1a. Mole fraction How many moles of X per mole of air? 1b. Volume mixing ratio how many liters of X per liter of air? 2. Partial pressure what is the

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2 1a. Mole fraction How many moles of X per mole of air? 1b. Volume mixing ratio how many liters of X per liter of air? 2. Partial pressure what is the pressure exerted by X in the air? Remember that for water, various units related to saturation vapor pressures (e.g. relative humidities) are also often used. 3. Mass mixing ratio how many kg of X per kg of air? 4. Number density (= number concentration) or molar concentration how many molecules or moles of X per m 3, liter or cm 3 of air? 5. Mass concentration how many g or kg of X per m 3, liter or cm 3 of air? 6. Column concentration how many molecules, moles, g or kg of X per m 2 or cm 2 column of air?

3 Very often, the amount of some substance is given in different units than what you need for your calculation. To convert one unit into another, you will typically need some of the following: The molar mass of the compound (from the periodic table ) The molar mass of air (around 29 g/mol, weʼll see why soon) The temperature and total pressure The ideal gas law: pv = nrt p=pressure (in Pa), V=volume (in m 3 ), n=amount (in moles) of a substance, R=8.314 JK -1 mol -1 and T=temperature (in Kelvin). p = (n/v) RT or (n/v) = p/rt are often more useful forms If you want to use per molecule units instead, replace n by N (the number of molecules) and R by k B = JK -1 When doing unit conversions, you can usually safely assume that all gases in the atmosphere behave like ideal gases. Then p tot V=n tot RT, and also p i V=n i RT separately for each compound i. p i is the partial pressure of compound i.

4

5 Trace gas concentration units: 1 ppm V = 1x10-6 mol mol -1 1 ppbv = 1x10-9 mol mol -1 1 pptv = 1x10-12 mol mol -1 The V subscript indicates that these are volume mixing ratios. It is often omitted; unless otherwise mentioned you can usually assume that mixing ratios are volume mixing ratios.

6 Daltonʼs law: Proper measure for phase changes (such as the condensation of water vapor) Evaporation of liquid water from a pan: No lid: water molecules escape from pan to atmosphere (evaporation) Add a lid: escaping water molecules collide on lid and return to surface; collision rate measures p H2O eventually, flux escaping = flux returning : saturation (p H2O,SAT ) cloud formation in atmosphere requires p H2O > p H2O,SAT T p H2O,SAT

7 Relative humidity (%) = 100 (P H2O /P H2O,SAT )

8 Dew point: Temperature T d such that P H2O = P H2O,SAT (T d )

9 Molar mass of dry air ( 78% N 2, 21% O 2, 1% Ar): M air = (0.78x28 g mol -1 ) + (0.21x32 g mol -1 )+ (0.01x40 g mol -1 ) = g mol g mol -1. Example: what is the mass mixing ratio of CO 2? (M=48 g/mol, ξ = 365 ppm v )

10 Radius of Earth: 6378 km Mean surface pressure: 984 hpa Total number of moles of air in atmosphere: Total number of molecules in the atmosphere:

11 When playing around with mass and volume units, please remember that the ideal gas law is normally given in terms of SI units. That is, masses are given in kilograms and volumes in cubic metres. Since molar masses are typically given in g/mol instead of kg/mol, and atmospheric chemists like to use both liters (1 L = m 3 ) and cubic centimetres (cm 3 = 10-6 m 3 ) as volume measures, it is easy to make mistakes of 3 to 9 orders of magnitude by forgetting to convert mass or volume units. Always check your units, and also remember to check if your answer makes sense!

12 Use: Proper measure for calculation of reaction rates optical properties of atmosphere C i and ξ i are related by the ideal gas law: 5. Mass concentration ρ i [g m -3 ]:

13 In many textbooks (and in the following sections of this course), molar or number concentrations are typically denoted by angular brackets. Thus, e.g. [H 2 SO 4 ] denotes the concentration of H 2 SO 4. The units are usually something like mol/l or molecules/cm 3, but that doesnʼt really matter as long as every concentration you are using has the same units. For purposes of manipulating and solving equations, concentrations are variables (or parameters) just like anything else. If you can do it for x, you can (usually) do it for [H 2 SO 4 ]! Just remember to check your final solution; absolute concentrations have to be positive of course

14 z thickness of a compounds layer of all molecules at surface Applications: satellite measurements (no vertical distribution), absorption of solar radiation

15 1 Dobson Unit (DU) = 0.01 mm ozone at STP = 2.69x10 16 molecules cm -2 THICKNESS OF OZONE LAYER IS MEASURED AS A COLUMN CONCENTRATION

16 Why do we use mixing ratios to express atmospheric composition? Answer: because ξ remains constant when the total air density, temperature or pressure changes mixing ratios are a robust measure of atmospheric composition! Mixing ratios for long-lived gases are essentially constant up to around 100 km altitude. Present composition of the Earths atmosphere (stable & well-mixed gases only) GAS Nitrogen (N 2 ) 0.78 Oxygen (O 2 ) 0.21 MIXING RATIO ξ i (dry air) [mol mol -1 ] Argon (Ar) Carbon dioxide (CO 2 ) 365x10-6 Neon (Ne) 18x10-6 Air also contains variable H 2 O vapor ( mol mol -1 ), aerosol particles and a lot of different unstable trace gases (pollutants etc). Trace gases Ozone (O 3 ) Helium (He) Methane (CH 4 ) Krypton (Kr) ( )x x x x10-6

17 Stratopause heating due to oxygen photochemistry Tropopause

18 a) Volume mixing ratio: no effect with height b) Mass mixing ratio: no effect with height, as long as the atmos- phere is well mixed. c) Number concentration: remarkably changing with height

19 Note: log scale!

20 Venus Earth Mars Radius (km) Surface pressure (atm) Mean temperature (K) CO 2 (mol/mol) x N 2 (mol/mol) 3.4x x10-2 O 2 (mol/mol) 6.9x x10-3 H 2 O (mol/mol) 3x10-3 1x10-2 3x10-4 D.J. Jacob

21 EARTH VENUS D.J. Jacob

22 N 2 CO 2 H 2 O oceans form CO 2 dissolves O 2 O 2 reaches current levels; life invades continents Outgassing Life forms in oceans Onset of photosynthesis 4.5 billion yrs. B.P 4 billion yrs. B.P. 3.5 billion yrs. B.P. 0.4 billion yrs. B.P. present D.J. Jacob

23 Formation of the Earth :4.6 First procaryotes (3.5) Denitrification (3.2) Oxygen producing Photosynthesis by cyanobacteria (2.3) Nitrification (1.8) Nitrogen fixation (1.5) Earliest eucaryotes (1.4) First shelled invertebrates (0.57) Primitive fish ( ) First land plants ( ) Jacobson, 2002

24 D.J. Jacob

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