular gas changes as its temperature and/or pressure changes as shown below.
A couple of very useful gas volume factors can be derived from the ideal gas law. These are illustrated in Example Problems 1 and 2.
Example Problem 1.
Volume of One Pound Mole of Gas at Standard Conditions
What is the volume of 1 pound mole (denoted "lb mole") of combustion gas at an absolute pressure of 14.7 psia and a temperature of 68°F? (These are EPA-defined standard conditions.)
Solution:
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Convert the temperature from relative to absolute scale (from °F to °R).
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Calculate the gas volume.
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Example Problem 2.
Volume of One Gram Mole of Gas at Standard Conditions
What is the volume of 1 gram mole (denoted "gm mole") of combustion gas at an absolute pressure of 760 mm Hg (29.92 in. Hg) and a temperature of 20°C? (These are EPA-defined standard conditions.)
Solution:
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Convert temperature from °C to °K and pressure from units of mm Hg to atm.
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Calculate the gas volume.
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TIP: It's easy to convert from moles to volume for an ideal gas (at EPA-defined standard conditions) by using these conversion factors:
1 lb mole of ideal gas occupies 385.4 ft3 (usually rounded to 385)
1 gm mole of ideal gas occupies 24.04 liters (usually rounded to 24 liters) or 0.02404 m3
These conversion factors will be used frequently throughout these modules.
The next lesson discusses gas flow rate, which is a concept closely related to gas volume.
Practice Problems
Ideal Gas Law
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Instructions:
- Complete the Practice Problems before proceeding to the next lesson. Click on the button below.