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The first component of CE251 covers physical processes which are important in the movement of pollutants through the environment and the processes used to control and treat pollutant emissions. We begin with an introduction to the units used to measure pollutant levels. This is followed in section 2 with a study of the use of material and energy balances. These balances provide tools which will be used throughout the course and are essential for the solution of a great number of environmental engineering and science problems. Material balances are the basis for reactor design, developed in section 3.

Section 4 describes advection and diffusion, the processes by which pollutants are transported through the environment. Transport of pollutants through the movement of wind and water currents---advection---is the mechanism by which pollutants can move great distances through the environment. On a smaller scale, however, diffusion (random motion) is often more important than advection. Even on larger scales, diffusion can be significant---for example, the movement of air pollutants on global scales can sometimes be best described as a process of turbulent diffusion.

The final section of Part I extends the description of transport processes with a look at the movement of particles in fluids, and, in a sort of reverse problem, the movement of fluid through porous soil. The rate of the particle movement or fluid flow is governed by the interplay of forces causing movement---such as the force of gravity---with drag forces which oppose movement. Section 5 covers the way in which these forces determine the speed of settling particles or of fluid flowing through soil.

Units of Concentration

Before beginning the main topics of this section, it is necessary to cover units of concentration which will be used throughout the course. Pollutant concentration is the most important determinant in almost all aspects of pollutant fate and transport in the environment and in engineered systems. Concentration is also the driving force which controls the rate of chemical reactions and pollutant effects, such as toxicity, are often determined by concentration.

Concentrations of pollutants and other chemicals are routinely expressed in a variety of units. The choice of units to use in a given situation depends on the pollutant, where it is located (e.g., air, water, or soil), and often on what the measurement will be used for. It is therefore necessary to become familiar with the units used and methods for converting between different sets of units.

Most of the ways concentration is represented fall into the categories shown in Table 1.

Mass Concentration Units

Concentration units based on pollutant mass include mass pollutant/total mass and mass pollutant/total volume. Examples of these are shown below. In these descriptions, is used to represent the mass of the pollutant, referred to as compound A.

Mass/mass Units: ppm.

Parts-per-million by mass (ppm, or ppm) is defined as the number of units of mass of pollutant per million units of total mass. That is,

This definition is equivalent to the following general formula, which is used to calculate ppm concentration from measurements of pollutant mass in a sample of total mass :


Note that the factor in equation 2 is really a conversion factor. It has implicit units as shown in explicitly here:

This factor is entirely equivalent to the factor of 10 which is used to convert fractions to percentages. When you use the equation

you are really following the following equation:

Similar definitions are used for the units ppb, ppt, and % by mass. That is, 1 ppb part per billion = 1 g pollutant per billion () g total, so that the number of ppb in a sample is equal to . Percent by mass is analogously equal to the number of g pollutant per 100 g total. Be cautious about interpreting ppt values---they can refer to either parts per thousand or parts per trillion ().

  Example .. Concentration in soil. A   1.0 kg sample of soil is analyzed for the pollutant trichloroethylene (TCE). The analysis indicates that the sample contains 5.0 mg of TCE. What is the TCE concentration in ppm?

Mass/volume Units: mg/l.

In water, units of are common. Note from Example 1.2 that, in water ppm is equivalent to mg/l. This is because the density of pure water is approximately 1000 g/l. Most aqueous solutions encountered in environmental engineering and science are dilute, meaning that dissolved material does not add significantly to the mass of the water, and the total density remains approximately 1000 g/l.

  Example .. Concentration in water. One liter of water is analyzed and found to contain 5.0 mg TCE. What is the TCE concentration in mg/l and ppm?
Solution: The concentration in units of mg/l is obtained simply by dividing the measured mass of TCE by the volume of water. No conversion is necessary, since the measured quantities are already in mass/volume units:

To convert to ppm, which is a mass/mass unit, it is necessary to convert the volume of water to mass of water, by dividing by the density of 1000 g/l:

For concentrations in the atmosphere, it is common to use units of mass/ air. For example, and are common.

  Example .. Concentration in gas. What is the carbon monoxide concentration (expressed in ) of a 10 l gas mixture which contains mole of CO?
Solution: In this case, we are presented with measured quantities which are in units of moles pollutant/total volume. To convert to mass of pollutant/total volume, we must convert moles of pollutant to mass of pollutant. This requires multiplying by the molecular weight. The next two lines of the solution are simply unit conversions, from grams to micrograms and from liters to cubic meters.

Note that the molecular weight of CO (28 g) is equal to 12 (molecular weight of C) plus 16 (molecular weight of O). Molecular weight calculations are covered in freshman chemistry---review your chemistry textbook if these concepts are not fresh.

Volume/volume and moles/moles Units.

Units of volume fraction or mole fraction are frequently used for gas concentrations. The most common volume fraction units are ppm (ppm by volume) which is defined as

Note that here, again, the factor is really a conversion factor, with units of volume fraction).

Also common is ppb (parts per by volume). Volume/volume units have the advantage that they are unchanged as gases are compressed or expanded. (Note that atmospheric concentrations expressed as decrease as the gas expands, since the pollutant mass remains constant but the volume increases.)

The Ideal Gas Law.

To convert gas concentration between mass/volume and volume/volume, we use the Ideal Gas Law, which states that


(Pressure) (Volume taken up)
= (No. of moles) (R, gas constant) (Temperature in Kelvin or Rankin).

R, the universal gas constant, is a useful constant to know and may be expressed in many different sets of units. Some of the most useful are displayed in Table 1. The gas constant may be expressed in a number of different sets of units---always include all the units in each term and cancel them out to ensure that you are using the correct value of R in equation 5.

The ideal gas law states that the volume taken up by a given number of molecules of any gas is the same, no matter what the molecular weight or composition of the gas, as long as the pressure and temperature are constant. Equation 5 can be rearranged to show that the volume taken up by n moles of gas is equal to


At standard conditions (P=1 atm, T=273 K), one mole of any pure gas will fill a volume of 22.4 l. As an exercise, use the values of R\ given in Table 1 with equation 6 to derive this result.

  Example .. Gas concentration in volume or mole fraction. A gas mixture contains 0.001 mole of sulfur dioxide () and 0.999 moles of air. What is the concentration, expressed in units of ppm?
Solution: The concentration in ppm is calculated using the formula

To solve, we can convert the number of moles of to volume using the ideal gas law (), also convert the total number of moles to volume, and then divide the two:

Substituting these volume terms in the equation for ppm, we obtain

Note that the terms in example 1.4 cancel out. This demonstrates a fact that can save you effort in calculating volume fraction or mole fraction concentrations--- for gases, volume ratios and mole ratios are equivalent. This is clear from the ideal gas law (equation 6), since at constant temperature and pressure the volume taken up by a gas is proportional to the number of moles. So, the following two equations are equivalent:

  Example .. Gas concentration conversion. The concentration of in air is 100 ppb. What is this concentration in units of ? (Temperature is 28 C and pressure is 1 atm. Remember that T ( K) is equal to T ( C) plus 273.)
Solution: To accomplish this conversion, we will use the ideal gas law to convert volume of to moles of , resulting in units of moles/l. These can be converted to using the molecular weight of . This method will be used to develop a general formula for converting between ppm and in the first homework assignment.

First, we use the definition of ppb to obtain a volume ratio for :

We must now convert the volume of in the numerator to units of mass. This is done in two steps. First, we convert the volume to a number of moles, using the ideal gas law. From the standard form of the ideal gas law (PV=nRT), solving for the number of moles n\ yields . So, we multiply the quantity of given in volume units by to obtain units of moles. Note the choice of value for R used below, which is taken from Table 1, based on the units used in the problem.

For the second step, we convert the moles of to mass of , using the molecular weight of and converting from g to g.

Partial Pressures.

Partial pressure units are also used to represent concentrations of gases. The total pressure exerted by a gas mixture may be considered as the sum of the partial pressures exerted by each component of the mixture. The partial pressure of each component is equal to the pressure that would be exerted if all of the other components of the mixture were suddenly removed. Partial pressure is commonly written as , where i is the gas being considered. For example, the partial pressure of oxygen in the atmosphere at ground level may be written as atm.

The ideal gas law states that, at a given temperature and number of moles of gas, pressure is directly proportional to the number of moles of gas present:


Therefore, pressure fractions are identical to mole fractions (and volume fractions). For this reason, partial pressure may be calculated as the product of the mole or volume fraction and the total pressure. That is,

Moles/volume Units.

Units of moles per liter (molarity, M) are often used to report concentrations of compounds dissolved in water. Molarity is defined as the number of moles of compound per liter of solution. Thus a M solution of nitric acid contains moles of per liter. Concentrations expressed in these units are read as molar. Thus, this solution would be described as ``\ molar.''

  Example .. Molarity. Convert the concentration of TCE found in example 1.2 (5.0 ppm) to units of M (molarity). (The molecular weight of TCE is 131.5 g.)
Solution: In water, ppm is equivalent to , so we have 5.0 mg/l of TCE. Conversion to molarity units requires only the molecular weight:

Often, concentrations below 1 M are expressed in units of millimoles per liter, or millimolar (1 mM = moles/l). Thus, the concentration of TCE in example 1.6 is 0.038 mM.

Other Types of Units

The units described here are the most common, but are not the only types of units you will encounter in environmental engineering problems. Some important additional ways to represent concentration include:

Lumped concentration.

Lumped concentrations are reported by element, and can include contributions from a number of different chemical compounds. For example, the phosphorus in a lake may be present in three chemical forms: HPO, HPO, and PO. Since phosphorus can be chemically converted between these three forms, it makes sense to report the total concentration, without specifying which form(s) are present. To avoid confusion regarding the molecular weight, which is different for the three forms, the atomic weight of phosphorus is used and concentration is reported in units of as phosphorus (mg/l P).

Representation by effect.

In some cases, ``concentrations'' are not used at all. Instead, the strength of a solution or mixture is defined by its effect in the environment. This method is used as a measure of the content of sewage effluent and other wastes in streams. Biological consumption of these wastes results in the removal of oxygen from the stream, and can result in fish kills in extreme cases. Instead of identifying the variety of compounds that may be present, it is more convenient to report the effect, in units of the number of mg of oxygen that can be consumed per liter of water. This unit is referred to as BOD---biochemical oxygen demand. Other similar ``concentration'' measures include COD (chemical oxygen demand), toxicity, and alkalinity.


  .. Unit Conversion. You are told that the concentration of a certain pollutant molecule in the air is x ppm, but need to compare the concentration to a standard which is expressed .
(a) Use the ideal gas law to calculate, in terms of x and the molecule's molecular weight M, the concentration of this molecule in units of . (Temperature is 25 C, and pressure is 1.0 atm.) Show all steps of your solution.
(b) Does your formula depend on temperature and/or pressure?

answer: (a) Conc. in , or

  .. A typical loaf of bread contains 120 mg of sodium in each 1 ounce slice.
(a) What is the concentration of sodium in the bread in ppm?
(b) Is that ppm or ppm? Which makes sense and why?
(Recall that 1 lb. = 16 oz., and 1 lb. = 0.454 kg. The atomic weight of Na is 23.0.)

answer: (a) 4200 ppm

  .. A chemist reports that the concentration of nitrite () plus nitrate () in a groundwater sample from a farming region is 0.850 mM (M). Nitrite and nitrate are often elevated in groundwater in farming regions due to nitrogen fertilization. Regulations require that the total concentration () be below 10.0 mg/l as N to avoid methemoglobinemia, or blue-baby syndrome, which can be fatal.
(a) What is the concentration of () expressed as mg/l as N?
(b) What is the concentration expressed as ppm as N?
(Atomic weight of nitrogen (N) is 14.0.)
(c) What is the concentration expressed as % by mass as N?

answer: (a) 11.9 mg/l---don't give the water to a baby!

  .. The concentration of ozone () in Los Angeles on a hot summer day (T = 30 C, P = 1 atm) is 125 ppb. What is the concentration in units of
(a) g/m?
(b) Number of moles of per 10 moles of air?

answer: (a) 241 g/m
(b) 0.125

  .. An empty balloon is filled with exactly 10 g of nitrogen () and 2 g of oxygen (). Pressure and temperature in the room are 1.0 atm and 25 C, respectively.
(a) What is the concentration in the balloon in units of percent by volume?
(b) What is the volume of the balloon after it's blown up, in l? (Use the ideal gas law.)

answer: (a) 14.9% by volume. (b) 10.3 l.

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Next: Mass and Energy Up: CE251 Part I Previous: Contents