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Module 2: Characteristics of Gases - Concentrations
Concentration Units of Measurement-
Volume Percent
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Partial Pressure
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Mole Fraction
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Parts Per Million (PPM)
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Calculator:
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Concentration Converter (Major Gas Constituents)
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Mass Per Cubic Meter
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TEQ Nanograms Per Cubic Meter (TEQ ng/m3)
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Calculator:
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Concentration Converter (Minor Gas Constituents)
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Summary of Concentration Units of Measure
Objectives
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Calculate the concentrations of gaseous pollutants in units of percent by volume, mole fraction, parts per million, milligrams per cubic meter, micrograms per cubic meter, and nanograms per cubic meter.
- Convert concentration data from one set of units to another.
Concentration Units of Measurement
Gases of interest in air pollution control are usually mixtures of several different compounds. For example, air is composed of three major constituents: nitrogen (N2) at approximately 78.1%, oxygen (O2) at approximately 20.9%, and argon at 0.9%. Many flue gas streams generated by industrial processes consist of the following major constituents: (1) nitrogen, (2) oxygen, (3) argon, (4) carbon dioxide (CO2), and (5) water vapor (H2O). Both air and industrial gas streams also contain minor constituents, including air pollutants, present at concentrations that are relatively low compared to these major constituents.
Note: Argon is usually not listed in most industrial gas analyses because it is chemically inert and difficult to measure. The argon concentration is often combined with the nitrogen concentration to yield a value of 79.0%. Argon will not be listed as a major constituent in these modules although it is implicit that this compound is present in air streams.
There is a need for ways to express both the concentrations of the major constituents of the gas stream and the concentrations of the pollutants present as minor constituents at relatively low concentrations. There are a variety of ways to express gas phase concentrations, which can easily be converted from one type of units to another. They include the following:
Major Constituents
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Volume percent
- Partial pressure
Both Major and Minor Constituents
- Mole fraction
Minor Constituents
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Parts per million (ppm)
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Milligrams per cubic meter (mg/m3)
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Micrograms per cubic meter (
g/m3)
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Nanograms per cubic meter (ng/m3)
All of the concentration units above can be expressed in a dry format as well as corrected to a standard oxygen concentration. These corrections are necessary because moisture and oxygen concentrations can vary greatly in gas streams, causing variations in pollutant concentrations. Information concerning the conversion of concentration data to a dry basis or a standard oxygen basis is presented later in this Module (see lessons on Dry Basis Conversions and Oxygen Basis Conversions).
Volume percent is one of the most common formats used to express the concentrations of major gas stream constituents such as oxygen, nitrogen, carbon dioxide, and water vapor. The format is very common partially because the gas stream analysis techniques used in EPA emission testing methods provide data directly in a volume percent format. For example, techniques such as ORSAT analyzers, FYRITE® analyzers, and combustion gas analyzers provide data in volume percent. In most cases, the data is provided in a dry format (discussed later).
The following equation can be used to calculate gas concentrations as volume percent for a gas mixture.
Concentration data expressed as volume percent have the same value at both actual and standard conditions, because any adjustments necessary to account for changes in temperature and pressure affect the numerator and denominator proportionally. This relationship is stated in the following equation:
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Where:
Concentration data expressed as volume percent have the same value in both American Engineering units and Cgs units. For these reasons, the volume percent format is a convenient means to use concentration data for major constituents.
Figure 1 (Volume Percent Concentration) shows typical concentrations of gases emitted from the stack of a coal-fired boiler.
Concentrations can also be expressed in terms of partial pressures. This expression refers to the part of the total pressure exerted by one of the constituent gases.
Gases composed of different chemical compounds such as molecular nitrogen and oxygen behave physically the same as gases composed of a single compound. At any given temperature, one mole of a gas exerts the same pressure as one mole of any other type of gas. All of the molecules move at a rate that is dependent on the absolute temperature, and they exert pressure. The total pressure is the sum of the pressures of each of the components. The equations below are often called Dalton's law of partial pressures.
Because the partial pressure value is related to the total pressure, concentration data expressed as partial pressure are not the same at actual and standard conditions. The partial pressure values are also different in American Engineering units and Cgs units.
Example Problem 1.
Calculate the Partial Pressure of Gases
What are the partial pressures if ambient air at standard conditions has a composition of 79% molecular nitrogen, 20.9% oxygen, and 0.0360% carbon dioxide? The total pressure is one atmosphere or 14.7 psia.
Solution:
The mole fraction is simply an expression of the number of moles of a compound divided by the total number of moles of all the compounds present in the gas.
Concentration data expressed as mole fractions have the same value at both actual and standard conditions, because any changes in the temperature and pressure would equally affect the numerator and denominator of Equation 8. The following equation applies to mole fraction concentration data.
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Where:
Concentration data expressed as mole fractions have the same value in both American Engineering units and Cgs units.
For ideal gases (most air pollution control situations) the mole fraction is an alternative way of expressing the volume percent.
Example Problem 2.
Calculate the Mole Fraction of Gases in a Mixture
A container holds 2 lb moles of ambient air with a composition of 79% molecular nitrogen, 20.9% molecular oxygen, and 0.1% other compounds. What is the mole fraction of molecular nitrogen and oxygen in the air?
Solution:
TIP: The mole fraction is a dimensionless number. It is the ratio of the volume percent of one component divided by the total (100%) volume percent. The volume percent units cancel out.
The parts per million by volume format is a useful means of expressing the concentrations of pollutants present at low concentrations (see Figure 2). It is defined in Equations 11 to 14.
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Where:
TIP: Note the relationship between Equations 11 and 12 and Equations 13 and 14. Once you know the gas concentration expressed as mole fraction or volume percent, you can calculate the concentration in ppm.
The units of parts per million (ppm) are used extensively in the air pollution control and industrial hygiene professions. This format is especially convenient for expressing concentration data because most air pollutants are present at concentrations ranging from 0.01 to 10,000 ppm. Therefore, the numerical values of concentrations expressed in ppm are easy to use.
Because concentration data expressed in ppm is a ratio of two volumes (the pollutant and the total gas sample, see Equation 13), the value is identical at both actual and standard conditions. Both of the volumes (numerator and denominator) are adjusted identically when accounting for changes in temperature and pressure. Accordingly, the following equation is correct.
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Where:
Because the ppm format is simply a ratio of volumes of moles, concentration expressed in ppm is the same in both American Engineering units and Cgs units.
Concentration data is frequently expressed in ppm due to the following: (1) the convenient numerical values, (2) the identical values for both actual and standard conditions (temperatures and pressures), and (3) the identical values for both American Engineering units and Cgs units.
Concentration Converter (Major Gas Constituents)
Purpose: This calculator converts concentrations of major gas constituents between the following units of measure: volume percent, mole fraction, partial pressure, and parts per million. Where partial pressure is involved in the calculation, the barometric pressure must also be supplied as input.
Restrictions on Use: Do not use commas when inputting values.
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.)
PPM Units
The term ppm will also be used interchangeably with the terms ppmv or ppm(v/v). Both of these alternative units simply state that the concentration has been expressed as a ratio of volumes as indicated by Equation 13. The additional terms of "v" or "(v/v)" are sometimes helpful because the term ppm is also used extensively with respect to liquid phase concentrations. When applied to liquid concentrations, ppm is exclusively calculated based on a mass ratio as indicated by Equation 16.
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Where:
The liquid concentration data is often stated in terms of ppm(w/w) to indicate that it has been calculated as a ratio of the mass of the pollutant divided by the mass of the total liquid sample.
In publications and projects concerning both liquid and gas phase concentration data, it is helpful to express the gas concentrations in ppmv or ppm(v/v) and the liquid concentrations in ppm(w/w). These distinctions minimize the possible errors due to the improper calculation of these values. When the term "ppm" is used in situations where only gas phase concentrations are being considered, it can usually be assumed that the ppm concentration data values were calculated in accordance with Equations 11 - 14.
Note: Throughout Basic Concepts in Environmental Sciences, the term ppm when applied to gases means ppmv or ppm(v/v), and the term ppm when applied to liquids means ppm(w/w).
Relationship Between Volume Percent and PPM
Show 100% volume concentration as ppm (Figure 3).
Show 50% volume concentration as ppm (Figure 4).
Show 1% volume concentration as ppm (Figure 5).
Example Problem 3.
Calculate Concentration Expressed as PPM
What is the concentration of sulfur dioxide, expressed as ppm, in a combustion gas having the following composition?
Solution:
Since gas concentrations are provided as volume percents, use the following equation:
Three different sets of units are used to express pollutant concentrations in terms of mass per cubic meter:
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Milligrams per cubic meter (mg/m3)
- Micrograms per cubic meter (µg/m3)
- Nanograms per cubic meter (ng/m3)
- Micrograms per cubic meter (µg/m3)
Milligrams per cubic meter are frequently used to express the concentrations of both gases and particulate that are present at moderately high concentrations. The units of micrograms per cubic meter (µg/m3) are used to express concentrations of pollutants that are present at very low concentrations. Metals and organic compound concentrations are often expressed in these units. For pollutants at extremely low concentrations, such as dioxin-furan compounds, the concentration data is expressed in nanograms per cubic meter. The relationships between these three sets of units are shown below in Equation 17.
These three different units of measure to express mass per cubic meter concentration data help avoid using awkward numbers that are too large or have too many decimal places. For example, an SO2 concentration of 2 mg/m3 is more convenient than the same concentration expressed as 2,000,000 ng/m3. A dioxin-furan concentration expressed as 400 ng/m3 is more convenient than the same concentration expressed as 0.0004 mg/m3.
The volume term in the denominator of these units for concentration can be either actual cubic meters or standard cubic meters. It is important to state the basis for the cubic meter volume because concentration data expressed as mass per cubic meter do not have the same numerical values at actual and standard conditions. The Table below shows abbreviated units of measure for concentration data at actual and standard conditions and how to distinguish actual cubic meters from standard cubic meters.
Converting Concentration Data from
Units of PPM to Mass Per Cubic Meter
Use Equation 18 or 19 to convert concentrations from parts per million to milligrams per standard cubic meter if the molecular weight of the compound is known.
Note: Once the mass per cubic meter concentration is calculated at standard conditions, it can be easily converted to actual conditions if necessary.
- Where: MWi is the molecular weight of Compound i expressed as lbm/lb mole
This equation can be simplified by combining the constant terms and canceling units:
- Where: MWi is the molecular weight of Compound i expressed as lbm/lb mole
Similar equations for converting ppm to micrograms per cubic meter and nanograms per cubic meter are provided below.
Concentration Converter (Minor Gas Constituents)
Purpose: This calculator converts concentrations of minor gas constituents between the following units of measure: parts per million, milligrams per cubic meter, micrograms per cubic meter, and nanograms per cubic meter.
Restrictions on Use: Inputs for mass per cubic meter concentrations may be entered at any temperature and pressure, but outputs for these concentrations are given at EPA-defined standard conditions of temperature and pressure [20°C (68°F) and 1 atm (14.7 psia)]. Do not use commas when inputting values.
Link to periodic table of elements.
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.)
Dioxin-furan compound concentrations are often expressed on a Toxic Equivalency Quotient (TEQ) basis rather than a total mass per cubic meter (nanograms per cubic meter basis). The TEQ format is an adjusted form of the concentration data that takes into account the substantially different toxicities of some of the dioxin-furan compounds. Data expressed in a TEQ basis are often considered to be more representative of the possible health impact of emissions than data expressed as total dioxin-furan compounds. The TEQ basis is used extensively in recently developed EPA regulations.
There are 210 different dioxin-furan compounds or isomers. The compound-to-compound differences depend on the location of chlorine atoms on the dioxin and furan rings shown in (Figure 6).
The dioxin-furan compounds can be divided into eight groups depending on the total number of chlorine atoms present on each molecule. The most toxic dioxin-furan compounds are believed to be those having from four to eight chlorine atoms. These are termed the tetra- to octa-dioxin furan compounds. The compound that is considered most toxic is 2,3,7,8 tetrachloro-p-dibenzo dioxin. The TEQ concentration is calculated by weighting factors that assign a value of 1.0 to 2,3,7,8 tetrachloro-p-dibenzo dioxin. The other sixteen compounds believed to be especially toxic are assigned weighting factors less than 1.0 as indicated in the following table.
A variety of weighting factors has been published based on different organizations' assessments of the relative toxicities of the dioxin-furan congeners. However, the International Toxic Equivalency Quotient (ITEQ) values are the most commonly used set of weighting factors and have been accepted by the U.S. EPA. Unless, otherwise specified, the ITEQ weighting factors should be assumed when reviewing dioxin-furan concentration data expressed on a TEQ basis.
The TEQ basis concentration data are almost always presented in standard conditions. Furthermore, the data is usually presented in Cgs form. There are no commonly used American Engineering units for TEQ data.
Example Problem 4.
TEQ Calculations
Calculate the dioxin-furan compound concentration on a TEQ basis using the following compound-by-compound catch weights (material recovered from sampling train) and the sample gas volume measured during the test. Use the ITEQ weighting factors and the following data:
Total sample volume during emission test = 3.1 DNm3
Note: It is apparent that the TEQ concentration data are lower than the measured concentration data for the seventeen isomers used in the TEQ calculation. Furthermore, the TEQ data are lower than the total dioxin-furan concentration values measured for all 210 isomers. The TEQ basis is used because medical researchers believe that the compounds included in the calculation are considerably more toxic than the other dioxin-furan compounds. Accordingly, dioxin-furan data calculated on a TEQ basis are more closely related to the possible adverse health effects of these emissions.
Summary of Concentration Units of Measure
The various concentration units of measure are selected primarily based on convenience. Conversions between the various units of measure are often needed to ensure that all of the units are consistent during calculations.
Tables 4 and 5 summarize the characteristics of the different concentration formats discussed in this Lesson.
Practice Problems
Concentrations
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Instructions:
- Complete the Practice Problems before proceeding to the next lesson. Click on the button below.