Advances in the Chemistry of Atmosphere

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Advances in the Chemistry of Atmosphere
Welcome to

• CHEM-ATOC 419/619

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COURSE OUTLINE

• Introduction Earths atmosphere, chemical
  composition and its vertical structure
• Radiation balance of atmosphere green house
  gases, absorption and photochemistry
• Oxidation potential of the atmosphere
  atmospheric oxidants and homogeneous chemistry
• Aerosols and heterogeneous chemistry
• Selected topics Chemistry of ozone hole and
  air pollution
• Formation process of cloud chemical reactions
  in and on cloud particles
• State-of-the-art field measurement techniques in
  atmospheric chemistry
• Atmospheric modeling 0, 1-D, 2-D and 3-D
  modeling
• Chemistry of the climate change
• Your research topics!

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Number Density

• The mean molecular weight of air Ma, is obtained
  by averaging the contributions from all its
  constituents i (1.9)
• it can be approximated (for dry air) from the
  molecular weights of N2, O2, and Ar
• (1.10)

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Exercises

• Calculate the number densities of air and CO2 at
  sea level for P 1013 hPa, T 0oC.

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Partial Pressure

• The partial pressure PX of a gas X in a mixture
  of gases of total pressure P is defined by
  Dalton's law
• (1.11)
• For our applications, P is the total atmospheric
  pressure. Similarly to (1.6), we use the ideal
  gas law to relate PX to nX
• (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.

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Partial Pressure

• Let us consider a pan of liquid water exposed to
  the atmosphere
• Evaporation of water from a pan
• Equilibrium between the liquid phase and the gas
  phase is achieved when a saturation vapor
  pressure PH2O,SAT is reached in the head space.

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Partial Pressure

• 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,
  PH2O,SAT increases as the temperature increases.
• Cloud formation in the atmosphere takes place
  when PH2O PH2O,SAT, and it is therefore
  important to understand how PH2O,SAT depends on
  environmental variables.

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Independent Variable

• 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
• (1.13)
• In the case of water, there is only one
  saturation vapor pressure for which liquid and
  gas are in equilibrium.

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Excercise
How many independent variables determine the
liquid-vapor equilibrium of the H2O-NaCl system?
What do you conclude regarding the 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 gas phase. Application of
the phase rule gives the number of independent
variables defining the equilibrium of the system
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.
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Partial Pressure

• 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
  250K.
• Phase diagram for water. The thin line is the
  saturation vapor pressure above supercooled
  liquid water.

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Saturation

• an air parcel is saturated when it holds the
  maximum amount of water vapour possible addition
  of any extra water vapour would lead to
  condensation
• the saturation vapour pressure is the vapour
  pressure at saturation (big surprise) it depends
  on temperature  "warmer air can hold more
  moisture"

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Partial Pressure

• In weather reports, atmospheric water vapor
  concentrations are frequently reported as the
  relative humidity (RH) or the dew point (Td). The
  relative humidity is defined as
• (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
• (1.15)
• At temperatures below freezing, one may also
  report the frost point, Tf corresponding to
  saturation with respect to ice.

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• 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
• Therefore, NaCl-H2O solutions exist at
  equilibrium in the atmosphere at relative
  humidities less than 100 the saturation water
  vapor pressure over a NaCl-H2O solution decreases
  as the NaCl mole fraction increases.

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• 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.

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Atmospheric stability

• Buoyancy in the atmosphere is determined by the
  vertical gradient of temperature.
• Consider a horizontally homogeneous atmosphere
  with a vertical temperature profile TATM(z). Let
  A represent an air parcel at altitude z in this
  atmosphere.
• Atmospheric Stability -dTATM/dz gt -dTA/dz
  indicates an unstable atmosphere

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Atmospheric Stability

• Assume that by some small external force the air
  parcel A is pushed upward from z to zdz and then
  released. The pressure at zdz is less than that
  at z. Thus the air parcel expands, and in doing
  so performs work (dW -PdV).
• Let us assume that the air parcel does not
  exchange energy with its surroundings as it
  rises, i.e., that the rise is adiabatic (dQ 0).
  The work is then performed at the expense of the
  internal energy E of the air parcel dE dW dQ
  -PdV lt 0. Since the internal energy of an ideal
  gas is a function of temperature only, the air
  parcel cools. This cooling is shown as the dashed
  line (adiabatic profile).

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Atmospheric Stability

• One might expect that as the air parcel cools
  during ascent, it will become heavier than its
  surroundings and therefore sink back to its
  position of origin on account of buoyancy.
• However, the temperature of the surrounding
  atmosphere also usually decreases with altitude.
  Whether the air parcel keeps on rising depends on
  how rapid its adiabatic cooling rate is relative
  to the change of temperature with altitude in the
  surrounding atmosphere.
• If TA(zdz) gt TATM(zdz), the rising air parcel
  at altitude zdz is warmer than the surrounding
  atmosphere at the same altitude. As a result, its
  density ? is less than that of the surrounding
  atmosphere and the air parcel is accelerated
  upward by buoyancy.

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Atmospheric Stability

• The atmosphere is unstable with respect to
  vertical motion, because any initial push upward
  or downward on the air parcel will be amplified
  by buoyancy. We call such an atmosphere
  convective and refer to the rapid buoyant motions
  as convection.
• On the contrary, if TA(zdz) lt TATM(zdz), then
  the rising air parcel is colder and heavier than
  the surrounding environment and sinks back to its
  position of origin vertical motion is suppressed
  and the atmosphere is stable.

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Atmospheric Stability

• The rate of decrease of temperature with altitude
  (-dT/dz) is called the lapse rate. To determine
  whether an atmosphere is stable or unstable, we
  need to compare its atmospheric lapse rate
  -dTATM/dz to the adiabatic lapse rate -dTA/dz.
• Note that stability is a local property of the
  atmosphere defined by the local value of the
  atmospheric lapse rate an atmosphere may be
  stable at some altitudes and unstable at others.
  Also note that stability refers to both upward
  and downward motions if an atmosphere is
  unstable with respect to rising motions it is
  equivalently unstable with respect to sinking
  motions. Instability thus causes rapid vertical
  mixing rather than unidirectional transport.

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Adiabatic Lapse Rate

• Fig. 3.21 Thermodynamic cycle
• In this cycle an air parcel T(z), P(z) rises
  adiabatically from z to zdz (process I), then
  compresses isothermally from zdz to z (process
  II), and finally heats isobarically at altitude z
  (process III).

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Adiabatic Lapse Rate

• The cycle returns the air parcel to its initial
  thermodynamic state and must therefore have zero
  net effect on any thermodynamic function.
  Consideration of the enthalpy (H) allows a quick
  derivation of the adiabatic lapse rate. The
  enthalpy is defined by
• (3.14)
• where E is the internal energy of the air parcel.
  
• The change in enthalpy during any thermodynamic
  process is
• (3.15)
• where dW -PdV is the work performed on the
  system and dQ is the heat added to the system.

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Adiabatic Lapse Rate

• Expanding d(PV) we obtain
• (3.16)
• For the adiabatic process (I), dQ 0 by
  definition so that
• (3.17)
• For the isothermal process (II), dE 0 (the
  internal energy of an ideal gas is a function of
  temperature only) and d(PV) 0 (ideal gas law),
  so that
• (3.18)

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Adiabatic Lapse Rate

• For the isobaric process (III), we have
• (3.19)
• where m is the mass of the air parcel and CP
  1.0 x103 J kg-1 K-1 is the specific heat of air
  at constant pressure.
• By definition of the thermodynamic cycle,
• (3.20)
• so that,
• (3.21)
• Replacing equation (dP/dz-?g) and m ?V into
  (3.13) yields the adiabatic lapse rate (commonly
  denoted G)
• (3.22)

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Adiabatic Lapse Rate

• Remarkably, G is a constant independent of
  atmospheric conditions. We can diagnose whether
  an atmosphere is stable or unstable with respect
  to vertical motions simply by comparing its lapse
  rate to 9.8 K km-1
• (3.23)
• Particularly stable conditions are encountered
  when the temperature increases with altitude
  (dTATM/dz gt 0) such a situation is called a
  temperature inversion.

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Latent heat release from cloud formation

• Cloudy conditions represent an exception to the
  constancy of G.
• Condensation of water vapor is an exothermic
  process, meaning that it releases heat (latent
  heat release). Cloud formation in a rising air
  parcel provides an internal source of heat that
  partly compensates for the cooling due to
  expansion of the air parcel (Figure below) and
  therefore increases its buoyancy.
• Effect of cloud formation on the adiabatic lapse
  rate

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• Summary

• Aerosols
• Partial pressure independent variables
• Saturation, impact of solutes in water uptake and
  condensation
• Stability and lapse rate