Vietnam part 2 CARL p1 39

In gaseous systems the rate of chemical transformation is influenced by pressure, temperature
and concentration of the reacting species. In order to understand a reactive gaseous system
such as that of the Earth’s atmosphere in is important first to characterise it in terms of the
aforementioned parameters. This part of the course therefore concentrates on the general
macroscopic characteristics of the atmosphere, particularly those of the Troposphere and
Stratosphere.

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The gaseous system of the Earth differs in several important ways from gas confined to a small
container, such as a balloon. The most important of these differences, as far as chemical
transformation is concerned, is that the former is exposed to photons (of the Sun) having
sufficient energy to break molecular bonds. These photons are both temporally and spatially
(in three dimensions) non-uniform.
Absorption of photons both by the atmosphere and by the Earth’s surface also gives rise to a
several distinct temperature gradients with altitude. Gravity leads to a pressure gradient with
altitude. Finally, the Earth’s atmosphere is subject to a changes in composition due to a
multitude of emissions of chemical species from the Earth’s surface. The combination of these
external influences leads to a very dynamic and complex chemical system.

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Throughout this course, and in publications concerning atmospheric chemistry and reaction
kinetics, several different units of pressure are used. This slide gives a summary of those most
commonly encountered and their relationship.

At atmospheric pressure and below, the relationship between pressure, temperature, volume,
and concentration, as given by the ideal-gas law is a very good approximation. The ideal gas
law essentially treats gaseous species as point objects. This is a very good approximation so

long as the volume of empty space is very much greater than the volume occupied by the
species (which is taken to be the volume over which the species has a significant
attractive/repulsive force). Can you estimate the volume of free space per cm3 at one
atmosphere pressure?
In this course, concentrations are often given in molecules per cubic centimetre (or just cm-3,
since “molecule” is not an SI unit), or may be expressed as a mixing ratio (e.g., ppm { in parts
per million). It is therefore instructive for you to have in mind the total concentration of
molecules at atmospheric pressure and room temperature, so that you are able to easily
calculate any species concentration given the pressure (i.e., altitude), temperature, and mixing
ratio.

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As will be demonstrated later in the course, some chemical reactions are fundamentally altered
by changes in pressure, but the most important concern here is to be able to define how
concentration changes with altitude since this influences the overall rates of chemical reactions
that occur in the gas-phase. Concentration is related to pressure and temperature via the idealgas law given in the previous slide.

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If one uses the expression for the rate of change of pressure with height and note that the air
density is related also to pressure by the ideal-gas law, then one has a differential equation that
can be easily solved if one assumes that the gravitational force and air temperature are constant
with altitude, z. Neither are constant with altitude, especially temperature, but nevertheless one
can arrive at a reasonably good approximation to the pressure variation with height above the

Earth’s surface. The exponent RT/gM is called the scale height and is equal to 7.4 km forT =
250 K assuming dry air. The pressure decreases by a factor e every 7.4 km, and halves about
every 5 km.

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Temporary pressure changes at constant altitude also occur due mainly to non-uniform heating
of the atmosphere by the surface. Significant variations in pressure (as far a concentrations are
concerned) at constant altitude do not occur due to the rapid motion of air masses from highto low-pressure regions. It must be stressed however that the direction of this motion is not the
direction of the pressure gradient (as explained in more detail later). This is because the initial
motion of the air mass might have a velocity component perpendicular to the pressure
gradient. In such a case the air mass at high pressure will circle around a low pressure region,
gradually spiralling inwards as energy is lost due to (for example) friction. The main interest
for atmospheric chemistry to pressure differences at constant altitude is the wind direction and
velocity, as this effects the transport direction and distances of pollutants.

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Notice from the previous slides that scale height is a function of temperature. The air of the
Troposphere is not directly heated by radiation from the Sun, rather it receives energy from the
Earth’s surface via conduction and convention. If two surface areas of the Earth have different
heating rates, the air masses close to those surfaces will heat at different rates also. This will
lead to a difference in lapse rate and therefore a pressure difference. A pressure difference at
high altitude will tend to be reduced by air motion. If the lapse rate is maintained this will lead
to an opposite pressure difference near the Earth’s surface. This, together with rising warm air
over land, will lead to overall circulation of air at the borders of land and oceans, commonly
known as the “sea breeze”. During the evenings, air circulation in the opposite direction can
occur due to the rapid radiative cooling of the land with respect to the oceans, giving rise to the

“land breeze”.
Why would one expect the land to both heat and cool more rapidly than a body of water?

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Dilution of chemical species emitted into the atmosphere is a very important consideration.
Chemical species emitted into the atmosphere can be moved from one place to another by
wind, but this alone would maintain a constant concentration. Dilution occurs only by
molecular diffusion, but, as you will see in the following slides, molecular diffusion in the
lower atmosphere is a relatively slow process and is normally important only over short
distances (a few meters or less). Turbulence, – the mixing of one fluid body with another – on
the other hand, acts over larger distances. An example of turbulent mixing would be to pour
blue paint and yellow paint into the same tin and vigorously mix the two paints with a stick.
Eventually the paint will appear green. However, on close inspection one would observe that
the yellow and the blue paint are still quite separate with very thin layers of each colour lying
next to each other. These give the appearance of green. In reality these very thin layers
eventually disappear due to molecular diffusion, but only if the layer are thin enough.
Turbulent (sometimes called “eddy”) mixing is a complicated phenomena to describe
mathematically. On a large enough spatial scale, however, turbulence can be treated as a
diffusion process having a similar relationship to molecular diffusion. Here, the effective
movement of particles per unit time through a unit area is proportional to the concentration
gradient dC/dx (given here as C/x: normally one has to consider all three spatial
dimensions, of course). The constant of proportionality is the diffusion coefficient. Molecular
diffusion coefficients can be related directly to the fundamental properties of the molecules.
Turbulent diffusion coefficients however are more phenomenological. They are usually found
to be several orders of magnitude larger than molecular diffusion coefficients. Note however
that there is a subtle difference in the definition of concentration gradient between molecular
and turbulent diffusion. This difference is pointed out on the next slide.

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From a distance, and taking average concentrations into account turbulent diffusion looks
much like molecular diffusion. But the important difference is that turbulent diffusion does not
mix two species on a microscopic scale that allows for any reaction. Only molecular diffusion
achieves this. Thus one requires for large gaseous systems a combination of turbulent diffusion
followed by molecular diffusion for rapid true mixing of gases.

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As mentioned on the previous slides, the molecular diffusion coefficient can be directly related
to the characteristics of the molecule. D12 is referred to as the binary diffusion coefficient that
describes the diffusion of one kind of molecular gas in another. For the for diffusion of N2 in
O2, or vice versa, D12 = 0.219 cm2 s-1 at 293 K and 1 bar. In the expression for D12, 12 is the
reduced molecular mass of the binary system 12 = mO2mN2/(mO2 + mN2). 12 is the collision
cross section of the colliding molecules (=(rO2 + rN2)2), where rO2 + rN2 is the average
distance between the two centre of masses of O2 and N2 on collision. Diffusion of larger
molecules will be slower than lighter molecules and molecule size has a greater impact than
molecular weight. Note also the influence on pressure and temperature on the diffusion
coefficient.
The rate of change of concentration due to molecular diffusion actually depends (sometimes
in a complex way) on the initial shape and size on the concentration distribution. For an initial
cylindrical distribution the characteristic diffusion time (the time for the concentration to
decrease by a factor e) is given above. Here 0 is a constant (= 2.4).

It is not the intention here that you understand the fundamentals of molecular diffusion, but
to appreciate the approximate time scales involved and that diffusion rate increase with
increasing temperature more rapidly than they decrease with increasing pressure. This is

important in the troposphere as (as you will see later) it means that the molecular diffusion
coefficient changes much less than would be expected in the lower atmosphere based simply
on considerations of pressure change.

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Whether a flow is considered to be turbulent or laminar (all components of the fluid travel in
the same direction) depends on the ratio of inertial to viscous forces. This ratio is given by the
Reynold’s number. The higher the Reynolds number, the higher the degree of turbulence. Note
that turbulence is proportional to flow velocity (relative to an object such as the Earth’s surface
or another air mass) and on the size of the system being considered.
Measurements show that for the meteorological turbulence near the surface, the turbulentdiffusion coefficient, K is about 105 cm2/s over land, and 103 cm2/s over the sea. Of course, K
it will also vary with the time of day, becoming larger in the morning and smaller in the night.
This figure is much greater than the diffusion coefficient for molecular diffusion (D ~ 1 to 0.05
cm2 s-1).

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The last slides dealing with diffusion show that in the absence of significant turbulence it is
possible for relatively large “blocks” of air of a few meters or more on either side to remain
intact as far as their composition is concerned (in the absence of fast chemical reactions). For
these blocks also, the exchange of heat from other masses of air by either conduction or
radiation is rather slow. One can then consider what happens to a given block of air that is
heated when it comes into contact with the Earth’s surface. The block of air will be heated and
through heating will expand. Suppose momentarily this block of air is less dense than the
surrounding air, which has not yet been heated to the same temperature. This block of air will
experience three kinds of forces. (1) gravity (2) pressure acting over area A from above (3)
pressure acting over area A from below. These forces must balance in order for the considered

block of air to remain at a fixed height otherwise it will accelerate upwards or downwards.
Notice that rapid acceleration increases the relative velocity of the gas block, this will increase
the Reynolds's number an lead to turbulent mixing in the vertical direction. Later it will be
demonstrated that rising air leads to a decrease in air temperature with altitude.

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The characteristics mixing times due to vertical turbulent diffusion is given here without any
proof. The value of the diffusion coefficient for turbulence, K, is found by observation to be on
average about 105 cm2 s-1 over land and on average about 103 over the oceans. If one uses the
value for K over land one arrives at typical times for species emitted from the Earths surface to
be considered uniformly mixed throughout that part of the atmosphere. Uniformly mixed does
not imply a consent concentration as one needs to consider both the change in pressure and the
chance in temperature with altitude. It must be emphasised that these characteristic times
depend very much on the location, time of day and time of year. In dessert regions for
example, the land (and the air above it) cools rapidly in the night. It is also heated rapidly in
the morning. This causes a large density differences and hence greater velocities that at other
locations. The greater velocities promote turbulent mixing leading to 1-day mixing heights of
up to 3 km. Note though that vertical mixing is a very slow process over the oceans.
In this simplified picture, the quadratic dependence of  on altitude leads to a concept of the
planetary boundary layer in which gases emitted from the Earth’s surface are considered to be
fully mixed within 24 hours. Beyond 10 km in altitude mixing slows down considerably
because the value of K changes. This will be covered later but suffice to say here than a fairly
abrupt temperature change occurs marking the end of the troposphere and the beginning of the
stratosphere. Input of gases to the Stratosphere can take several years by this process.
As you will see later, in some regions of the atmosphere air masses can be transported much
more rapidly than indicated in the diagram on this slide. This occurs when two large air masses
collide. In this situation one (or both) is (are) rapidly forced upwards or downwards in a very
short time compared to the turbulent mixing times given above.

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We next consider how temperature changes in the atmosphere. The surface of the Earth and
the atmosphere is heated almost entirely by interaction with the photons of the Sun. Much of
the Suns photons that are directed to the Earth are absorbed by the Earths surface, which
therefore warms up. For low energy photons, especially those lying in the visible region of the
spectrum, solids are much less selective in absorption of photons than are gases. The reason
for this is simply that the solids have many more energy levels available for absorption. For
wavelengths short enough to cause molecular dissociation or ionisation gases do have an
effectively continuous range of energy levels. The continuity comes about because the
resulting fragments can travel away from one another at any velocity, thus leading to a
continuous range of possible energies for absorption. Thus our upper atmosphere tends to be
heated directly by the Sun’s photons and our lower atmosphere is heated by thermal
conduction from the Earth’s surface, followed by convection due to buoyancy. The next slides
will consider the consequence of this to the lower atmosphere.

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If you throw light ball at a heavy stationary wall and the collision is perfectly elastic the ball
will not loose kinetic energy, though its direction of travel will change. If the wall happens to
be light and is pushed backwards by the ball, the ball will loose kinetic energy on impact. The
same phenomena occurs when a gas expands against an external pressure. If there is no source
of heat input to the expanding gas during this period, the gas is said to expand adiabatically.
The temperature change of the gas as it expands depends on the energy it expends during
expansion, which is equivalent to force multiplied by distance. For the above situation,
expansion is against a constant external pressure. In the atmosphere, expansion or compression
of a mass of air will likely be accompanied by a change in height. In such a cause, pressure

change needs to be considered also.

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The page is an attempt to convince the reader that adiabatic expansion does occur in the
atmosphere. Here a model has been set up of a mass of air of 1 m diameter. Rising pockets of
air on smaller scales are not realistic when looking at what generally happens globally since
large regions are often heated fairly uniformly given rise to gas pockets that are often much
larger than 1 m in diameter. One must therefore take this example as a fairly stringent test for
adiabatic expansion.

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We now consider a general situation, but having several simplifying assumptions. The first
assumption is that the mass of gas remains intact as it ascends or descends. The second
assumption is that it is ideal – mainly implying that no condensation of water vapour takes
place. Thirdly, it neither gains or loses heat as it ascends or descends – the process is adiabatic.
One begins with the differential form of the first law of thermodynamics, which is a
statement of the conservation of energy. One can also express the ideal-gas law in differential
form. When these are equated and dP is substituted using the results of the previous slide, one
arrives at an expression for the rate of change of temperature with altitude.

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So, according to the formulations on the previous page, the temperature of the air should
decrease linearly with altitude at a rate of 9.8 K per km. Under these conditions air will
accelerate upwards or downwards if its T,z co-ordinates do not correspond to the line of the

graph above. The formulations of this first section of the course predicts that at the top of the
highest mountains the air pressure should be about 1/3 of that at the Earth’s surface and the air
temperature should be about 210 K. Whilst the former is very close to the actual pressure the
latter is not for two reasons. The first reason is that the Sun directly heats the surface of the
mountain, and the second reason is that the lapse rate of the atmosphere is a little less that 9.8
K per km.

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Atmosphere exhibiting a large degree of turbulence due to vertical motions of air masses are
said to be unstable, whilst those having little vertical motion are stable. As far as pollution is
concerned, unstable atmospheres are desirable as this leads to rapid dilution of pollutants
emitted from the Earth’s surface. The measure of stability of an atmosphere is the rate of
change of air temperature with height. This might be different from the ideal lapse rate due to
local heating conditions. If the temperature of the atmosphere decreases more rapidly with
height than the ideal lapse rate then movement of a heated air mass upwards will cause
increased upwards acceleration leading eventually to very turbulent mixing. At the other
extreme, the temperature may increases with altitude, this is called an inversion. When a rising
air mass reaches the bottom of an inversion, it is not compelled to rise much further since at
the same pressure it would be forced downwards as it would eventually have a lower
temperature, and hence be more dense, than the surrounding air. Very warm air can penetrate
thin inversion layers. Why?

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Inversion occurs often in the evenings when the sky is cloudless. Under these conditions, the
Earth’s surface cools more rapidly than the air above it via radiation to space (in the far
infrared spectral region peaking at about 10 m). In the morning, as the sun rises, the warmed

surface heats the air in contact with it via conduction, and the inversion layer rises and
becomes thinner during the morning. At higher altitudes one may also encounter an inversion
layer caused by descending air masses that lead to local compression and therefore heating.
The slow sinking of air in areas of high pressure is an important factor in air mass
modification. This slow sinking or "subsiding" is then responsible for the development for a
large number of the inversions that form in the free atmosphere, well above the earth's surface.
These subsidence inversions are formed by the slowly sinking air being heated by adiabatic
compression. These subsiding layers are more stable than they were at their original higher
altitudes. Subsiding air almost never continues (intact) downward to the Earth's surface. Near
the Earth's surface there is always, however slight, some turbulent mixing taking place. This
slow sinking is therefore almost always counteracted by the turbulent mixing. Subsidence
inversions are nearly always found well above ground level at altitudes ranging from about 2
km to 6 km.
Hot air balloonists above a subsidence inversion may find that they ‘bounce’ back up as they
try to descend. Such a place is ideal for souring birds if it is low enough and one can often
observe an accumulation of fine particles (giving rise to haze) at the top of a subsidence
inversion.

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Inversions may rapidly occur at weather fronts. Here warm air is rapidly transported
(advected) to higher altitudes as it passes over a cooler air mass. Moisture in the warmer air
may condense in these fronts leading to cloud formation and rain. A warm front usually has a
much lower slope than a cold front and the resulting clouds are formed more slowly leading to
lighter but more extensive rain and area of which an inversion occurs. A cold front, which
usually travels more quickly than a warm front, has a rather steep gradient leading to more
rapid, and larger, cloud formation with heavy localised showers. For the latter, the inversion
usually covers a shorter horizontal distance.

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Low-level inversions are very important for the distribution of pollutants. Here are four
idealised scenarios of emissions from a stack and the subsequent progress of a plume.
(a) When the atmosphere is neutrally stable, that is, when the lapse rate of an air parcel
matches that of the atmosphere, the plume “cones”, or spreads out, in all directions as it travels
downwind from the stack.
(b) If the atmosphere is stable, the plume cannot spread vertically but can disperse
horizontally, producing a fan.
(c) The worse scenario is fumigation, which occurs when stack emissions are dispersed to the
ground by the overturning of the atmosphere below an inversion layer. The inversion layer
prevents the air from ascending further, leading to high ground-level pollutant concentrations.
The concentration at a distance will be higher in certain areas if the wind speed is low as
turbulent mixing in the horizontal direction may not occur and the flow will be laminar.
(d) The injection of stack emissions above a stable layer results in a lofting of the emissions.
No vertical mixing occur in the lower, stable air.

Not shown here is the situation similar to (a) except that the lapse rate of air is slightly less
than the lapse rate of the emitted plume. Under such a situation oscillation occurs in which the
plume rises, then falls several times before mixing with the surround air. Such a plume can
look like a damped sinusoidal wave.

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Air behaves non-ideally at certain times due to the condensation of water vapour. The
temperature at which water vapour in an air parcel will begin to condense depends, for the
most part, on the partial pressure of water in the air parcel. Gaseous water can exist in
equilibrium with either its liquid or solid phase along the boundary indicated in the graph

above. This is known as the saturation vapour pressure of water and depends strongly on
temperature. Humidity of the air is a measure of how close to saturation with gaseous water is
the air parcel, thus percentage humidity depends on temperature and is not a direct indication
of the concentration of gaseous water in the air. Another measure of water content is the dew
point. The dew point of a given mass of air is the temperature at which this air would be 100 %
saturated with gaseous water (at water temperature of the air parcel will the water begin to
condense). It must be noted thought that condensation is not always guaranteed. It is possible
to have a situation known as super-saturation for which the gaseous water vapour
concentration is above its saturation vapour pressure without any condensation. The reason
this happen is one of conservation of energy. The process of condensation requires that two
water molecules come together and stay together after forming a very weak (compared to
normal covalent bonds) bond. Nearly always, subsequent collisions will break such a bond.
What needs to happen is that the water molecules first bonds to a surface. A second water
molecule can bond to this first one and also to the surface, thereby being less likely to be
removed from the vicinity of the first by collision . The whole process is actually kinetically
complex, but the result is condensation and formation of the liquid. Since there is always dust
in the atmosphere condensation will always occur, but it usually requires slightly
supersaturated liquids.
Interestingly, a similar process can occur in the reverse direction. It is possible to heat water

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quite some way above its boiling point if the water is very pure and the container is very
smooth (such as a brand new glass). If it remains very still and is heated in a microwave oven,
for example) the water will not boil at 100 Celsius. One should be aware though that as soon
as it is touched or significantly disturbed in any way (by opening the door of the oven, for
example) it can boil very violently, appearing as an explosion.

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