Über die Autorin bzw. den Autor

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.

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"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

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"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

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Introduction to Atmospheric Chemistry

PRINCETON UNIVERSITY PRESS

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

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

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