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.
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.
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.
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 ().
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.
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.
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.
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.)
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.
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:
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 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,
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.''
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.
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:
.. 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
(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
(b) Number of moles of per 10 moles of air?
answer: (a) 241 g/m
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.