HW # Soluions Cron Mss Prolem: ssuming n erge surfce pressure of m, n erge ropospheric emperure of 55 K, n glol CO mixing rio of 385 ppm, wh is he curren mospheric Cron reseroir (in unis of g m -? Compre your pproximion wih Tle.3 in W+H. Surfce pressure of m cn e use o esime he mss of ir oer column, p mg/, yieling m/ g m -. We wn o now how much of his mss is cron. The rio of CO molecules o ir molecules is gien y he mixing rio of 385 ppm. Th CO is well mixe mens h his lue hols hroughou he mosphere. The rio of cron mss o ir mss is he mixing rio imes he cron mss per CO molecule ( MU iie y he ir mss per ir molecule (9 MU. 385 ppm x (/9.6x -4. This is he frcion of he g m - column mss which is cron. Therefore he cron column uren is.6 g m -. This grees spo on wih W+H. Lewis Srucures: Using he oe rules, eermine he moleculr srucure for ClCO. Hin: C is he cener. Cl Cl C O Henry s Lw: Wh is he equilirium concenrion of HCO3 in freshwer le, neglecing oher processes, gien moern-y CO mixing rio of 385 ppm? H CO.34 M m - p CO ξp 3.85x -4 m H CO 3 (.34 M m - (3.85x -4 m.3x -5 M Dissoluion of SO ino clou rops is imporn o he sulfur cycle, ecuse oxiion o sulfe occurs more efficienly in he queous phse hn in he gseous phse. The Nionl mien ir Quliy Snrs he se nnul erge limis of.3 ppm for SO. Using he Henry s Lw coefficien from S+P Tle 7., fin he pproxime equilirium concenrions (in M of he soluion species, HSO3 in clou rops his mixing rio. ssume emperure of 5 C, n pressure of 95 m. H SO.3 M m - p SO ξp.8x -8 m H CO 3 (.3 M m - (3x -8 m 3.4x -8 M
S+P prolem 3.: This prolem uses wh we lerne ou ermoleculr recions n pplies i o he conersion of NO o niric ci i NO + OH + M HNO 3 + M eing ermoleculr recion, we now h his is he sum of hree recions, where we he roppe he inermeiry prouc HNO 3 * in he oe recion re (see S+P. Thus his ne recion oesn follow he rrhenius form. Inse, he recion re is oine from Tle. R (T,zNO OH ( ( T, z + ( ( T.x ( T.5x 3 ( T M.6 ( T M/ ( T 3 T 6 cm molecule 3 3 cm molecule s { + log ( ( T M / ( T } s (,,c Where (TM is he re for he low-pressure limi (i.e. mping collisions of HNO 3 * wih M re rre enough o e limiing fcor, n (T is he re for he high pressure limi (he re of collisions eween NO n OH is he limiing fcor. You cn see from he form of ( h he slower re omines. The concenrion for he rnsiion eween low n high pressure limis, M, is foun where (TM (T, his mes he enominor in (, n hus M.5x 9 molecules cm -3. Using p MT, we he p.5 m. We e T 3 K for lc of guince from he prolem. Here I plo he soluion wih IDL.
S+P prolem 3.4: Collision heory preics R C π ( r + r 8T π m OHCHF + m 3 Plugging n chugging yiels R C 3.6x -6 m 3 molecule - s - OHCHF 3 3.6x - cm 3 molecule - s - OHCHF 3 Thus he frcion of collisions leing o recion, γ /3.6x - 7.7x -7, or less hn one in million. This is rre recion! Firs, he O sie of OH hs o hi he H sie of he HCF 3. Furhermore, he collision hs o e priculrly energeic n he on so he OH cn ig ino he elecron shell n pull ou he H om wihou eing eflece firs noe he reliely srong energy rrier (he -E/T erm in seen in Tle. for his recion (This ws iscusse in clss on Mony. See S+P iscussion in secion 3..3 if you woner wh I m ling ou. Furhermore, he O sie of OH is he more negie sie, n hus he elecron shell roun he fluorocron will e rcing he H in he OH, furher complicing he recion S+P Prolem 3.6: This prolem els wih heerogeneous recion (no iscusse in clss, u foun in S+P secion 3.7. I follows irecly from collision heory wih hree simplificions: he spee of he erosol pricle will e negligile compre o h of he gs molecule, so g ; he rius of he gs molecule will e negligile compre o h of he erosol, so r ; n 3 inse of n rrhenius form for he recion efficiency, we jus use fixe frcion, γ. (Don ge confuse h S+P hs ¼ ou fron of (3.36. Th s jus ecuse hey use p pricle surfce re, n he o pu he ¼ ou fron o coner c o cross-secionl re, which is more relen for collision heory. Using hese simplificions, we ge R γr g γπr C 8T πm γπ g n ( r + r N Where he erm in fron of he N O 5 is he firs orer re coefficien 7.5x -4 s -. I es n N O 5 molecule ou minues o fin n rec on he surfce of n erosol pricle O 5 n N O 5
S+P prolem 3.8: C ( is equilen o, ( C ( So he concenrion equions re C (,,c. pr -- Sole explicily ( is simple o sole, -. (3 Using his in (, we ge (4 Ting our lesson from he eigenecor/eigenlue nlysis, we ll see h his prolem hs soluions of he form. + (4 Which yiels ( + Now we jus group erms wih he sme eigenlue (ecy re, n use he iniil coniion h o ge ( (5, n
(6 ( ( Finlly, we cn sole for C y inegring (c wih (6 n using he iniil coniion h C C ( (7 You cn chec h his srs zero n hs ime eriie of zero, consisen wih he iniil coniions for C h we impose, n he fc h C s source, which is, is lso zero. You cn lso see h s >> / + /, hen C, which is wh we expec h eeryhing sring in eenully ens up s C.. pr jusify PSS for PSS for ses h he source n sin erms for re fr lrger hn heir ifference, / fer some iniil equilirium recion ime. Using scle nlysis on (, we cn formlly express his coniion s, << ~ (8 T PSS is concerne wih he longer imescles of se of recions fer pseuo sey se hs een reche. If we se T o e he lrger of / or /, hen we ge << (9 smller of, The only wy for his o wor is if <<. Here s n lerne rgumen using he eigenlue/eigenfuncion nlysis. PSS is jusifie when he wo eigenlues (i.e. jusmen res re well sepre. In his cse, he eigenlues re simply n (you cn o he mh. Plugging hese in o sole for he eigenecors, we see h he eigenlue correspons o n eigenecor where /( - n he eigenlue correspons o ecy purely in. If >>, we he ery oring soluion h he rpi eigenecor poins long he / - line, which simply mens h coners ino ery rpily hrough ( unil i reches se prllel o he secon eigenecor, which poins long. You will noe h his is he sme s PSS prolem where ( is se o zero. Since he prolem se ou seing ( o zero (no (, we he o moe on.
In he oher cse, where.>>, quicly equilires (inepenenly of unil i is on he line efine y he s eigenecor. The firs eigenecor in his limi preics h / / <<. fer reching his pseuo-equilirium, n ecy ogeher owrs zero he slower re. This is more meningful use of PSS, hn he.>> cse, simply ecuse here is some se where n re oh nonzero n in pseuo-equilirium.. Use PSS o sole prolem Seing ( yiels The soluion for ( is sill (3. Comining (3 n ( yiels Inegring (c using ( yiels / ( -. (3 ( / - ( C -- ( You coul he lso goen ( y noing h + + C, n <<, yieling C. You cn esily reconcile ( n ( wih (6 n (7 in he limi h <<.