3

Basic Chemical Concepts

The physicist is interested in quantities such as mass, velocity, force, acceleration, energy, and angular momentum, as discussed in Chapter 2. The chemist focuses on a detailed examination of the properties of matter. Here we ask, What is an atom? How is an atom assembled from its basic constituents, known as protons, neutrons, and electrons? How do atoms link to form complex structures such as molecules? We discuss the concepts of oxidation and reduction, the significance of acids and bases, and the notion of chemical equilibrium. We conclude with an introduction to photochemistry. We will apply the material developed here to both the atmosphere and ocean in more detail later. The discussion of acid-base chemistry will be particularly relevant for the treatment of carbon chemistry developed in Chapter 11 and for the treatment of acid rain as presented in Chapter 18. Section 3.1 introduces the properties of atoms and the processes by which they link to form molecules. The nature of chemical bonding is discussed in Section 3.2. Properties of acids and bases are described in Section 3.3, which includes an introduction to the concept of chemical equilibrium. A molecular level treatment of energy is presented in Section 3.4, highlighting the distinction between energy associated with electronic motion and that with vibrational and rotational motion of the nuclei. Reaction energetics is discussed in Section 3.5. Summary remarks are presented in Section 3.6.

3.1 3.2 3.3 3.4 3.5 3.6

Atoms and Molecules 19 Chemical Bonds 21 Acids and Bases 23 Energy on the Molecular Level 25 The Energetics of Reactions 27 Summary 30

3.1 Atoms and Molecules Earth and its atmosphere are composed of vast numbers of minute particles known as atoms. We may think of atoms as the building blocks of matter. Often, atoms are joined together in more complex units known as molecules. Atoms are composed of nuclei and electrons. Nuclei are positively charged, while electrons carry a negative charge. The laws of electromagnetism dictate that oppositely charged particles attract each other, while particles of the same charge repel. The attraction of opposites constrains the electrons of an atom to remain in relatively close proximity to the nucleus and is responsible for the existence of atoms and molecules as composite entities. The simplest atom, hydrogen, has a single electron. The hydrogen electron describes an almost spherical orbit around the nucleus, maintaining an average separation of about 5 × 10−9 cm. Atomic physicists, accustomed to very small length scales, find it convenient to use a unit for distance other than the centimeter. They adopt as the standard of length a distance of 10−8 cm, referred to as one angstrom (Å), honoring the Swedish physicist Anders Ångström (1814–1874). The average distance separating the electron and the nucleus of a hydrogen atom is about 0.5 Å. The nucleus itself is divisible. The nucleus of an atom is composed of protons and neutrons. A proton has an electric charge equal and opposite

19

20

Basic Chemical Concepts

to the charge of an electron. Neutrons in contrast are electrically neutral. Protons and neutrons have approximately the same mass. By standards we are accustomed to in everyday life, protons and neutrons are tiny: they individually weigh 1.67 × 10−24 g. However, they are giant in comparison with electrons, the mass of an electron is only 9.1 × 10−28 g. Protons and neutrons are bound together in the nucleus of an atom by a force known as the nuclear force. Nuclear forces are much stronger than the gravitational and electrostatic forces we have encountered so far. This allows protons to remain in close proximity to each other, despite the mutual repulsion resulting from their electromagnetic interaction. The properties of an atom are determined by the number of protons in its nucleus, a quantity known as the atomic number. Each element (hydrogen or oxygen, for example) is associated with a specific number of protons in its nucleus. In its electrically neutral (normal) form, the number of electrons orbiting the nucleus of an element is exactly equal to the number of protons in the nucleus. An individual element may occur with differing numbers of neutrons. Atoms formed in this manner are known as isotopes of the element and have similar chemical properties. The total number of protons plus neutrons defines the mass number. The nucleus of the oxygen atom, for example, contains eight protons. There are three distinct isotopes of oxygen, containing eight, nine, and ten neutrons, respectively. The most abundant isotope of oxygen has eight neutrons, corresponding to a mass number of 16. The second most abundant has ten neutrons, hence a mass number of 18, while the isotope with nine neutrons, with a mass number of 17, is relatively rare. Water (H2O), composed of molecular aggregates each containing two atoms of hydrogen (H) joined to one atom of oxygen (O), may contain oxygen of all three isotopic types. The lighter molecules, formed from oxygen with a mass number of 16, evaporate more readily from the liquid phase than their heavier counterparts. This has an interesting consequence; water vapor in the atmosphere and in precipitation is isotopically light compared to water in the ocean, from which it is ultimately derived. In comparison with water in the ocean, water vapor in the atmosphere contains a relatively larger abundance of oxygen atoms with a mass number of 16 relative to atoms with mass numbers of 17 and 18. This physical effect has been exploited by geochemists to open a powerful window to the study of the past climatic states of our planet, as we shall see in Chapter 10. During ice ages, vast quantities of water evaporated from the ocean, precipitated from the atmosphere, and then were stored in ice sheets covering large parts of the American and European continents—the quantity of water removed from the ocean was sufficient to lower the sea level by more than a hundred meters. As expected, water in ice sheets was isotopically light, while water remaining in the ocean was correspondingly heavy. The isotopic composition of oxygen in ocean water is recorded in the composition of shells of organisms that grow in the sea. Large numbers of

shells formed by organisms that lived in the past are preserved in the sediments of the ocean today. By extracting a core of sediment from the seafloor, we can recover the shells of these ancient organisms, and, by analyzing their isotopic composition, we can look back in time, drawing quantitative conclusions regarding the mass of water removed from the ocean and stored in continental ice sheets as a function of time. In this fashion, scientists have been able to reconstruct the composition of the ocean and to identify the changing patterns of climate—alternating ice ages and interglacials— characterizing the state of our planet for the past several million years. In similar fashion, water samples removed from the ancient ocean can be recovered by drilling through present-day vestigial ice sheets in Greenland and Antarctica. Isotopic measurements of this water can be used to infer the temperature of the atmosphere from which the water precipitated, providing an invaluable record of high-latitude temperatures. Such ice also contains air bubbles trapped by accumulating snow; analysis of this air provides a beautiful and indispensable record of atmospheric composition dating back 450,000 years. This record includes indisputable evidence for the global significance of human activity over the past several centuries. Carbon dioxide (CO2) accounted for about 280 molecules per million molecules, or parts per million (ppm), of the atmosphere since the end of the last ice age, about 15,000 years ago, until the early part of the nineteenth century. The concentration of CO2 has steadily risen to about 360 ppm at present, reflecting additions of CO2 to the atmosphere due to destruction of forests and burning of fossil fuels. We shall return to this topic in Chapter 11, when we discuss the function of the global carbon cycle. We can think of an atom as a miniature solar system. In this analogy, the nucleus, at the center, is the Sun. Electrons play the role of the planets, orbiting the parent nucleus. The universe contains many atoms, many suns. According to the laws of quantum mechanics, electrons are required to occupy constrained and well-defined orbits, arranged in what quantum physicists call shells. The first shell, closest to the nucleus, is known as the K shell and can accommodate two electrons. The second shell, somewhat more removed, can hold up to eight electrons and is known as the L shell. Hydrogen, with a single proton, has a single electron; in its most stable, or lowest, energy state, the electron in hydrogen occupies the K shell. Helium (He), with two protons, has two electrons: this completes the capacity of the K shell. Lithium (Li), with three protons, has three electrons: two occupy the K shell, while the third falls into the more extended, less tightly bound L shell. The universe of atoms can be constructed by adding protons to nuclei, and electrons to shells, until their carrying capacity is exhausted. Adding electrons to the L shell, after lithium, we sequentially form beryllium (Be), boron (B), carbon (C), nitrogen (N), oxygen (O), fluorine (F), and neon (Ne). Neon, with ten protons and ten electrons, exhausts the capacity of both the K and L shells.

Chemical Bonds

The universe of atoms is summarized in Plate 1 (see color insert) and Table 3.1 with a diagram known as the periodic table, attributed to the Russian physicist Dmitri Mendeleev (1834–1907), who first devised this arrangement of the elements. The chemical properties of atoms, their ability to form composite entities by bonding to other atoms, are primarily determined by the number of electrons in the outermost shell of electrons. The periodic table is organized so that elements in a given column have similar arrangements of their valence (outermost) electrons. Thus, atoms in the same column of the periodic table have similar chemical properties, and it is this feature that makes the table so extraordinarily useful to chemists. As we shall see, atoms go to great lengths to either give up or borrow electrons from other atoms in order to develop a fully populated outer shell of electrons. Atoms like helium or neon have it made from the start, since their outer shells are already fully populated. As a consequence, they lead a rather lonely existence; we refer to atoms with complete shells as inert or noble gases, an appropriate title given their obviously aloof and superior status. The family of noble gases, including argon (Ar), krypton (Kr), and xenon (Xe), in addition to helium and neon, appears in the rightmost column of the periodic table. On an atomic basis, the most abundant constituent of the atmosphere is nitrogen, followed by oxygen and hydrogen. These elements do not normally appear singly as atoms. Rather, they are present as aggregates of atoms, as molecules. Nitrogen appears as molecular nitrogen, N2. Oxygen is present mostly as O2, while water vapor, H2O, is the predominant form of hydrogen.

3.2 Chemical Bonds Before we can begin to appreciate atmospheric chemistry, we need to understand the nature of the forces binding atoms together in molecules. Why is it that some molecules, such as N2, are exceptionally stable while others, such as O2, are relatively reactive? When we draw in a breath of air, we indiscriminately inhale N2 and O2 and everything else in the air. Molecular nitrogen passes through our lungs and is exhaled (returned to the atmosphere) without changing its chemical state. Molecular oxygen, on the other hand, combines with carbon and is released as carbon dioxide, CO2. The comparatively inert character of N2 is related ultimately to the strength of the forces binding the atoms together in the associated molecular compound. It is important that we understand the forces allowing particular groups of atoms to exist as stable molecular entities. The simplest interatomic force is that responsible for bonding a sodium (Na) atom to chlorine (Cl) in sodium chloride, NaCl. Sodium belongs to the family of elements known as the alkali metals (a name derived from the Arabic word alquilim, meaning the ashes of the plant saltwort, used in making soda ash). The alkali metals occupy the first column of the periodic table and are distinguished by having a single electron in their outermost populated shell. Chlorine

21

is a member of the class of elements known as the halogens. The halogens, missing a single electron to complete their outermost orbital shell, occupy the column penultimate to the right of the periodic table. It is relatively easy to remove the valence electron from an alkali metal; given a choice, the element would prefer to lose its lonely outermost electron and assume the characteristics of a noble gas, with its remaining orbital shells fully occupied. In a similar fashion, chlorine is eager to gain an electron to complete its outermost shell. Aspirations of both elements are satisfied in the molecule NaCl. We can think of this molecule as a combination of a sodium atom that has given up an electron and a chlorine atom that received it. The sodium atom, missing an electron, has a net positive electric charge, while the chlorine atom, with its extra electron, has a compensatory charge of the opposite sign. The atoms are held in place in the molecule by the electrostatic force associated with these oppositely signed charges. We refer to bonding of this type as ionic. The configuration of NaCl is illustrated schematically in Figure 3.1. The simplest electrically neutral molecule is that formed by the combination of two atoms of hydrogen, H2. The electrons in H2 are shared. If the two protons were to coalesce, forming a single nucleus, the molecule would resemble a helium atom. In practice, though, the positive charges keep the protons apart. The electrons are shared between the two protons. They provide on the average a concentration of negative charge between the protons, as schematically illustrated in Figure 3.2; the resulting electrostatic forces account for the stability of the composite entity. When electrons are shared, bonding is said to be covalent. The protons in H2 maintain a separation of about 0.74 Å, which may be compared with the average displacement of about 2.8 Å separating the nuclei in NaCl. The relatively large size of the NaCl molecule may be attributed to the size of its component atoms. Stripped of one electron, a sodium atom (denoted by Na+ ) has a radius of about 1 Å, while the chlorine atom with its additional electron (denoted by Cl− ) has a radius of about 1.8 Å. If we attempted to squeeze the atoms closer, their electron shells would overlap, giving rise to a strong opposite repulsive force. We may attribute the great stability of the nitrogen molecule to the fact that the component atoms share three pairs of electrons. Each atom is able, at least part of the time, to complete its outer shell by borrowing electrons from its neighbor. It requires more than twice as much energy to fragment N2 as to break apart H2. The oxygen molecule, in which two pairs of electrons are shared, presents an intermediate case. We refer to the bond connecting the atoms in an N2 molecule as a triple bond; that joining the atoms in O2 is a double bond, while that linking the atoms in H2 is a single bond. Sometimes, to emphasize the nature of the bonds, chemists prefer to indicate nitrogen, oxygen, and hydrogen molecules with the symbols N≡N, O=O, and H−H, rather than the more economical notation, N2, O2, and H2. We shall generally opt for economy in what follows.

22

Basic Chemical Concepts

Table 3.1 Chemical symbols of the elements Symbol

Element

Symbol

Element

Symbol

Element

Ac Ag Al Am Ar As At Au B Ba Be Bh Bi Bk Br C Ca Cd Ce Cf Cl Cm Co Cr Cs Cu Db Dy Er Es Eu F Fe Fm Fr Ga Gd

Actinium Silver Aluminum Americium Argon Arsenic Astatine Gold Boron Barium Beryllium Bohrium Bismuth Berkelium Bromine Carbon Calcium Cadmium Cerium Californium Chlorine Curium Cobalt Chromium Cesium Copper Dubnium Dysprosium Erbium Einsteinium Europium Fluorine Iron Fermium Francium Gallium Gadolinium

Ge H Ha He Hf Hg Ho Hs I In Ir K Kr La Li Lr Lu Md Mg Mn Mo Mt N Na Nb Nd Ne Ni No Np O Os P Pa Pb Pd Pm

Germanium Hydrogen Hahnium Helium Hafnium Mercury Holmium Hassium Iodine Indium Iridium Potassium Krypton Lanthanum Lithium Lawrencium Lutetium Mendelevium Magnesium Manganese Molybdenum Meitnerium Nitrogen Sodium Niobium Neodymium Neon Nickel Nobelium Neptunian Oxygen Osmium Phosphorus Protactinium Lead Palladium Promethium

Po Pr Pt Pu Ra Rb Re Rf Rh Rn Ru S Sb Sc Se Sg Si Sm Sn Sr Ta Tb Tc Te Th Ti Tl Tm U V W Xe Y Yb Zn Zr

Polonium Praseodymium Platinum Plutonium Radium Rubidium Rhenium Rutherfordium Rhodium Radon Ruthenium Sulfur Antimony Scandium Selenium Seaborgium Silicon Samarium Tin Strontium Tantalum Terbium Technetium Tellurium Thorium Titanium Thallium Thulium Uranium Vanadium Tungsten Xenon Yttrium Ytterbium Zinc Zirconium

Covalent bonding allows the synthesis of structures more complex than the diatomic (two-atom) species discussed above. The principles are similar. In the water molecule, hydrogen atoms are linked to the oxygen atom by single bonds. The oxygen atom completes its outer shell by borrowing two electrons, one from each of the hydrogen atoms. At the same time, the oxygen atom contributes two electrons to the partnership, one to each hydrogen atom, allowing the shells of the hydrogen atoms also to be filled. Carbon, located near the middle of the second row of the periodic table, is a “switch-hitter”: it can be stabilized by either giving up or receiving electrons. The central atom in carbon dioxide (CO2), carbon, is linked to each of the oxygen atoms by a double bond. The carbon atom in CO2 surrenders two electrons to each oxygen atom, completing the

L shell of the oxygen atoms while simultaneously adjusting itself to an electron configuration analogous to helium. The carbon atom in CO2 is said to be oxidized; it has given up electrons. The carbon atom in CH4 forms single bonds with each of the four hydrogen atoms. It is on the receiving side of electron transfer in this case, completing its L shell by borrowing four electrons, one from each of the hydrogen atoms; the carbon atom in CH4 is said to be reduced. The oxidation (or reduction) state of an element in a compound is represented by a number obtained according to the following rule. We assign an oxidation number of −2 to each oxygen atom in the compound (assuming that oxygen, gaining two electrons, carries a charge of −2), while to each hydrogen atom we associate a number of +1 (assuming that hydrogen, surrendering one electron, acquires a charge +1).

Acids and Bases

H Na

H

Cl

+

+

0

0

–

–

Figure 3.1 Configuration of NaCl. Lower graph shows the distribution of charge.

The oxidation number of the element is determined by subtracting the sum of the numbers assigned to each oxygen and hydrogen atom from the electrical charge of the compound. Thus, the sum of the oxidation numbers of each constituent equals the residual charge of the compound. Example 3.1: Determine the oxidation number of the specified elements in the following compounds: a) carbon in carbon dioxide (CO2) b) carbon in methane (CH4) c) nitrogen in ammonium ion (NH4+ ) d) nitrogen in nitrate ion (NO3–) Answers: a) We assign an oxidation number of − 2 for each oxygen. C + 2(O) = electrical charge of compound C + 2(− 2) = 0 C = +4 b) We assign an oxidation number of +1 for each hydrogen. C + 4(H) = 0 C + 4(+1) = 0 C = −4 c) N + 4(+1) = +1; N = − 3 d) N + 3(− 2) = − 1, N = +5

23

■

Elements with positive oxidation numbers, such as the carbon atom in CO2 or the nitrogen atom in NO3− , are said to be oxidized (they gave up electrons). Elements with negative oxidation numbers, such as carbon in CH4 or nitrogen

Figure 3.2

Same as Figure 3.1, but for H2.

in NH4+ , are said to be reduced (they were on the receiving side of electron transfer). The oxidation number of elements in compounds with identical nuclei (referred to as homonuclear), such as H2, N2, and O2, where the rule stated above is inapplicable, is assigned a value of zero—electrons are shared equally, and there is no net transfer of charge. In addition to stable molecules such as N2, O2, H2O, and CO2, the atmosphere also includes an important group known as free radicals. A free radical is a compound characterized by an odd number of electrons. Free radicals are exceptionally reactive; they go to great lengths to pair off their lonely electrons. Among the more important radicals in the atmosphere are NO, NO2, OH, HO2, Cl, ClO, Br, and BrO. As we shall see, much of atmospheric chemistry is concerned with complex chains of reactions involving radicals. These chains play a dominant role in the synthesis of O3 in urban environments; also, they are pivotally involved in removal of O3 from the stratosphere. We return to a more detailed discussion of radical chemistry in Chapters 13, 14, 15, and 17.

3.3 Acids and Bases The atmosphere contains a suite of soluble gases known as acids (from the Latin word acidus, meaning sour). An acid’s characteristic property is the hydrogen content of its associated compound that, when placed in water, dissociates (comes apart), and is released as a positively charged proton. The dissociation process for sulfuric and nitric acid (H2SO4 and HNO3), two of the more important acidic components of the air, may be summarized by reaction equations as follows: H2 SO4 → H+ + HSO− 4 HNO3 → H + +

NO− 3

(3.1) (3.2)

24

Basic Chemical Concepts

The arrows in (3.1) and (3.2) indicate transformation of the reactants, appearing on the left, to the products, appearing on the right. The protons formed in (3.1) and (3.2) attach immediately to one or more water molecules. The proton in (3.1) and (3.2) should be thought of not as an isolated H+ but rather as a larger molecular unit such as H3O+ (formed by attaching the proton to a water molecule) in the liquid phase, or as an even more complex aggregate such as H9O4+ (produced by bonding H+ to as many as four neighboring water molecules). We can sidestep this complication by denoting the proton released in (3.1) and (3.2) by H+ (aq), explicitly distinguishing between the relatively complex form of H+ in aquatic media as compared with the relatively simple configuration of the element in the gas phase. Protons, being small and mobile, are exceptionally reactive. They can fit in almost anywhere, displacing a diversity of elements in a variety of compounds. Add a metal such as zinc to a strong acid and you can watch it dissolve before your eye. Marble statues preserved from antiquity crumble under the attack of acid rain. Aluminum, stable for thousands of years in soils, is leached to groundwater by acid rain and transported to streams and lakes. Fish die. It is astonishing to think that all of this damage is effected by simple protons. Complementing the acids is a family of compounds known as bases, which have the ability to absorb protons in solution. Ammonia gas, NH3, provides a simple example of a base; added to solution, NH3 absorbs a proton and is converted to NH4+ by the reaction NH3 + H+ (aq) → NH 4+

(3.3)

Water can serve as both an acid and a base. Its role as an acid is illustrated by the reaction H2 O → H+ + OH− ,

(3.4)

while its function as a base is exemplified by H+ + H2 O → H3 O+

(3.5)

The composite reaction is summarized by the equation H2 O + H2 O ↔ H3 O+ + OH−

(3.6)

The reaction indicated in (3.6) can proceed either to the right or to the left. In equilibrium, the number of reactions per unit time producing H3O+ and OH− is exactly equal to the number of compensatory reactions involved in removal of these species; otherwise, water would decompose completely, transforming irreversibly to H3O+ and OH− . Thermodynamic equilibrium corresponds to a condition where all possible reactions, including those involving the radiation field (light), are reversible. Consider a reaction of substance A with substance B forming substances C and D, represented by A+B↔C+D

(3.7)

In thermodynamic equilibrium, the concentrations of A, B, C, and D may be shown to be related according to the equation

[C][D] = K, [A][B]

(3.8)

where [X] denotes the concentration of species X and K is a quantity known as the equilibrium constant. The value of K depends on temperature and pressure, on the nature of the compounds A, B, C, and D, and on the choice of units used to specify concentration. Concentrations in liquid media are most frequently specified in units of moles per liter (moles l−1). A liter is defined as a volume of 1 × 103 cm3, equivalent to a cube measuring 10 cm on each side. A mole of a chemical substance X corresponds to a number of individual units (atoms, molecules, etc.) of X equal to 6.02 × 1023. The number 6.02 × 1023 is known as Avogadro’s number, named after the Italian physicist Amedeo Avogadro (1776–1856). The utility of the molar concept arises as a consequence of the relation between Avogadro’s number and the mass number of a compound. A mole of hydrogen atoms (with a mass number of 1) has a mass of 1 g; a mole of oxygen atoms (with a mass number of 16) has a mass of 16 g, while a mole of oxygen molecules (each molecule containing two atoms of O corresponding to a mass number of 32) has a mass of 32 g. A liter of water has a mass of 1 × 103 g, corresponding to 55.6 moles of H2O molecules [(1000 g)/(18 g mol−1)]. It is important to remember that a mole is a measure of the number of units of a substance; it is not a measure of mass, although the latter can be readily derived if we know the mass number of the constituent material. Returning to reaction (3.6), in equilibrium we can write [H3 O+ ][OH− ] =K (3.9) [H2 O] The concentration of H2O is not significantly altered by chemical reactions in solution. It is convenient, and usual, to set [H2O] equal to 1 in applying concepts of thermodynamic equilibrium to the liquid phase; this requires a simple redefinition of units for the equilibrium constant K. With [H3O+ ] and [OH− ] expressed in units of mol l−1, K has the value 10−14 mol2 l−2. The concentration of positive charge must exactly equal the concentration of negative charge in any finite-sized volume; any imbalance would be immediately removed by the strong associated electrostatic force field. Thus, for pure water, [H3 O+ ] = [OH− ] (3.10) Substituting for [OH− ] in the revised equation (3.9), we find [H3 O+ ]2 = 10−14 mol2 l−2

(3.11) +

It follows that the concentrations of H3O (equivalent to H+ (aq)) and OH− in pure liquid water are both equal to 10−7 mol l−1. More complex mixtures contain charged species in addition to H+ (aq) and OH− . These species must be considered in writing an equation for the charge balance analogous to (3.10). In general, the concentration of H+ (aq) can differ significantly from [OH− ]. Concentrations of H+ (aq)

Energy on the Molecular Level

and OH− are constrained by (3.9), however, to satisfy the relation [H+ (aq)][OH− ] = 10−14 mol2 l−2

(3.12)

The concentration of H+ (aq) is expressed conventionally in terms of a quantity known as pH. The pH of a solution is defined by the relation pH = − log10 ( [H+ (aq)] ),

(3.13)

Acid hydrochloric hydrofluoric acetic carbonic water

pK for selected solutions Reaction HCl ↔ H+ (aq) + Cl– HF ↔ H+ (aq) + F– CH3COOH ↔ H+ (aq) + C2H3O2– H2CO3 ↔ H+ (aq) + HCO3– H2O ↔ H+ (aq) + OH–

pK very small 3.2 4.7 6.4 14.0

−1

+

where [H (aq)] is measured in units of mol l . The pH of pure water is 7.0. Solutions with a pH of less than 7.0 are said to be acidic; solutions with a pH higher than 7.0 are defined as basic. Values of pH for some common solutions are given in Table 3.2. The strength of an acid is measured by the degree of dissociation of the compound in solution. For a representative acid, HA, strength can be calculated using the equilibrium constant, K, for the corresponding dissociation reaction: H2 O + HA ↔ H3 O+ + A− +

(3.14)

−

The concentrations of HA, H (aq), and A satisfy the equilibrium equation [H+ (aq)][A− ] =K (3.15) [HA] The concentration of A− is equal to that of HA when [H+ (aq)] equals K. Defining a quantity pK analogous to pH according to pK = − log10 (K),

(3.16)

where K is measured in units of mol l−1, we see that dissociation of HA is essentially complete when the pH of the solution is greater than its pK. Values of pK for selected acids are given in Table 3.3. Compounds characterized by large values of K and small values of pK dissociate readily and are classified as strong acids. Somewhat arbitrarily, we associate the family of strong acids with values of K larger than 10−6 (values of pK less than 6). With this convention, hydrochloric (HCl), nitric (HNO3), and sulfuric (H2SO4) acids are classified as strong; carbonic acid (H2CO3), formed by adding CO2 to water, is defined as a weak acid. As we shall see, the presence of CO2 in the atmosphere ensures that rain should be naturally acidic; under pristine conditions, we expect a pH for rain in equilibrium with the

Table 3.2

Table 3.3

25

pH for selected solutions

Solution lime juice vinegar carbonated water pure water sea water stomach antacid household ammonia typical drain cleaner

pH 1.8 3.0 5.6 7.0 8.4 10.0 11.0 13.0

current level of atmospheric CO2 of about 5.6. The pH of rain falling in eastern parts of North America today is typically less than 4.0, often as low as 3.0. The surplus acidity is due mainly to sulfuric and nitric acid formed from SO2 and NO2 introduced to the atmosphere as by-products of fossil fuel combustion. The pH of rain falling in the western United States is often as high as 7.0; acids in this instance are neutralized, in part by NH3 produced mainly from cattle feedlots, in part by carbonate dust blown into the air from naturally occurring alkaline soils of the West. We return to this topic later in connection with the discussion of the nitrogen cycle in Chapter 12 and the discussion of acid rain in Chapter 18.

3.4 Energy on the Molecular Level An atom or molecule can respond to an input of energy in a number of different ways. If we smash an atom with a fast moving electron or proton, or with another atom or molecule, the atom can speed up, gaining kinetic energy. If the energy of the collision partner is large enough, in addition to changing the kinetic energy of the target, we can induce a change in the orbital motion of the electrons in the atomic target. This could also be effected by absorption of light. We could, for example, force the electron in the normal, ground state of the hydrogen atom to flip from the K to the L shell by delivering an amount of energy equivalent to about 1.6 × 10−11 ergs. To cause such an internal adjustment in a mole of hydrogen atoms (with a mass of 1 g) would require the expenditure of about 1013 ergs of energy, equivalent to 2.3 × 105 calories (1 calorie is equal to 4.19 × 107 ergs). To place this in context, one calorie would suffice to raise the temperature of a gram of liquid water by 1° C. Obviously, large quantities of energy are required to alter the electronic structure of an atom or molecule. The smallest particles in nature obey a set of rules distinct from, though consistent with, those discussed earlier in connection with the larger macroscopic world. Properties of microscopic particles are prescribed by the laws of quantum mechanics. According to quantum mechanics, the motion of electrons in an atom or molecule is restricted to certain welldefined energy states or levels, associated, for example, with the orbital shells described above. A molecule can store energy internally, not only in orbital motion of its bound electrons but also through motion of its component nuclei. There are two important modes of nuclear motion: the molecule as a whole can rotate about its center of mass; in addition, the

26

Basic Chemical Concepts

nuclei can vibrate, like particles linked by a spring. The different modes of nuclear motion are illustrated for a diatomic molecule in Figure 3.3. The particular state of a molecule is specified by a set of (quantum) numbers separately defining the condition of its electrons and nuclei. The state of an atom is completely defined by specifying the shells occupied by its electrons. As noted above for hydrogen, relatively large quantities of energy are required to change the electronic state (orbital configuration) of an atomic system. If the transition is to be effected by absorption of light, we need radiation of relatively short wavelength (ultraviolet, for example, in the case of hydrogen). Much smaller quantities of energy (longer wavelengths of light) suffice to alter the vibrational state of a molecule. It is even easier to induce a change in rotation. As we shall see in Chapter 6, the atmosphere is bathed in two separate radiation fields, one originating in the sun, consisting mainly of relatively short wavelengths in the visible and ultraviolet portions of the spectrum, the other arising largely at the surface, comprising for the most part longer wavelengths in the infrared portions of the spectrum. Absorption of sunlight by atmospheric gases is primarily associated with changes in the electronic structure of molecules. Absorption of surface radiation is largely due to changes in the vibrational and rotational states of molecules.

Molecular oxygen, for example, absorbs sunlight at wavelengths of less than 2400 Å. The electronic configuration of the molecule is altered. In its new state the molecule is unstable; its nuclei fly apart spontaneously, resulting in the production of two separate atoms of oxygen. The process is summarized as follows: (3.17) h +O2 → O + O, where h denotes a photon of light. Reaction (3.17) exemplifies a process known as photodissociation; it defines the first important step in the synthesis of stratospheric O3. Not all molecules are able to alter their vibrational and rotational states by absorption of light. The capacity to do so is confined to molecules with a particular configuration of electric charge, a distribution associated with what is known as an electric dipole. At large distances, a dipole looks like a barbell, with clusters of positive and negative charge on either end of the bar (molecule), as illustrated in Figure 3.4. This condition is satisfied, for example, by the water molecule. Carbon dioxide is a linear molecule in its ground (lowest energy or most stable) state. The molecule can bend, however; in this configuration it also has the capacity to interact with radiation. The separate vibrational modes of CO2 are depicted in Figure 3.5, while the vibrational modes of H2O are illustrated in Figure 3.6. Water and CO2, together with O3, are the most important absorbers of infrared radiation in the atmosphere. Together, they are responsible for

+

+

–

–

+

+

–

–

+

–

Dipolar structure

+ 1

Rotation H

–2

O

H + 1 Vibration

Figure 3.3

Modes of nuclear motion for a diatomic molecule.

Water molecule

Figure 3.4 Charge distribution for an electric dipole (upper diagram) and an indication of the approximate dipolar configuration of the water molecule (lower diagram).

The Energetics of Reactions

27

3.5 The Energetics of Reactions

O

C Symmetric stretch

O

The first law of thermodynamics states that if heat is added to a system, it may be used either to increase internal energy or to do work. Expressed in mathematical form (see Section 7.3), the first law of thermodynamics is given by the relation ∆Q = ∆E + P∆V,

O

O

C Bending mode

O

Figure 3.5

C Asymmetric stretch

O

Vibrational modes of CO2. Source: UPL 1994.

raising the temperature of Earth by almost 40° C. It is interesting to note that the major constituents of the atmosphere, the homonuclear diatomic molecules N2 and O2, are essentially transparent to light, not only in the infrared but also for the most part in the visible portion of the light spectrum. In the absence of H2O, CO2, and O3, Earth would be freezing cold, and life as we know it would be impossible.

(3.18)

where ∆Q measures the quantity of heat added to the system, ∆E defines the changes in internal energy, P and V denote the pressure and volume of the system, respectively, and P∆V provides a measure of the work expended in changing the volume by an amount ∆V. Suppose that, as a result of the addition of heat, the system is transformed from an initial state A to a final state B. With obvious notation, the change in internal energy is given by ∆E = EB − EA

(3.19)

If the change in the state of the system takes place at a constant pressure P, the work expended in the transition from A to B may be written in the form P∆V = P(VB − VA ) = PVB − PVA

(3.20)

It follows that ∆Q = (EB − EA ) + (PVB − PVA )

(3.21)

∆Q = (EB + PVB ) − (EA + PVA )

(3.22)

or

Defining a quantity H by the relation H = E + PV,

(3.23)

the first law of thermodynamics may be rewritten as O Symmetric stretch

(3.24)

∆Q = ∆H

(3.25)

or H

H

O Bending mode

∆Q = (HB − HA )

H

H

O Asymmetric stretch

H

Figure 3.6

Vibrational modes of H2O.

H

The quantity H defined in equation (3.23) is known as the enthalpy of the system. Note that, if a system evolves at constant pressure from state A to state B, the quantity of heat expended in the transition ∆Q is given simply by the difference between the final and initial values of enthalpy (∆H). If ∆H is positive (if the enthalpy of state B is higher than that of state A), heat is expended in the transition from A to B (∆Q is positive). On the other hand, if H is negative (HB is less than HA), heat will be released (∆Q will be negative). Note also that the quantity of heat evolved (or expended) in the transition from A to B is independent of the path followed in effecting the transition. For example, if the transition from A to B were to proceed through an intermediate state C, the net change in heat would still be expressed as a difference between the enthalpies of the final (B) and initial (A) states. The heat evolved (or expended) depends on the difference between the enthalpies of the states involved in the transition.

28

Basic Chemical Concepts

It is useful to introduce the concept of standard states of the elements, meaning states for which enthalpies may be conveniently set equal to zero. Enthalpies for compounds assembled from specific combinations of elements may then be expressed with reference to zero points established for the appropriate standard states. Standard states for elements are selected on the basis of the form in which we expect to find the elements under typical laboratory conditions for temperatures of interest. In what follows, we focus attention on reactions taking place at room temperature (298 K). Standard states for a number of key elements are indicated in Table 3.4. When the standard state is identified as a gas, it is assumed that the pressure is low enough so that the gas may be considered from a thermodynamic point of view as a perfect gas. If the standard state is identified as either a liquid or a solid, the state is assumed to be present at a pressure of 1 atm. Heats of formation for a number of compounds of interest in the atmosphere are given in Table 3.5. Heats of formation are expressed in terms of the change in enthalpy involved in assembling a compound from the appropriate mix of its component elements, assuming that the elements are initially supplied in their standard states. Changes in enthalpies listed here are expressed in units of kilocalories per mole (kcal mol− 1), that is, the values of ∆H given here define the heat (in kcal) expended (positive values of ∆H) in forming a mole of a specific compound. Consider CH4 for example. To form a molecule of CH4 from the elements in standard states, we begin with 1 mole of C as graphite and 2 moles of H as H2. The change in enthalpy involved in forming 1 mole of CH4 at a temperature of 298 K is equal to −17.88 kcal mol− 1; that is, 17.88 kcal of heat are released in forming a mole of CH4 at 298 K. The following examples illustrate how the data in Table 3.5 may be used to estimate the changes in enthalpy associated with specific reactions. If the change in enthalpy is negative, heat is released in the reaction and the reaction is said to be exothermic. If the change in enthalpy is positive, heat must be supplied and the reaction is said to be endothermic. If the value of ∆H is large and positive, it is unlikely that the reaction can proceed under atmospheric conditions.

Table 3.4 Standard states for selected elements at 298 K Element

Standard state

∆ H (298 K)

H C N O F S Cl Br

H2, gas C(graphite), solid N2, gas O2, gas F2, gas S(rhombic), solid Cl2, gas Br2, liquid

0 0 0 0 0 0 0 0

Example 3.2: Estimate the change in enthalpy associated with the reaction N + NO → N2 + O at a temperature of 298 K. Answer: Using the data in Table 3.5, the changes in enthalpy associated with formation of N, NO, N2, and O are given by ∆ H(N) = +113.0 kcal mol–1 ∆ H(NO) = +21.57 kcal mol–1 ∆ H(N2) = 0 kcal mol–1 ∆ H(O) = +59.57 kcal mol–1 The change in enthalpy associated with formation of the reactants N and NO is given by ∆ H(reactants) = +113.0 + 21.57 = 134.57 kcal mol–1. The change in enthalpy associated with the products is given by ∆ H(products) = 0 + 59.57 = 59.57 kcal mol–1. The change in enthalpy associated with the reaction is given by ∆ H(reaction) = ∆ H(products) − ∆ H(reactants) = 59.57 − 134.57 = − 75.0 kcal mol–1 The reaction is strongly exothermic.

■

Example 3.3: Estimate the change in enthalpy associated with the reaction N + O2 → NO + O at a temperature of 298 K. Answer: The changes in enthalpies associated with formation of N, O2, NO, and O are given by ∆ H(N) = +113.0 kcal mol–1 ∆ H(O2) = 0 kcal mol–1 ∆ H(NO) = +21.57 kcal mol–1 ∆ H(O) = +59.57 kcal mol–1 (All values are expressed in units of kcal mol–1.) Thus, ∆ H(reactants) = +113.0 kcal mol–1 ∆ H(products) = +21.57 + 59.57 = +81.14 kcal mol–1 ∆ H(reaction) = 81.14 − 113.0 = − 31.86 kcal mol–1 This reaction is also strongly exothermic but less so than the reaction in Example 3.2. ■ Example 3.4: Estimate the change in enthalpy associated with the reaction ClO + BrO → Cl + Br + O2. Answer: The changes in enthalpies associated with formation of ClO, BrO, Cl, Br, and O2 are given by ∆ H(ClO) = +24.4 kcal mol–1 ∆ H(BrO) = +26.0 kcal mol–1 ∆ H(Cl) = +28.9 kcal mol–1

Table 3.5 Changes in enthalpy associated with formation of 1 mole of listed species at a temperature of 298 K Species

∆ Hf (298) (kcal/mol)

Species

∆ Hf (298) (kcal/mol)

H H2 O O(1D) O2 O2 (1) O2(1) O3 HO HO2 H2O H2O2 N N2 NH NH2 NH3 NO NO2 NO3 N2O N2O3 N2O4 N2O5 HNO HONO HNO3 HO2NO2 C CH CH2 CH3 CH4 CN HCN CH3NH2 NCO CO CO2 HCO CH2O COOH HCOOH CH3O CH3O2 CH2OH CH3OH CH3OOH CH3ONO CH3ONO2 CH3O2NO2 C2H C2H2 C2H2OH C2H3 C2H4

52.1 0.00 59.57 104.9 0.00 22.5 37.5 34.1 9.3 2.8 ± 0.5 − 57.81 − 32.60 113.00 0.00 85.3 45.3 − 10.98 21.57 7.9 17.6 ± 1 19.61 19.8 2.2 2.7 ± 1 23.8 − 19.0 − 32.3 − 12.5 ± 2 170.9 142.0 93 ± 1 35 ± 0.2 − 17.88 104 ± 3 32.3 − 5.5 38 ± 3 − 26.42 − 94.07 10 ± 1 − 26.0 − 53 ± 2 − 90.5 4±1 4±2 − 3.6 ± 1 − 48.2 − 31.3 − 15.6 − 28.6 − 10.6 ± 2 133 ± 2 54.35 30 ± 3 72 ± 3 12.45

C2H5 28.4 ± 0.5 − 20.0 C2H6 57 ± 2 CH2CN CH3CN 15.6 − 11 ± 3 CH2CO − 5.8 CH3CO − 39.7 CH3CHO − 4.1 C2H5O − 10 ± 3 CH2CH2OH − 56.2 C2H5OH − 49.6 CH3CO2 −6 ± 2 C2H5O2 − 41 ± 5 CH3COO2 − 30.0 CH3OOCH3 39.4 C3H5 C3H6 4.8 22.6 ± 2 n-C3H7 19 ± 2 i-C3H7 − 24.8 C3H8 − 44.8 C2H5CHO − 51.9 CH3COCH3 − 62 ± 5 CH3COO2NO2 F 19.0 ± 0.1 F2 0.00 − 65.14 ± 0.2 HF − 23.4 ± 1 HOF FO 26 ± 5 5.9 ± .4 F2O 6±1 FO2 5±2 F2O2 − 15 ± 7 FONO − 16 ± 2 FNO − 26 ± 2 FNO2 2.5 ± 7 FONO2 CF 61 ± 2 − 44 ± 2 CF2 − 112 ± 1 CF3 − 223.0 CF4 − 166.8 CHF3 − 58 ± 2 CHF2 − 107.2 CH2F2 −8 ± 2 CH2F − 56 ± 1 CH3F − 41 ± 15 FCO − 153 ± 2 COF2 − 157 ± 2 CF3O − 148 ± 5 CF3O2 − 214 ± 5 CF3OH − 360 CF3OOCF3 − 184 ± 4 CF3OOH − 183 ± 3 CFOF − 63 ± 2 CH3CH2F − 17 ± 2 CH3CHF − 124 ± 2 CH2CF3 − 120 ± 1 CH3CHF2 − 71 ± 2 CH3CF2

Species CH3CF3 CF2CF3 CHF2CF3 Cl Cl2 HCl ClO ClOO OClO ClOO2 ClO3 Cl2O Cl2O2 Cl2O3 HOCl ClNO ClNO2 ClONO ClONO2 FCl CCl2 CCl3 CCl3O2 CCl4 CHCl3 CHCl2 CH2Cl CH2Cl2 CH3Cl ClCO COCl2 CHFCl CH2FCl CFCl CFCl2 CFCl3 CF2Cl2 CF3Cl CHFCl2 CHF2Cl CF2Cl COFCl CH3CF2Cl CH2CF2Cl C2Cl4 C2HCl3 CH2CCl3 CH3CCl3 CH3CH2Cl CH2CH2Cl CH3CHCl Br Br2 HBr HOBr BrO

∆ Hf (298) (kcal/mol) − 179 ± 2 − 213 ± 2 − 264 ± 2 28.9 0.00 − 22.06 24.4 23.3 ± 1 22.6 ± 1 >16.7 52 ± 4 19.5 31 ± 3 37 ± 3 − 18 ± 3 12.4 3.0 1.3 5.5 − 12.1 57 ± 5 17 ± 1 2.7 ± 1 − 22.9 − 24.6 23 ± 2 29 ± 2 − 22.8 − 19.6 −5 ± 1 − 52.6 − 15 ± 2 − 63 ± 2 7±6 − 22 ± 2 − 68.1 − 117.9 − 169.2 − 68.1 − 115.6 − 67 ± 3 − 102 ± 2 − 127 ± 2 − 75 ± 2 − 3.0 − 1.9 17 ± 2 − 34.0 − 26.8 22 ± 2 17.6 ± 1 26.7 7.39 − 8.67 − 14 ± 6 26 ± 5

Species BrNO BrONO BrNO2 BrONO2 BrCl CH2Br CHBr3 CHBr2 CBr3 CH2Br2 CH3Br CH3CH2Br CH2CH2Br CH3CHBr l l2 Hl CH3l CH2l lO lNO lNO2 S S2 HS H2S SO SO2 SO3 HSO HSO3 H2SO4 CS CS2 CS2OH CH3S CH3SOO CH3SO2 CH3SH CH2SCH3 CH3SCH3 CH3SSCH3 OCS

JPL. “Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling,” (Pasadena, Cal: Jet Propulsion Lab, 1994): 194

∆ Hf (298) (kcal/mol) 19.7 25 ± 7 17 ± 2