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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 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 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 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 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 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 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 and turbulent diffusion This difference is pointed out on the next slide 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 10 This picture illustrates some measurements of water vapour content (here expressed as dew point) and air temperature with altitude One can see the abrupt change in the lapse rate as the cloud begin to form For a brief altitude interval the relative humidity remain at 100 %, this is the cloud above this the water vapour content is very small and no further cloud formation will occur in this region, but might at higher altitudes Notice that many cloud formations are not continuous, this is because warm rising air needs to be compensated by cooler falling air The situation most often leads to intermittent columns of rising and falling air Clouds are basically the tops of columns of rising air parcels containing sufficient water vapour 26 In spite of the various inversions that occur in the lower atmosphere, on average on a global scale the temperature of the lower atmosphere decreases with altitude in a similar manner to that predicted by the dry adiabatic lapse rate The average rate of decrease is a little less than this at about K per km At heights of about 10 km however a very large and sustained inversion occurs that extends for 15 to 20 km over which the temperature increases by about 70 K These two temperature regions define the Troposphere and the Stratosphere, respectively The Troposphere – containing 80 % of the atmospheric mass and nearly all of the water vapour, is characterised by strong vertical turbulent mixing, whereas the Stratosphere is dry with relatively little turbulance This inversion greatly slows down any mixing of tropospheric air with stratospheric air, but it does occur, especially in regions of rapidly ascending air parcels as in the tropical regions The border between the Troposphere and Stratosphere is called the Tropopause Its height changes with latitude, being the highest above the Equator (18 km) and the lowest above the polar regions (8 km) As will be demonstrated later, the Stratosphere is not heated significantly by contact with the Earth’s surface but is rather heated directly by the Sun’s photons as a result of several photochemical processes 27 Before we look at the energy input to the atmosphere we look at global air circulation patterns One of the main forces behind global air circulation is the Coriolis effect This slide demonstrates that according to an observation point on Earth to the North of a projectile which is fired Northward, the projectile will appear to bend to the West due to the different tangential velocities of the observer and the projectile Such effects only become apparent over large distances What happens though to an object fired in the Northern Hemisphere along a line of latitude? This is explained on the next page 28 The fact that an object will not continue in an initially Westerly or Easterly direction if it remains at constant altitude is a simply argument in geometry: it is not necessary to have a rotating Earth If you were to fire a projectile at a sufficiently high speed on the Equator in the direction of the East or West at constant altitude it would, baring any obstacles, travel all the way around the globe and hit you in the back! Would this happen if you were not on the Equator? To see this, travel North until you are m from the North Pole and fire the projectile again East Will the projectile travel around the pole in a m radius (following a constant Easterly or Westerly latitude) and hit you in the back? No! The projectile travels South (and East or West) It would continue to travel in a relatively straight line but again the Coriolis effect always causes any North – South motion to deflect We thus find in all cases that an apparent force is exerted perpendicular to the direction of motion, to the RIGHT in the Northern Hemisphere and to the LEFT in the Southern Hemisphere A sample calculation: = 7.5 10-5 s-1 ; v = 10 m/s (36 km/hr, 21.6 mph); l is 42 N (Boston), sin(l)= 0.67 Coriolis acceleration = 10-3 ms-2 The change in velocity is: 3.6 m s-1 in hour (3600 s), during which the parcel travels 36 km in its original direction 29 The change in velocity would be 86 m s-1 in 24 hours if the Coriolis acceleration stayed the same over the whole period Obviously this will not be the case Deflection of an object by the Coriolis force y = [ (x)2 / v ] sin() (a) A snowball traveling 10 m at 20 km/h in Boston (42N): 20 km/h = 5.5 m/s; =7.5 10-5 s-1 ; sin ()=.67; x=10 y = 9.1 10-4 m (b) A projectile traveling 1000 km at 2000 km/h at 42 N v = 555 m/s, x=1 106 m; y = 9.05 105 m At Boston ( = 42N), we find that a snowball traveling 10 m at 20 km/h is displaced by y = mm (negligible), but a projectile traveling 1000 km at 2000 km/h is shifted 100 km (important!) Note the importance of (x)2 29 30 As seen earlier, pressure differences give rise to a force This force, if acting alone, will cause an air mass to travel in the direction of the pressure gradient However, the Coriolis effect, gives rise to motion that is perpendicular to the direction of motion of the air mass The two effects will be balanced when the pressure gradient force balances with the Coriolis “force” In this balanced condition, the air will tend to follow along the isobars (lines of constant pressure) At low altitudes however the air masses are subject to a (greater) frictional force due to the vicinity of the Earth’s surface This causes the air to move toward lower pressures In the surface boundary layer the Coriolis “force” is apparently negligible as friction is very large This causes air to flow much closer to the direction of any pressure gradients Note that the Coriolis “force” is proportional to velocity, thus any reduction in velocity (due to friction) will decrease this apparent force The geostrophic approximation is a simplification of very complicated atmospheric motions This approximation is applied to air systems and circulations, away from the Equator of the order of several hundred kilometer or more 31 Because air parcels will tend to travel away from high pressures and towards low pressures the Coriolis effect will cause the direction of air circulation around high pressures to be opposite of that around low pressures Please note, the general direction of circulation around low and high pressure regions is for large scale structures that are influenced by the Coriolis effect On a smaller scale and (especially) close to the ground, air may circulate in either direction This circulation is due simply to existing angular momentum of the air masses (a golf ball rotating around a hole before falling in is an example of this) 32 The first diagram shows the differences in the amount of power received at the Earth's surface as a function of latitude and that emitted by the Earth's surface as a function of latitude That the two lines are not superimposed means that the energy difference must be transported from the Equator to the poles Since thermal conduction is very slow, both the Oceans and the atmosphere transport energy, driven by density differences caused by temperature gradients This then accounts for the general variability in temperature on a daily basis and also has great consequences for the effects of global warming if the ocean and atmospheric circulation patterns were to change 33 34 The Coriolis Effect also changes the picture of air circulation proposed by Hadley Air masses travelling North from the Equator will tend to bend before reaching high latitudes Likewise, air parcels travelling South will tend to bend before reaching lower latitudes This prevents one large circulation cell from being formed in each hemisphere Certainly, two separate cells can be envisaged, but an even number of circulation cells in each Hemisphere is prohibited on symmetry considerations How- ever a circulation pattern with three cells per Hemisphere is allowed and, although this is not a perfect picture, it gives a reasonable idea of the large scale features of atmospheric circulation Of particular note are latitudes in which very strong vertical mixing can take place on time scales considerably less than that based on the typical turbulent diffusion times discussed earlier 35 The overall picture is of course more complex The main perturbing effects are due to the asymmetry of land distribution, the differences in surface reflectivity's (and, therefore, heating rates), and heat transport by the ocean currents 36 37 38 This is the final page of Part - Macroscopic Characteristics of the Earth's Atmosphere 39 [...]... 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 .21 9 cm2 s-1 at 29 3 K and 1 bar In the expression for D 12, 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) ,... (x )2 / v ] sin() (a) A snowball traveling 10 m at 20 km/h in Boston (42N): 20 km/h = 5.5 m/s; =7.5 10-5 s-1 ; sin ()=.67; x=10 y = 9.1 10-4 m (b) A projectile traveling 1000 km at 20 00 km/h at 42 N v = 555 m/s, x=1 106 m; y = 9.05 105 m At Boston ( = 42 N), we find that a snowball traveling 10 m at 20 km/h is displaced by y = 1 mm (negligible), but a projectile traveling 1000 km at 20 00... Hemisphere A sample calculation: = 7.5 10-5 s-1 ; v = 10 m/s (36 km/hr, 21 .6 mph); l is 42 N (Boston), sin(l)= 0.67 Coriolis acceleration = 1 10-3 ms -2 The change in velocity is: 3.6 m s-1 in 1 hour (3600 s), during which the parcel travels 36 km in its original direction 29 The change in velocity would be 86 m s-1 in 24 hours if the Coriolis acceleration stayed the same over the whole period... 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... 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) 12 The last slides dealing with diffusion show that in the absence of significant... 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 21 Inversions may rapidly occur at weather fronts Here... several times before mixing with the surround air Such a plume can look like a damped sinusoidal wave 23 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... 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 22 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... 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... 42 N), we find that a snowball traveling 10 m at 20 km/h is displaced by y = 1 mm (negligible), but a projectile traveling 1000 km at 20 00 km/h is shifted 100 km (important!) Note the importance of (x )2 29 30 As seen earlier, pressure differences give rise to a force This force, if acting alone, will cause an air mass to travel in the direction of the pressure gradient However, the Coriolis effect, gives
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