TOPIC 2 THE ATMOSPHERE AND ITS RELATION TO THE CRUST AND HYDROSPHERE

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TOPIC 2THE ATMOSPHERE AND ITS RELATION TO THE
CRUST AND HYDROSPHERE

• Required reading All of Chapter 2 in Andrews et
  al. (1996) (1st ed.) or Chapter 3 of Andrews et
  al. (2004) (2nd. ed.) all of Chapters 9 and 23
  in Faure (1998).

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FORMATION OF CRUST AND ATMOSPHERE

• Planets of solar system probably formed from
  remnants of supernovas, i.e., disc-shaped clouds
  of hot gases.
• Condensing vapors formed solids that coalesced to
  form planetesimals (small bodies).
• Accretion of planetesimals lead to formation of
  inner planets (Mercury-Venus-Earth-Mars).
• Large outer planets condensed from gases at much
  lower temperatures.

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ACCRETION OF EARTH

• As accretion built up the Earth to its present
  mass, it heated up owing to
• radioactive decay of unstable isotopes
• kinetic energy from impacts
• Heating melted Fe and Ni which sank to the center
  forming the core.
• Subsequent cooling permitted solidification of
  remainder to form mantle of roughly
  Mg-Fe-silicate composition.
• Crust, hydrosphere and atmosphere formed from
  upper mantle during the early history of Earth.

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THE CRUST

• Crust is shell of volume lt0.0001 of total Earth
  volume a small but important part (to us).
• Crust evolved through time as incompatible
  elements were removed from mantle by partial
  melting.
• Relative elemental abundances O gt Si gt Al gt Fe gt
  Ca gt Na gt Mg.

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Andrews et al. (1996)
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THE ATMOSPHERE

• Volatile elements escaped from mantle during
  crust formation (e.g., volcanic degassing). Some
  were retained to form atmosphere.
• Primitive atmosphere, probably CO2 N2 with
  minor H2 and H2O(vapor). Modern atmosphere had to
  await evolution of life.

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THE HYDROSPHERE

• Bulk of water at Earths surface is in oceans
  (gt97) and in polar ice-caps and glaciers.
• lt1 is continental fresh water, most stored as
  groundwater.
• Source of water not well known
• water bound as OH (bound in silicates) in
  meteorites?
• water-rich comets?
• As Earths surface cooled to 100C, water could
  condense. From existence of old sedimentary
  rocks, we know the ocean existed by 3.8 B.Y.

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Andrews et al. (1996)
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ORIGIN OF LIFE

• Synthesis of biologically important molecules
  probably took place in restricted, specialized
  environments, such as surfaces of clay minerals,
  or near submarine hydrothermal vents.
• Life probably began in oceans 4.2-3.8 B.Y. ago,
  but no fossils exist. Earliest fossil bacteria
  3.5 B.Y. old.
• Earliest reactions to synthesize organic material
  probably based on S from hydrothermal vents
• CO2(g) 2H2S(g) ? CH2O 2S(s) H2O(l)

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DEVELOPMENT OF PHOTOSYNTHESIS

• H2O(l) CO2(g) ? CH2O(s) O2(g)
• This reaction had great effect on Earth. First,
  O2 was consumed by oxidizing surface compounds
  and minerals. Eventually, the rate of supply
  exceeded consumption and O2 built up.
• Life adapted to use O2 produced, which is
  otherwise toxic.
• O2 underwent reactions to form O3 (ozone), which
  protects the surface from UV radiation.

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THE ATMOSPHERE

• The smallest of Earths geological reservoirs
  particularly susceptible to pollution.
• Mixing time very short, so contamination very
  quickly spreads throughout the globe, but is also
  diluted rapidly.
• Bulk composition of atmosphere very similar world
  wide.
• Lower atmosphere (troposphere) is well mixed by
  convection.

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• At 15-25 km, the atmosphere is heated by
  absorption of UV by O2 and O3. Stabilizes upper
  atmosphere (stratosphere) against mixing. This is
  where ozone layer occurs.
• Above 120 km, mixing is so weak that gas
  molecules can separate gravitationally - H2 and
  He are enriched at the top, O2 and N2 at bottom.
• Definitions
• Heterosphere where gravitational separation
  occurs
• Homosphere well-mixed part of atmosphere
• Turbopause separates heterosphere and homosphere

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Andrews et al. (1996)
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ASIDE PARTIAL PRESSURE(BOX 2.3 ANDREWS -
1996BOX 3.1 ANDREWS - 2004)

• The total pressure of a mixture of gases is the
  sum of the pressures of the individual
  components. For example, in the atmosphere
• Ptotal PO2 PN2 PCO2 PH2 PAr
• Daltons Law

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IDEAL GAS LAW

• PV nRT
• P pressure, V volume, n moles of gas, T
  absolute temperature (K), R gas constant
  8.314 J mol-1 K-1 1.987 cal mol-1 K-1
  0.0820575 atm L mol-1 K-1
• An ideal gas is one whose component molecules
  occupy no measurable volume and exert no forces
  of attraction or repulsion on one another.
• Real gases approach ideality at low pressure and
  high temperatures.

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GASEOUS MIXTURES

• P1V n1RT P2V n2RT P3V n3RT
• and
• (P1 P2 P3)V PTV (n1 n2 n3)RT
• so
• P1 x1PT P2 x2PT P3 x3PT
• The partial pressure of a gas is equal to the
  total pressure multiplied by the mole fraction of
  that gas.

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BAROMETRIC LAW

• PZ P0exp(-z/H)
• PZ - pressure at altitude z, P0 pressure at
  ground level, H - scale height ? 8.4 km.
• The barometric law gives the pressure of a gas as
  a function of altitude.
• Daltons law implies
• nZ n0exp(-z/H)
• (partial pressures and number of moles are
  related)

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CHARACTERISTICS OF THE ATMOSPHERE

• Air pressure drops exponentially with height.
• 90 of atmospheric gas molecules are in
  troposphere.
• The remainder are in the stratosphere ? low mass
  of upper atmosphere ? high sensitivity to
  contaminants.
• Pollutants in upper atmosphere will be held in
  layers, hindering dispersal and dilution.

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COMPOSITION OF THE ATMOSPHERE

• Water and CO2 are somewhat variable in abundance.
• Most gases are relatively constant in abundance.
• Most attention is focused on reactive trace gases.

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Andrews et al. (1996)
Same as Table 3.1 in Andrews et al. (2004)
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ASIDE CHEMICAL EQUILIBRIUM (BOX 2.4 - ANDREWS ET
AL., 1996 SECTIONS 9.1 and 9.2 - FAURE, 1998)

• Consider the reaction
• A B ? C D
• At equilibrium it must be true that

Where aA ?ACA aB ?BCB etc. (In general ai
?iCi) In dilute solutions ?i ? 1, so ai ? ci.
Box 3.2 in Andrews et al. (2004)
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LAW OF MASS ACTION

• Le Chatliers Principle If a system at
  equilibrium is perturbed, the system will react
  in such a way to minimize the change.
• Example Hydrolysis of urea
• NH2CONH2(aq) H2O(l) ? 2NH3(g) CO2(g)

aNH2CONH2 ?NH2CONH2cNH2CONH2 aH2O ? 1 (usually)
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• For gases we have
• aNH3 ?NH3PNH3 aCO2 ?CO2PCO2
• In dilute solutions ?i ? 1, and at low pressures,
  where gases behave ideally, ?i ? 1, so

A more general form aA bB ? cC dD
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STEADY STATE OR EQUILIBRIUM HOW MUCH METHANE
SHOULD BE IN THE ATMOSPHERE?

• How much CH4 should be present in the atmosphere
  if this trace gas is in equilibrium with the more
  abundant gases?
• CH4(g) 2O2(g) ? CO2(g) 2H2O(g)

This suggests that CH4 pressure should be very
low, but exactly how low?
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Andrews et al. (1996)
Same as Table 3.1 in Andrews et al. (2004)
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• PO2 ? 0.21 atm PCO2 ? 3.6x10-4 atm PH2O ? 0.01
  atm

PCH4 8x10-147 atm But the partial pressure of
methane actually measured is 1.7x10-6 atm, much
larger than that expected at equilibrium. Whats
wrong? Clearly, trace gases in the atmosphere may
not be in chemical equilibrium with other
components in the atmosphere.
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STEADY STATE

• A steady state is a situation in which the
  sources and sinks of a component in the
  atmosphere are just in balance, so the
  concentration remains approximately constant.
• Appropriate analogy is a leaky bucket.

F ? flux of component in or out mass/time A ?
total amount of component in atmosphere ? ?
residence time in the atmosphere
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STEADY STATE CALCULATIONS FOR METHANE

• Fin (CH4) 500 Tg/yr note Tera 1012
• Total mass of atmosphere 5.2x1018 kg
• Total mass of CH4 (1.7 mol/106
  mol)(5.2x1018)(16/29)
• 4.8 x 1015 g A

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WHAT IS THE MEANING OF RESIDENCE TIME (?)?

• The residence time is a measure of the average
  length of time an individual molecule stays in
  the atmosphere (assuming atmosphere is well
  mixed).
• Very important characteristic describing steady
  state systems.
• In general, compounds with high ? tend to build
  up to relatively high concentrations. However,
  even though compounds with low ? are removed
  rapidly, this high reactivity may itself be a
  cause for concern.

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Also, low ? implies insufficient time for mixing,
so the composition of species with low ? should
be quite variable.
Andrews et al. (1996)
Same as Figure 3.3 in Andrews et al. (2004)
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Andrews et al. (1996)
Same as Table 3.3 in Andrews et al. (2004)
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ATMOSPHERIC BOX MODEL
Reservoir (atmosphere)
Sink
Source
The main goal is to identify sources and sinks of
components in the atmosphere, as well as
reactions among components in the atmosphere.
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GEOCHEMICAL SOURCES

• I. Wind-blown dusts and sea sprays (probably most
  important).
• Dusts not very reactive, so have little effect on
  atmospheric chemistry.
• Sea spray has greater effect NaCl is hygroscopic
  ? tiny NaCl particles attract water and form an
  aerosol.
• The aerosol droplets can be important sites for
  chemical reactions. Example
• H2SO4(aer) NaCl(aer) ? HCl(g) NaHSO4(aer)

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GEOCHEMICAL SOURCES (CONTINUED)

• II. Ablation from meteorites. Most important for
  metals. Small source but important in low-density
  upper atmosphere.
• III. Volcanoes
• Large sources of dust and gases.
• Dust can block sunlight.
• Gases SO2, CO2, HCl, HF
• Acid rain a serious problem on the flanks of
  some volcanoes in Hawaii.
• Volcanic sources are very discontinuous.

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ASIDE ACIDS AND BASES(BOX 2.5 - ANDREWS ET AL.,
1996 SECTION 9.3 - FAURE, 1998 BOX 3.3 -
ANDREWS ET AL., 2004)

• Bronsted definition
• Acid any substance that can donate a proton
• Base any substance that can accept a proton
• HCl(aq) ? H Cl-
• NaOH(aq) H ? Na H2O(l)
• Lewis definition
• Acid any substance that can accept electrons
• Base any substance that can donate electrons
• H3BO3(aq) OH- ? B(OH)4-
• H2O(l) ? H OH-
• H3BO3(aq) H2O(l) ? B(OH)4- H

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ACIDS AND BASES(CONTINUED)

• Acids and bases react together to form salts and
  water
• 2KOH(aq) H2SO4(aq) ? K2SO4(aq) H2O(l)
• The strength of an acid or base is defined as the
  degree to which it dissociates.
• Strong acids and bases
• HCl(aq) ? H Cl-
• NaOH(aq) ? Na OH-

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ACIDS AND BASES(CONTINUED)

• Weak acids and bases
• HF(aq) ? H F-
• B(OH)4- ? B(OH)3(aq) OH-

It is sometimes convenient to use the notation
pKX pKX -log KX pKA -log KA pKB -log
KB A small pKA ? strong acid large pKA ? weak
acid.
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GEOCHEMICAL SOURCES(CONTINUED)

• IV. Radioactive decay of elements in rocks can
  release gases
• 40K ? 40Ar(g) ?
• 226Ra ? 222Rn(g) ?
• 238U ? 234Th ? (? 4He)
• 222Rn is a radioactive gas with a half-life of
  3.8 days. It is extremely dangerous compared to
  other radioactive elements because it is a gas.

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BIOLOGICAL SOURCES

• I. Not a significant, direct source of particles.
• II. Living forests
• A. O2 and CO2 involved in respiration and
  photosynthesis
• B. terpenes (pinene, limonene) - odor of forests
• C. organic acids, aldehydes, etc. (see Box 2.7)

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BIOLOGICAL SOURCES(CONTINUED)

• III. Micro-organisms
• A. Most important in creating trace gases
• B. Methane (CH4) generated by anaerobic systems
• Damps soils, marshes, rice paddies
• Digestive tracts of cattle
• C. Soils rich in N-compounds contribute N-gases
• NH2CONH2(aq) H2O(l) ? 2NH3(aq) CO2(g)

ammonia released under alkaline conditions, fixed
as NH4 under acidic conditions NH3(aq) H ?
NH4
urea (animal urine)
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BIOLOGICAL SOURCES(CONTINUED)

• D. Some micro-organisms (nitrosomonas) oxidize
  NH3 during respiration
• 2NH3(g) 2O2(g) ? N2O(g) 3H2O(l)
• N2O(g) is an important and stable trace gas.
• E. Micro-organisms in ocean are great sources of
  trace gases.
• Seawater is rich in SO42-, Cl- (F-, Br-, I-).
  Marine organisms metabolize these elements to
  produce S- and halogen-containing gases.
• Seawater is not a significant source of N-bearing
  gases.

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BIOLOGICAL SOURCES(CONTINUED)

• Dimethyl sulfide (DMS)
• Produced by marine phytoplankton (Phaeocystis
  pouchetti) in upper layers of ocean.
• (CH3)2SCH2CH2COO-(aq) ? (CH3)2S(g)
  CH2CHOOH(aq)
• beta-dimethylsulfoniopropionate DMS
  acrylic acid
• (DMSP)
• Carbonyl sulfide
• CS2(g) H2O(g) ? OCS(g) H2S(g)
• carbon disulfide carbonyl sulfide
• Flux of OCS to atmosphere is less than DMS, but
  OCS is more stable, so attains higher
  concentrations. Both gases are insoluble in water.

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ASIDE GAS SOLUBILITY(Box 2.8 Andrews 1996 Box
3.4 - Andrews 2004)

• Solubility of gases usually treated as an
  equilibrium process
• CO2(g) ? CO2(aq)
• Henrys law constant KH cCO2/PCO2 (mol L-1
  atm-1)
• The larger KH, the more soluble the gas.
• Some gases react with H2O, increasing their
  solubility
• HCHO(g) ? HCHO(aq)
• formaldehyde
• HCHO(aq) H2O ? H2C(OH)2(aq)
• methylene glycol

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GAS SOLUBILITY (CONTINUED)

• Another important example
• CO2 H2O ? H2CO3(aq)
• carbonic acid
• PROBLEM 1 What is the concentration of carbon
  monoxide in a drop of rain in equilibrium with
  the atmosphere?
• From Table 2.3 we obtain PCO 100x10-9 atm, and
  from Table 1 we have KH 0.001 mol L-1 atm-1.
• KH cCO/PCO
• cCO KHPCO (100x10-9 atm)(0.001 mol L-1 atm-1)
• 10-10 mol L-1

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TABLE 1 SOME HENRYS LAW CONSTANTS AT 15C
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GAS SOLUBILITY(CONTINUED)

• PROBLEM 2 What is the partial pressure of H2O2
  (hydrogen peroxide) in an atmosphere in
  equilibrium with a lake water containing 10-6 mol
  L-1 H2O2?
• KH 2x105 mol L-1 atm-1
• PH2O2 CH2O2/KH (10-6 mol L-1)/(2x105 mol L-1
  atm-1)
• 5x10-12 atm 0.005 ppbv

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REACTIVITY OF TRACE GASES

• Gases with short ? are those that are easily
  removed. Some are removed by absorption by
  plants, solids, or water (physical removal). Most
  are removed by chemical reactions.
• The most reactive entity (moiety) in the
  atmosphere is the hydroxyl (OH) radical.
• Radical a reactive molecular fragment (moiety),
  usually possessing an unpaired electron.
• Formed by photochemical reactions
• O3(g) h? ? O2(g) O(g)
• O(g) H2O(g) ? 2 OH(g)

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REACTIVITY OF TRACE GASES(CONTINUED)

• The OH radical reacts very quickly with many
  atmospheric components and therefore has a very
  short ?.
• It is an important contributor to acid rain
• NO2(g) OH(g) ? HNO3(g)
• from auto emissions
• Some gases have limited reactivity with OH OCS,
  N2O, CH4 and CFCs (chlorofluorocarbons
  refrigerants and aerosol repellents).

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REACTIVITY OF TRACE GASES(CONTINUED)

• Gases with low reactivity to OH can build up and
  reach the stratosphere, where they react with O,
  and therefore interfere with ozone production
• O O2(g) ? O3(g)
• Anything that reacts with O will affect ozone
  production.
• CFCs cause damage to atmospheric ozone.
• N compounds from SSTs were a concern, but now
  N2O produced at ground level is more important.
  This gas is produced by combustion processes,
  ironically in automobile engines with catalytic
  converters.

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OZONE(Box 2.9 Andrews 1996 Section 3.10 Andrews
2004)

• O2(g) h? ? 2 O(g)
• (? lt 242 nm)
• O2(g) O(g) ? O3(g)
• These ozone production reactions are balanced
  with ozone destruction reactions to maintain a
  steady state.
• O3(g) h? ? O2(g) O(g)
• O3(g) O(g) ? 2O2(g)

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ADDITIONAL OZONE DESTROYING REACTIONS

• NO(g) O3(g) ? O2(g) NO2(g)
• NO2(g) O(g) ? NO(g) O2(g)
• O3(g) O(g) ? 2O2(g)
• OH(g) O3(g) ? O2(g) HO2(g)
• HO2(g) O(g) ? OH(g) O2(g)
• O3(g) O(g) ? 2O2(g)
• Chlorine from CFCs gives rise to
• Cl(g) O3(g) ? O2(g) ClO(g)
• ClO(g) O(g) ? Cl(g) O2(g)
• O3(g) O(g) ? 2O2(g)

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OZONE(CONTINUED)

• According to the previous reactions, OH, Cl,
  and NO all act as catalysts.
• Catalyst a chemical species which increases the
  rate of a reaction, but is not itself produced or
  consumed overall.
• This is what makes the loss of the ozone layer
  such a difficult problem a single pollutant
  molecule can be responsible for the destruction
  of a large number of O3 molecules.

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Dobson units denote thickness of ozone layer at
sea-level P and T. Each unit 0.01mm.
Mean October levels of ozone above Halley Bay
Antarctica
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URBAN ATMOSPHERE

• Primary pollutant a pollutant compound directly
  released to the atmosphere (e.g., smoke, CO, CO2,
  etc.).
• Secondary pollutant a pollutant compound formed
  as a product of chemical reactions in the
  atmosphere.

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LONDON SMOGPRIMARY POLLUTION

• Urban air pollution was primarily the product of
  combustion of fuels.
• The rapid development of pollution coincided with
  the transition to fossil fuel burning.
• Normal, complete fuel combustion is described by
• 4CH 5O2(g) ? 4CO2(g) 2H2O(g)
• Neither CO2 nor H2O are particularly toxic.
  However, during incomplete combustion we get CO
• 4CH 3O2(g) ? 4CO(g) 2H2O(g)

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LONDON SMOG(CONTINUED)

• And also smoke particles
• 4CH O2(g) ? 4C(s) 2H2O(g)
• At low temperatures, we might also get PAHs
  (polycyclic aromatic hydrocarbons) such as
  benzo(?)pyrene, which are carcinogenic.

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LONDON SMOG(CONTINUED)

• Fuel contaminants may also be a problem
• 4FeS2(s) 11O2(g) ? 8SO2(g) 2Fe2O3(s)
• Sulfur is highest in coals and fuel oils.
• Smoke and SO2 are primary pollutants.
• SMOG combination of smoke and fog (water
  droplets).
• SO2(g) H2O(l) ? H HSO3-
• 2HSO3- O2(aq) ? 2H 2SO42-
• Fog droplets containing H2SO4 caused respiratory
  diseases.

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LOS ANGELES SMOGSECONDARY POLLUTION

• Use of greater volatility liquid fuels in motor
  vehicles caused a new type of air pollution.
• The major pollutants are not themselves emitted
  by motor vehicles, but are formed by reactions
  involving primary pollutants.
• Photochemical smog smog whose formation is
  catalyzed by sunlight.
• Fuel is burned in air, not pure O2, which has
  important consequences.

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LOS ANGELES SMOG (CONTINUED)

• O(g) N2(g) ? NO(g) N(g)
• N(g) O2(g) ? NO(g) O(g)
• N2(g) O2(g) ? 2NO(g)
• Next, NO is oxidized in smog to give NO2(g) (see
  Box 2.11 in Andrews 1996 or Box 3.6 in Andrews
  2004 for details). NO2 is a brownish gas that
  absorbs light.
• NO2(g) h? ? NO(g) O(g)
• O(g) O2(g) ? O3(g)
• Thus, ozone (a respiratory irritant) is produced
  as a secondary pollutant.

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VOLATILE ORGANIC COMPOUNDS (VOCs)

• VOCs may also be released from fuel combustion.
• VOCs cause two problems
• They aid in NO2 production.
• CH4(g) 2O2(g) 2NO(g) h? ? H2O HCHO(g)
  2NO2(g)
• They lead to formation of aldehydes (eye
  irritants and carcinogens)
• PAN peroxyacetylnitrate - important eye irritant
  in photochemical smog.

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LEADED VS. UNDLEADED GASOLINE

• Leaded gasoline contained tetraethyl lead -
  Pb(C2H5)4 which resulted in Pb pollution of air,
  soils and waters.
• Some unleaded gasoline contains benzene, which is
  a carcinogen and contributor to photochemical
  SMOG.
• Some gasoline contains MTBE (methyl tertiary
  butyl ether) which was added to improve air
  quality as a fuel oxygenate, but now has
  contaminated water supplies where gasoline has
  leaked or spilled.

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EFFECTS OF AIR POLLUTION

• H2SO4 formed in smog can be an important agent of
  corrosion
• H2SO4(aq) CaCO3(s) H2O(l) ? CO2(g)
  CaSO42H2O(s)
• Gypsum causes two problems
• 1) It dissolves in rain.
• 2) Increased volume leads to mechanical stress.
• Ozone attacks rubber, plastics, pigments and dyes.

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REMOVAL PROCESSES

• Wet deposition removal of soluble components in
  rain or snow.
• Oxidation is an important acid-forming process.
• Organic compounds ? carboxylic acids (acetic,
  formic)
• Sulfur compounds ? H2SO4
• Organosulfur compounds ? MSA (methanesulfonic
  acid or CH3SO3H
• Nitrogen compounds ? HNO3
• Rain is usually acidic due to presence of
  dissolved CO2 (pH 5.6). These acids can lower
  pH further.
• Dry deposition Direct removal of gaseous or
  particulate pollutants onto surface of the Earth.

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ACID-BASE SPECIATION CALCULATIONS
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MONOPROTIC ACIDS

• What are the pH and concentrations of all species
  in a 0.1 mol L-1 HF solution?
• 1) Write out important species H, OH-, HF0, F-.
• 2) Write out all independent reactions and their
  equilibrium constants
• HF0 ? H F-
• H2O(l) ? H OH-

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• 3) Write out mass-balance expressions
• 0.1 mol L-1 ?F F- HF0
• 4) Write out the charge-balance expression
• H F- OH-
• 5) Make reasonable assumptions
• HF is an acid, so H gtgt OH- the
  charge-balance becomes
• H ? F- X
• and the mass-balance becomes
• HF0 0.1 - X

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• 6) Solve quadratic equation

a -1 b -10-3.2 -6.31x10-4 c 10-4.2
6.31x10-5
X1 -0.00825 X2 0.00765 H F-
7.65x10-3 mol L-1 pH -log H 2.12 HF0
0.1 - 0.00765 0.0924 mol L-1
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• 7) Check assumption 1.318x10-12 ltlt 7.65x10-3, so
  OH- ltlt H.
• What if we assumed HF0 gtgt F-, i.e., HF0 ?
  0.1? This might be valid because HF is a weak
  acid.
• 10-3.2 X2/0.1
• X2 10-4.2
• X 10-2.1 0.00794
• H F- 7.94x10-3 mol L-1 pH 2.10
• HF0 0.1 - 0.00794 0.092 mol L-1
• The above answer is only 8 different from 0.1.
  It seems in any case where KA lt 10-3.2, the above
  assumption should be good!

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POLYPROTIC ACID

• What is the pH and concentration of all species
  in a 0.1 mol L-1 solution of H3PO4?
• 1) Species H, OH-, H3PO40, H2PO4-, HPO42-,
  PO43-
• 2) Mass action expressions
• H3PO40 ? H2PO4- H
• H2PO4- ? HPO42- H
• HPO42- ? PO43- H

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• H2O(l) ? H OH-
• 3) Mass-balance
• 0.1 mol L-1 H3PO40 H2PO4- HPO42-
  PO43-
• 4) Charge-balance
• H H2PO4- 2HPO42- 3PO43- OH-
• 5) Assumptions
• a) Because H3PO40 is an acid H gtgt OH-
• b) Because H2PO4- and HPO42- are very weak acids
  and H3PO40 is only moderately weak
• H3PO40 gt H2PO4- gtgt HPO42- gtgt PO43-
• so, 0.1 H3PO40 H2PO4-
• and H H2PO4- X.

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• 10-3.1 - 10-2.1X - X2 0

X1 0.0245 X2 -0.0324 H H2PO4-
0.0245 mol L-1 pH 1.61 H3PO40 0.1 - 0.0245
0.0755 mol L-1
So HPO42- 10-7.0 mol L-1
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• PO43- 10-17.79 1.62x10-18 mol L-1
• OH- 10-14/10-1.61 10-12.39 4.07x10-13 mol
  L-1

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THE pH OF NORMAL RAINWATER

• The pH of normal, unpolluted rainwater is
  controlled by carbonic acid equilibrium
• CO2(g) ? CO2(aq) ? H2CO30
• What is the pH of rainwater in equilibrium with
  atmospheric CO2 (PCO2 10-3.5 atm)?
• 1) Species CO2(g), H2CO30, HCO3-, CO32-, H,
  OH-.
• 2) Mass action
• CO2(g) H2O(l) ? H2CO30

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• H2CO30? HCO3- H
• HCO3- ? CO32- H
• H2O(l) ? H OH-
• 3) Instead of a mass-balance we have PCO2
  10-3.5 atm
• 4) Charge balance
• H HCO3- 2CO32- OH-
• 5) Assumptions
• a) H2CO30 is an acid so H gtgt OH-
• b) HCO3- is a weak acid so HCO3- gtgt CO32-
• Therefore, H HCO3- X

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H2CO30 (10-1.5)(10-3.5) 10-5 mol L-1
X2 (10-6.3)(10-5.0) 10-11.3 X H
HCO3- 10-5.65 2.24x10-6 mol L-1 pH
5.65 So the pH of pure, normal rainwater is
acidic! Check assumption OH- 10-14/10-5.65
4.47x10-9 so H gtgt OH-
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pH OF RAIN ACIDIFIED WITH SO2

• The concentration of SO2 in the atmosphere is
  usually less than that of CO2, but SO2 is more
  soluble in water and forms a stronger acid.
• What is the pH of a rain droplet in equilibrium
  with an atmosphere with PSO2 5x10-9 atm?
• We proceed as in previous example, but we assume
  that the effect of CO2 can be neglected because
  SO2 produces a stronger acid.
• 1) Species SO2(g), H2SO30, HSO3-, SO32-, H, OH-

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• 2) Mass action
• SO2(g) H2O(l) ? H2SO30
• H2SO30 ? HSO3- H
• HSO3- ? SO32- H
• H2O(l) ? H OH-
• 3) Instead of mass-balance PSO2 5x10-9 atm
• 4) Charge-balance H HSO3- 2SO32-
  OH-

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• 5) Assumptions
• a) Because H2SO30 is an acid H gtgt OH-
• b) HSO3- is a weak acid so HSO3- gtgt SO32-
• Therefore, H HSO3- X
• H2SO30 KHPSO2 2.0 x 5x10-9 10-8 mol L-1
• K1 2x10-2 X2/10-8
• X2 2x10-10
• X H HSO3- 1.414x10-5 mol L-1 pH
  4.85
• OH- 10-14/10-4.85 7.07x10-10 mol L-1
• Note that only a very small amount of SO2 in the
  atmosphere can result in significant
  acidification of rain!

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EFFECT OF OXIDATION OF SO2

• What would the pH of a droplet of rain be if all
  the SO2 in the atmosphere were oxidized to H2SO4?
• Assume that 1 m3 of atmosphere contains 0.001 dm3
  of liquid water and the temperature is 15C.
• Because H2SO4 is a strong acid, we can assume
  that it is totally dissociated. Thus, we can
  solve this problem simply by calculating the
  concentration of SO2 in moles L-1.
• If PSO2 5x10-9 atm, then 1 m3 of atmosphere
  contains 5x10-9 m3 of SO2. To convert to moles,
  we must know how much volume a mole of gas
  occupies at 15 C and 1 atm.

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USE IDEAL GAS LAW

• PV nRT
• P 1 atm n 1 mol R 0. 0820575 atm L
  moles-1 K-1 T 288.15 K
• V
• (1 mol)(0.0820575 atm L moles-1 K-1)(288.15 K)/1
  atm
• 23.65 L 23.65x103 cm3 (1 m/100 cm)3 0.02365
  m3
• Thus, 1 m3 of air would contain 5x10-9/0.0237
  2.11x10-7 moles of SO2. If all this SO2 is
  oxidized and removed into a droplet of H2O of
  volume 0.001 dm3, this would result in 2.11x10-4
  mol L-1 of H2SO4. This yields 4.22x10-4 mol L-1
  H or pH 3.37.

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