Vietnam part 2 CARL p1 39

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.. It is therefore

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

2

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

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

4

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 ideal-gas law given in the previous slide

6

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

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 high-

to 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

8

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?

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

10

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

As mentioned on the previous slides, the molecular diffusion coefficient can be directly related

to the characteristics of the molecule D 12 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, D 12 = 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 = m O2 m N2 /(m O2 + m N2) 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

12

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

turbulent-diffusion 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)

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

14

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

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

16

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

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

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

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

20

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?