Introduction to Atmospheric Chemistry - Hardcover

Jacob, Daniel J.

Hardcover

ISBN 10: 0691001855 ISBN 13: 9780691001852

Publisher: Princeton University Press, 2000

Synopsis

Atmospheric chemistry is one of the fastest growing fields in the earth sciences. Until now, however, there has been no book designed to help students capture the essence of the subject in a brief course of study. Daniel Jacob, a leading researcher and teacher in the field, addresses that problem by presenting the first textbook on atmospheric chemistry for a one-semester course. Based on the approach he developed in his class at Harvard, Jacob introduces students in clear and concise chapters to the fundamentals as well as the latest ideas and findings in the field. Jacob's aim is to show students how to use basic principles of physics and chemistry to describe a complex system such as the atmosphere. He also seeks to give students an overview of the current state of research and the work that led to this point. Jacob begins with atmospheric structure, design of simple models, atmospheric transport, and the continuity equation, and continues with geochemical cycles, the greenhouse effect, aerosols, stratospheric ozone, the oxidizing power of the atmosphere, smog, and acid rain. Each chapter concludes with a problem set based on recent scientific literature. This is a novel approach to problem-set writing, and one that successfully introduces students to the prevailing issues. This is a major contribution to a growing area of study and will be welcomed enthusiastically by students and teachers alike.

About this title

About the Author

Daniel J. Jacob is the Gordon McKay Professor of Atmospheric Chemistry and Environmental Engineering at Harvard University. He has taught the undergraduate atmospheric chemistry course at Harvard since 1992. He has published over 100 research papers in atmospheric chemistry journals.

From the Back Cover

"I can actually imagine a rigorous and challenging undergraduate course making it through this whole text in one semester, which is not the case for its competitors. The problem sets are excellent . . . truly unique."--Hiram Levy, Princeton University

From the Inside Flap

"I can actually imagine a rigorous and challenging undergraduate course making it through this whole text in one semester, which is not the case for its competitors. The problem sets are excellent . . . truly unique."--Hiram Levy, Princeton University

Excerpt. © Reprinted by permission. All rights reserved.

Introduction to Atmospheric Chemistry

By DANIEL J. JACOB

PRINCETON UNIVERSITY PRESS

Copyright © 1999 Princeton University Press
All right reserved.
ISBN: 978-0-691-00185-2

Contents

Preface...........................................................xi1 – Measures of Atmospheric Composition.....................32 – Atmospheric Pressure....................................143 – Simple Models...........................................244 – Atmospheric Transport...................................425 – The Continuity Equation.................................796 – Geochemical Cycles......................................877 – The Greenhouse Effect...................................1158 – Aerosols................................................1469 – Chemical Kinetics.......................................15710 – Stratospheric Ozone....................................16411 – Oxidizing Power of the Troposphere.....................20012 – Ozone Air Pollution....................................23113 – Acid Rain..............................................245Numerical Solutions to Problems...................................257Appendix. Physical Data and Units.................................259Index.............................................................261

Chapter One

Measures of Atmospheric Composition

The objective of atmospheric chemistry is to understand the factors that control the concentrations of chemical species in the atmosphere. In this book we will use three principal measures of atmospheric composition: mixing ratio, number density, and partial pressure. As we will see, each measure has its own applications.

1.1 Mixing Ratio

The mixing ratio C_X of a gas X (equivalently called the mole fraction0 is defined as the number of moles of X per mole of air. It is given in units of mol/mol abbreviation for moles per mole , or equivalently in units of v/v volume of gas per volume of air since the volume occupied by an ideal gas is proportional to the number of molecules. Pressures in the atmosphere are sufficiently low that the ideal gas law is always obeyed to within 1%.

The mixing ratio of a gas has the virtue of remaining constant when the air density changes (as happens when the temperature or the pressure changes). Consider a balloon filled with room air and allowed to rise in the atmosphere. As the balloon rises it expands, so that the number of molecules per unit volume inside the balloon decreases; however, the mixing ratios of the different gases in the balloon remain constant. The mixing ratio is therefore a robust measure of atmospheric composition.

Table 1-1 lists the mixing ratios of some major atmospheric gases. The most abundant is molecular nitrogen (N₂) with a mixing ratio [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] mol/mol; N₂ accounts for 78% of all molecules in the atmosphere. Next in abundance are molecular oxygen (O₂) with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] mol/mol, and argon (Ar) with ITLITL_Ar = 0.0093 mol/mol. The mixing ratios in table 1-1 are for dry air, excluding water vapor. Water vapor mixing ratios in the atmosphere are highly variable (10^-6-10^-2 mol/mol). This variability in water vapor is part of our everyday experience as it affects the ability of sweat to evaporate and the drying rate of clothes on a line.

Gases other than N₂, O₂, Ar, and H₂O are present in the atmosphere at extremely low concentrations and are called trace gases. Despite their low concentrations, these trace gases can be of critical importance for the greenhouse effect, the ozone layer, smog, and other environmental issues. Mixing ratios of trace gases are commonly given in units of parts per million volume (ppmv or simply ppm), parts per billion volume ppbv or ppb), or parts per trillion volume (pptv or ppt); 1 ppmv = 1 × 10^-6 mol/mol, 1 ppbv = 1 × 10^-9 mol/mol, and 1 pptv = 1 × 10^-12 mol/mol. For example, the present-day CO₂ concentration is 365 ppmv (365 × 10_-6 mol/mol.

1.2 Number Density

The number density n_x of a gas X is defined as the number of X molecules of X per unit volume of air. It is expressed commonly in units of molecules cm^-3 number of molecules of X per cm³ of air). Number densities are critical for calculating gas-phase reaction rates. Consider the bimolecular gas-phase reaction

X + Y → P + Q. (R1)

The loss rate of X by this reaction is equal to the frequency of collisions between molecules of X and Y multiplied by the probability that a collision will result in chemical reaction. The collision frequency is proportional to the product of number densities n_Xn_Y. When we write the standard reaction rate expression

d/dt [X] = -k[X][Y] (1.1)

where k is a rate constant, the concentrations in brackets must be expressed as number densities. Concentrations of short-lived radicals and other gases that are of interest primarily because of their reactivity are usually expressed as number densities.

Another important application of number densities is to measure the absorption or scattering of a light beam by an optically active gas. The degree of absorption or scattering depends on the number of molecules of gas along the path of the beam and therefore on the number density of the gas. Consider in figure 1-1 the atmosphere as extending from the Earth's surface (z = 0) up to a certain top (z = z_T) above which number densities are assumed negligibly small the meaning of z_T will become clearer in chapter 2). Consider in this atmosphere an optically active gas X. A slab of unit horizontal surface area and vertical thickness dz contains n_x dz molecules of X. The integral over the depth of the atmosphere defines the atmospheric column of X as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.2)

This atmospheric column determines the total efficiency with which the gas absorbs or scatters light passing through the atmosphere. For example, the efficiency with which the ozone layer prevents harmful solar ultraviolet radiation from reaching the Earth's surface is determined by the atmospheric column of ozone (problem 1.3).

The number density and the mixing ratio of a gas are related by the number density of air n_a (molecules of air per cm³ of air): n_x = C_Xn_a. (1.3)

The number density of air is in turn related to the atmospheric pressure P by the ideal gas law. Consider a volume V of atmosphere at pressure P and temperature T containing N moles of air. The ideal gas law gives

PV = NRT, 1.4

where R = 8.31 J mol^-1 K^-1 is the gas constant. The number density of air is related to N and V by

n_a = A_vN/V (1.5)

where A_v = 6.022 x 10²³ molecules mol^-1 is Avogadro's number. Substituting equation (1.5) into (1.4) we obtain

n_a = A_vP/RT (1.6)

and hence

n_X = A_vP/RT C_X (1.7)

We see from 1.7 that n_x is not conserved when P or T changes.

A related measure of concentration is the mass concentration ρ_X, representing the mass of _X per unit volume of air (we will also use ρ_X to denote the mass density of a body, i.e., its mass per unit volume; the proper definition should be clear from the context. ρ_X and n_X are related by the molecular weight M_X (kg mol-1) of the gas:

ρ_x = n_XM_X/A_v. (1.8)

The mean molecular weight of air M_a is obtained by averaging the contributions from all its constituents i:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.9)

and can be approximated for dry air from the molecular weights of N₂, O₂, and Ar:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.10)

In addition to gases, the atmosphere also contains solid or liquid particles suspended in the gaseous medium. These particles represent the atmospheric aerosol; "aerosol" is a general term describing a dispersed condensed phase suspended in a gas. Atmospheric aerosol particles are typically between 0.01 and 10 µm in diameter (smaller particles grow rapidly by condensation while larger particles fall out rapidly under their own weight). General measures of aerosol abundances are the number concentration (number of particles per unit volume of air) and the mass concentration (mass of particles per unit volume of air). A full characterization of the atmospheric aerosol requires additional information on the size distribution and composition of the particles.

Exercise 1-1 Calculate the number densities of air and CO₂ at sea level for P = 1013 hPa, T = 0°C.

Answer. Apply (1.6) to obtain the number density of air n_a. Use International a System SI base units at all times in numerical calculations to ensure consistency:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

After you obtain the result for n_a in SI base units, you can convert it to the more commonly used unit of molecules cm^-3: n_a = 2.69 x 10¹⁹ molecules cm^-3. The air density at sea level does not vary much around the world; the sea-level pressure varies by at most 5%, and the temperature rarely departs by more than 15% from 273 K, so that n_a remains within 25% of the value calculated here.

The number density of CO₂ is derived from the mixing ratio [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ppmv:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Exercise 1-2 In surface air over the tropical oceans the mixing ratio of water vapor can be as high as 0.03 mol/mol. What is the molecular weight of this moist air?

Answer. The molecular weight M_a of moist air is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where M_a,dry = 28.96 × 10^-3 kg mol^-1 is the molecular weight of dry air derived in (1.10), and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. For [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] mol/mol we obtain M_a = 28.63 × 10^-3 kg mol^-1. A mole of moist air is a lighter than a mole of dry air.

1.3 Partial Pressure

The partial pressure P_X of a gas X in a mixture of gases of total X pressure P is defined as the pressure that would be exerted by the molecules of X if all the other gases were removed from the mixture. Dalton's law states that P_X is related to P by the mixing ratio C_X:

P_X = C_X P. (1.11)

For our applications, P is the total atmospheric pressure. Similarly to (1.6), we use the ideal gas law to relate P_X to n_x:

P_X = n_X/A_v RT. (1.12)

The partial pressure of a gas measures the frequency of collisions of gas molecules with surfaces and therefore determines the exchange rate of molecules between the gas phase and a coexistent condensed phase. Concentrations of water vapor and other gases that are of most interest because of their phase changes are often given as partial pressures.

Let us elaborate on the partial pressure of water [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], commonly called the water vapor pressure. To understand the physical meaning of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], consider a pan of liquid water exposed to the atmosphere (figure 1-2a). The H₂O molecules in the liquid are in constant motion. As a result of this motion, H₂O molecules at the surface of the pan evaporate to the atmosphere. If we let this evaporation take place for a long enough time, the pan will dry out. Let us place a lid on top of the pan to prevent the H₂O molecules from escaping (figure 1-2b). The H₂O molecules escaping from the pan bounce on the lid and must now eventually return to the pan; a steady state is achieved when the rate at which molecules evaporate from the pan equals the rate at which water vapor molecules return to the pan by collision with the liquid water surface. The collision rate is determined by the water vapor pressure [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] in the head space. Equilibrium between the liquid phase and the gas phase is achieved when a saturation vapor pressure [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is reached in the head space. If we increase the temperature of the water in the pan, the energy of the molecules at the surface increases and hence the rate of evaporation increases. A higher collision rate of water vapor molecules with the surface is then needed to maintain equilibrium. Therefore, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] increases as the temperature increases.

Cloud formation in the atmosphere takes place when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and it is therefore important to understand how [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] depends on environmental variables. From the phase rule, the number n of independent variables determining the equilibrium of c chemical components between a number p of different phases is given by

n = c + 2 - p. (1.13)

In the case of the equilibrium of liquid water with its vapor there is only one component and two phases. Thus the equilibrium is determined by one single independent variable; at a given temperature T, there is only one saturation vapor pressure [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for which liquid and gas are in equilibrium. The dependence of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on T is shown in figure 1-3. Also shown on the figure are the lines for the gas-ice and liquid-ice equilibria, providing a complete phase diagram for water. There is a significant kinetic barrier to ice formation in the atmosphere because of the paucity of aerosol surfaces that may serve as templates for condensation of ice crystals. As a result, cloud liquid water readily supercools (remains liquid) down to temperatures of about 250 K, and the corresponding curve is included in figure 1-3.

In weather reports, atmospheric water vapor concentrations are frequently reported as the relative humidity RH or the dew point (T_d). The relative humidity is defined as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.14)

so that cloud formation takes place when RH > 100%. The dew point is defined as the temperature at which the air parcel would be saturated with respect to liquid water:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.15)

At temperatures below freezing, one may also report the frost point T_f corresponding to saturation with respect to ice.

Exercise 1-3 How many independent variables determine the liquid-vapor equilibrium of the H₂O-NaCl system? What do you conclude regarding the 2 ability of sea salt aerosol particles in the atmosphere to take up water?

Answer. There are two components in this system: H₂O and NaCl. Liquid-vapor equilibrium involves two phases: the H₂O-NaCl liquid solution and the 2 gas phase. Application of the phase rule gives the number of independent variables defining the equilibrium of the system:

n = c + 2 - p = 2 + 2 - 2 = 2.

Because n = 2, temperature alone does not define the saturation water vapor pressure above a H₂O-NaCl solution. The composition of the solution i.e., the mole fraction of NaCl) is another independent variable. The presence of NaCl molecules on the surface of the solution slows down the evaporation of water because there are fewer H₂O molecules in contact with the gas phase 2 (Figure 1-2). Therefore, NaCl-H₂O solutions exist at equilibrium in the 2 atmosphere at relative humidities less than 100%; the saturation water vapor pressure over a NaCl-H₂O solution decreases as the NaCl mole fraction 2 increases. In this manner, sea salt aerosol particles injected to the atmosphere by wave action start to take up water at relative humidities as low as 75% not at lower relative humidities, because the solubility constant of NaCl in H₂O places an upper limit on the mole fraction of NaCl in a NaCl-H₂O solution). The same lowering of water vapor pressure applies for other types of aerosol particles soluble in water. The resulting swelling of particles by uptake of water at high humidities reduces visibility, producing the phenomenon known as haze.

(Continues...)

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Edition details

• Publisher: Princeton University Press
• Publication date: 2000
• Language: English
• ISBN 10: 0691001855
• ISBN 13: 9780691001852
• Binding: Hardcover
• Number of pages: 280