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Home , Mixing ratio

ATM 507 Problem Set #1 due Tues., Sept. 13, 2011

(note: late problem sets will not receive full credit unless you make prior arrangements!)

Watch your units - make sure they are consistent - check conversions and cancellations! Also – watch significant figures!!! No answer should have more than 2 or 3 significant figures (without a very good reason).

1. Convert a (absolute ) of 7.5x1012 molecules cm-3 to an appropriate volume mixing ratio at a) 1 atm, 20°C. b) 100 mbar, 243 K. c) 800 mbar, 0°C.

-3 2. Convert a concentration of SO2 of 0.1 ppmv to μg m at T = 298 K and 1 atm. Do the same for 0.1 ppmv of NO, NO2, and O3.

3. From the following table a) At 10 km altitude, to what absolute concentration does a mixing ratio of 3 ppmv correspond? b) At 10 km altitude, to what volume mixing ratio does an absolute concentration of 1.7x1010 molecules cm-3 correspond? c) At what altitude does a mixing ratio of 3 ppmv correspond to an absolute concentration of 5.1x1011 molecules cm-3? d) An OH mixing ratio of 10 pptv corresponds to what absolute at i) 0 and ii) 25 km altitude?

Atmospheric Parameters Altitude (km) (K) H (km) [M] (cm-3) Pressure (mb) 0 288.8 8.6 2.5(19) 1013.0 5 259.3 7.7 1.5(19) 542.0 10 229.7 6.8 8.5(18) 269.0 15 212.6 6.3 4.2(18) 122.0 20 215.5 6.4 1.8(18) 55.0 25 218.6 6.5 8.3(17) 25.0 30 223.7 6.6 3.7(17) 11.5 35 235.1 7.0 1.7(17) 5.4 40 249.9 7.4 7.7(16) 2.7 45 266.1 7.9 3.8(16) 1.4 50 271.0 8.0 2.0(16) 0.73 55 265.3 7.9 1.1(16) 0.38 60 253.7 7.5 5.7(15) 0.20 65 237.0 7.0 3.0(15) 0.10 70 220.2 6.5 1.5(15) 0.046 75 203.4 6.0 7.4(14) 0.021 80 186.7 5.5 3.4(14) 0.0089 85 170.0 5.0 2.3(14) 0.0055

4. Concentrations of aerosol constituents are sometimes expressed as ppbv ( fraction) to enable comparison with gaseous concentrations expressed in ppbv. For aerosols, the unit ppbv () is evaluated as RT x concentration of aerosol constituent in nanomoles li-1. - a) Show that for the nitrate ion, NO3 , 1 ppbv (mole fraction) is equivalent to 2.14 ppbm (mass fraction) and 2.58 μg m-3 at 293 K and 1 atm. + b) Show that for the ammonium ion, NH4 , 1 ppbv (mole fraction) is equivalent to 0.625 ppbm (mass fraction) and 0.75 μg m-3 at 293 K and 1 atm. 2- c) If 1 ppbv of SO2 gas is converted to sulfate aerosol (SO4 ) at 298 K and 1 atm, what is the resulting mass concentration of the sulfate aerosol in µg m-3?

5. a) Calculate the mass of the atmosphere. For the purposes of this problem, you may assume that the earth is a smooth sphere with radius = 6378 km, and that the column density of air is given by W = pz/g, where pz is the pressure and g is the acceleration due to gravity. You should use T = 288 K (mean surface temperature) wherever T is required. Use consistent units and make sure they cancel properly! (A more sophisticated estimate is given in Warneck, pp 12-13.) b) The Earth's ozone layer, if compressed to 1 atm pressure, would cover the surface of the planet to a depth of about 3 mm. What is the total mass of this ozone? How many ozone molecules is this? c) What is the mass fraction of ozone in the total atmosphere? d) What is the of ozone in the total atmosphere? (Use 28.8 g/mole for the molecular weight of air.)

6. Water vapor in the atmosphere is most commonly measured as relative humidity, RH. The relative humidity indicates, for a given temperature, the ratio of the actual ambient water vapor pressure to the saturation water vapor pressure - multiplied by 100 and expressed as a percent. To use the water vapor concentration in a chemical calculation one needs to convert RH to concentration units. If the temperature (°C), pressure (mbar), and RH (%) are known, the steps in this procedure are as follows:

I. Calculate the saturation vapor pressure for water:

17.* 2693882 T embar().exp(= 6 1078 ) sat T + 237. 3

IIa. If volume mixing ratio is desired

(/)*RH100 e f = sat HO2 pRHe− [( /100 )*sat ]

IIb. If absolute concentration is desired

[(RH /100 )* e * 1000 ( dyne / cm21 )( mbar )− ] [](H O molecules cm−3 )= sat 2 138.*×+ 10−−16erg K 1 (. T 27316)

a) Calculate the water vapor volume mixing ratio and absolute concentration if T = 30°C, p = 1000 mbar, and RH = 90%. b) Calculate the water vapor volume mixing ratio and absolute concentration if T = 5°C, p = 800 mbar, and RH = 50%.