藉由热力学观念讨论GAS-PHASE.ppt

1、Ch 9. Thermodynamics of Aerosols,CONTENTS,9.1 Thermodynamics Principles 9.2 Aerosol Liquid Water Content 9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Effect 9.4 Thermodynamics of Atmospheric Aerosol Systems,CONTENTS,9.1 Thermodynamics Principles 9.1.1 Internal Energy and Chemical

2、 Potential 9.1.2 The Gibbs Free Energy 9.1.3 Conditions for Chemical Equilibrium 9.1.4 Chemical Potentials of Ideal Gases and Ideal Gas Mixtures 9.1.5 Chemical Potential of Solutions 9.1.6 The Equilibrium Constant,Chemical Potential,藉由熱力學觀念討論Gas-Phase、Aqueous Phase、Solid Phase三相平衡 SOLID=LIQUID Chemi

3、cal Potential =f(T, P, ni) ni:the moles of species i,9.1 Thermodynamics Principles,9.1.3 Conditions for Chemical Equilibrium,自發性反應趨向減少Gibbs free energy之方向進行,CONTENTS,9.2 Aerosol Liquid Water Content 9.2.1 Chemical Potential of Water in Atmospheric Particles 9.2.2 Temperature Dependence of the DRH 9.

4、2.3 Deliquescence of Multicomponent Aerosols 9.2.4 Crystallization of Single and Multicomponent Salts,DRH(deliquescence relative humidity) Low RH aerosol solid Deliquescence：當RH開始增加至DRH時，氣膠內特定組成會開始吸收水分，藉以維持其其熱力學平衡關係，因而變為水相。每一物種之DRH並不相同。 Crystallization：當RH下降時，其水分會揮發形成結晶，但此RH與DRH並不相同。 例如 (NH4)2SO4 ,

5、fig 9.4,9.2 Aerosol Liquid Water Content,9.2 Aerosol Liquid Water Content,9.2 Aerosol Liquid Water Content,DRH、Deliquescence、 Crystallization ：與G相關,Deliquescence and Crystallization,Deliquescence 當RHDRH，Liquid之Gibbs free energy較低，因而致使 (NH4)2SO4以Liquid存在 當RH=DRH，兩者之Gibbs free energy相同，因而致使Solid會開始吸收水

6、分 Gibbs free energy變化圖 Crystallization 當RH下降至DRH時，水分並不會在此時揮發。RH持續下降，使氣膠成為超飽和溶液。帶其達到臨界超飽和(Critical Supersaturation)後，即發生再結晶現象,Gibbs free energy變化圖,9.2.1 Chemical Potential of Water in Atmospheric Particles,Water Vapor (atmosphere): the order of grams per m3 of air. H2O concentration in the aerosol is

7、 less than 1 mg/m3 of air 氣膠相內水之濃度變化並不會影響大氣中水蒸氣之濃度 氣膠熱力學模式計算時，可將ambient RH視為一常數,9.2.1 Chemical Potential of Water in Atmospheric Particles,Water Activity Pw: the water vapor pressure(in atm) w: the water activity in solution 純水平衡 w=1，pw=pw0(T, saturation vapor pressure) (9.61) 、(9.62)可得,9.2.1 Chemic

8、al Potential of Water in Atmospheric Particles,Water Activity 由於Pw/Pw0即為相對濕度(01)之定義 大氣氣膠中之水活性(w)即為相對濕度(RH) 單一鹽類於DRH，H2O於氣相與氣膠相平衡 ws: the water activity of the saturated solution of the salt at T (It can be calculated from thermodynamic arguments ),9.2.2 Temperature Dependence of the DRH,單一鹽類之DRH會隨溫度

9、改變(推導)、(應用) n: the solubility of S in water(moles of solute/mole of water) (A、B、C) Hs: the enthalpy of solution of the salt(data),The solubility of S in water,The enthalpy of solution of the salt,DRH理論值與量測值比較,(NH4)2SO4之DRH變化較小，即接近常數 NaNO3之DRH變化較大,DRH理論值與量測值比較(續),混合鹽類(Mixed-Salt)之DRH會下降,Temperature D

10、ependence of the DRH,(a)式：水之冷凝熱(-Hv)即為水之蒸發熱 (Hv)之負值 (b)式：鹽類之溶解熱(Hs),The overall enthalpy change,溶液中水蒸氣於此溫度之變化=Clausius-Clapeyron equation,純水,結合(9.67) 、(9.68) 代入DRH關係式,Temperature Dependence of the DRH(續),代入n=A+BT+CT2，積分範圍T0T,T0=298 K,9.2.3 Deliquescence of Multicomponent Aerosols,多成分氣膠(Multicomponen

11、t Aerosols)之吸水行為與單一鹽類相同。KCl-NaCl之deliquescence growth、evaporation、crystallization如fig 9.7。,Hydroscopic growth and evaporation of a mixed-salt particle,Initial 66% mass KCl 34% mass NaCl 混合鹽類之DRH較低,推導雙電解質造成之DRH改變,Gibbs-Duhem equation：用於計算單一電解質加入單一溶質水溶液中之DRH改變 於溫度T、壓力p，包含雙電解質(1,2)、水(w) n1、n2、nw：the nu

12、mbers of moles of electrolytes of 1, 2, and water 1、2、w：chemical potential,9.2.3 Deliquescence of Multicomponent Aerosols,9.2.3 Deliquescence of Multicomponent Aerosols,初時假設electrolyte 1與固相鹽類1平衡，此時並不包含electrolyte 2。 加入electrolyte 2， electrolyte 1之化學潛能尚未改變，即d1=0。 electrolyte 2和H2O之化學潛能,m2: the molali

13、ty of electrolyte 2 Mw: the molecular weight of water,推導雙電解質造成之DRH改變,9.2.3 Deliquescence of Multicomponent Aerosols,積分m2=0m2 Wexler and Seinfeld(1991) 由上式可知加入electrolyte 2後，water activity會減少，因而降低DRH 得知 (實例，NH4NO3 and NH4Cl) 1.DRH時之水活性最小(m2=0，左右兩項相等) 2.混合鹽類之DRH恆小於單一鹽類之DRH,推導雙電解質造成之DRH改變,9.2.3 Delique

14、scence of Multicomponent Aerosols,NH4NO3 and NH4Cl,兩電解質混合後，潮解點相對濕度會降低，最低達51%。,1,2,3,4,5,6,7,9.2.3 Deliquescence of Multicomponent Aerosols,NH4NO3 and NH4Cl,1,2,3,4,5,6,7,不同RH時，氣膠內組成變化,9.2.3 Deliquescence of Multicomponent Aerosols,氣膠內組成變化(RH),氣膠內組成：40%NH4NO3、60%NH4Cl RH：40%90%(increase) No evaporati

15、on and condensation,Eutonic point:最低DRH之相對組成點 如表9.4,DRH*(Mutual deliquescence points),9.2.3 Deliquescence of Multicomponent Aerosols,多於三物種之相轉換圖(如圖9.9) Solid:(NH4)2SO4、NH4HSO4、(NH4)3H(SO4)2)、NH4NO3 (Solid lines區分各主導solid，為phase boundary，線上為共存。Label : DRH) Aqueous:H+、NH4+、HSO4-、SO42-、NO3- (Dashed line

16、s說明反應發生方向) Total Hydrogen= total moles of protons and bisulfate ions Total Sulfate=total moles of sulfate and bisulfate ions Dotted line乃指反應發生方向(path lines) ，乃指低於DRH之RH(solid)減少時之進行方向。如：1 mole (NH4)2SO4形成必須消耗2 moles NH4+、1mole SO42-，因而X、Y會改變。,9.2.3 Deliquescence of Multicomponent Aerosols,9.2.4 Crys

17、tallization of Single and Multicomponent Salts,1.再結晶過程會有延遲現象。 2.多種鹽類組成之粒狀物會顯示多個再結晶點，如圖9.7。KCl-NaCl之組成有兩階段蒸發過程：KCl(65%)、NaCl(62%) 3.Spann and Richardson(1985)：氣膠組成介於NH4HSO4和(NH4)2SO4組成，crystallization RH:10%40%，於大氣中氣膠並不會呈現固體,CONTENTS,9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Ef

18、fect Aerosol : curved interface(not flat) The effect of curvature：在此之前所討論之物種蒸汽壓皆於一平面上，此一節將討論物種A於氣膠粒狀物表面上之蒸汽壓，其受曲面之影響 Gibbs free energy 藉由形成單一液滴之Gibbs free energy變化，引入表面張力相(Derived) G=Gdroplet-Gpure vapor (Result),G for the formation of a single drop,Species A、radius Rp、n molecules NT: total number o

19、f vapor initially After the drop forms: vapor, N1=NT-n gl、gv:the G of a molecules (Liquid and Vapor) : surface tension Rp: the radius of curvature n:the number of molecules in the drop (gl-gv) (9-13) at T, dni=0 dg=vdp or dg=(vl-vv)dp vvvl， dg=-vvdp vv=kT/p,Gibbs free change for formation of a dropl

20、et,Bulk free energy,Surface tension,The behavior of G as a function of Rp,S1 Small Rp: Surface tension term dominates Large Rp: Bulk free energy dominates,9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Effect,The Kelvin effect(Derived),液滴曲面對平衡蒸汽壓之影響 於一外凸液面，要拉住一分子之其他液體分子數目比於一平面之液體數目

21、為少，因而可知，與一液滴達到平衡之蒸汽分子所產生之氣壓要比平面液體之蒸汽壓高。,9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Effect,The Kelvin effect,Gmaximum G* at Rp=Rp* the equilibrium at this point is metastable S:Saturation ratio(pA/pA0) :surface tension or M:the molecular weight of the substance l:the liquid-phas

22、e density,The Kelvin Effect,Table 9.5為水與有機物之表面張力。298 K時，五種有機物之分子量(M/)為水之36倍，但其表面張力皆為水之1/3倍。,9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Effect,The Kelvin Effect,Fig 9.12為H2O、DOP(typical organic compound)於不同粒徑時，受Kelvin effect影響之大小,9.3 Equilibrium Vapor Pressure Over a Curved Surf

23、ace: The Kelvin Effect,H2O：於0.1 m時，增加2.1%；於0.01 m時增加23%，可知約50 nm時，Kelvin effect影響顯著。 較高分子量有機物，如DOP：200 nm時，則需加以考量,成長區,蒸發區,CONTENTS,9.4 Thermodynamics of Atmospheric Aerosol Systems 9.4.1 The H2SO4-H2O system 9.4.2 The Sulfuric Acid-Ammonia-Water System 9.4.3 The Ammonia-Nitric Acid-Water System 9.4.

24、4 The Ammonia-Nitric Acid- Sulfuric Acid-Water System 9.4.5 Other Inorganic Aerosol Species,9.4.1 The H2SO4-H2O system,H2SO4-hydroscopic, extremely low RH,9.4 Thermodynamics of Atmospheric Aerosol Systems,Dp/Dp0:particle growth factor Dpoln(pH2SO4/p0H2SO4):Kelvin effect parameter How to use fig 9.13

25、(1 m H2SO4-H2O droplet),9.4.1 The H2SO4-H2O system,9.4.1 The H2SO4-H2O system,The saturation vapor pressure of pure sulfuric acid, p0H2SO4 p0H2SO4=1.31.010-8 atm(1310 ppb) at 296 K (T dependence) H2SO4蒸汽壓於表面之變化，為H2SO4-H2O 混合物內組成、溫度之函數 RH50%，H2SO440% by mass，xH2SO40.1(T=20 C)，H2SO4 equilibrium vapor

26、pressure10-12 mmHg。 H2SO4gasSO42-aerosol,9.4.1 The H2SO4-H2O system,The effect on the composition of atmospheric H2SO4-H2O droplets. Particle size1 m，negligible Kelvin effect For smaller particles the H2SO4 mole fraction in the droplet is highly dependent on particle size. The water concentration in

27、creases as the RH increase.,9.4.1 The H2SO4-H2O system,The composition of atmospheric H2SO4-H2O droplets The vapor pressure of H2SO4(g) is zero over atmospheric particles The whole systembisulfate dissociation reaction Keq(298 K)=1.0110-2(mol/kg) The molar ratio of HSO4- to SO42- The ratio is propor

28、tional to H+ H+,pH,HSO4-,9.4.2 The Sulfuric Acid-Ammonia-Water System,T, RH, NH3, H2SO4, determine the aerosol composition 30%, 298 K, 10 g/m3 H2SO4,9.4 Thermodynamics of Atmospheric Aerosol Systems,0.5 1 1.25 2,NH3,H2SO4,H2O , total mass ,9.4.2 The Sulfuric Acid-Ammonia-Water System,75%, 298 K, 10

29、g/m3 H2SO4,9.4 Thermodynamics of Atmospheric Aerosol Systems,Molar ratio=2, form (NH4)2SO4, loss water Liquid phaseSolid Phase,9.4 Thermodynamics of Atmospheric Aerosol Systems,9.4.2 The Sulfuric Acid-Ammonia-Water System,NH3/H2SO4 molar ratio2 Ammonia also exist in the gas phase,9.4.3 The Ammonia-N

30、itric Acid-Water System,NH3(g)+HNO3(g)NH4NO3(s) Condition:high NH3、high HNO3、lowSO42- 2 Cases for NH4NO3 Ambient RHDRHLiquid,9.4 Thermodynamics of Atmospheric Aerosol Systems,9.4 Thermodynamics of Atmospheric Aerosol Systems,NH3(g)+HNO3(g)NH4NO3(s),Ambient RHDRHSolid Equilibrium condition (chemical

31、potential of ideal gases and solids) Kp(ppb2): estimated by vant Hoff equation, shown as fig9.19, it is sensitive to T change,NH3(g)+HNO3(g)NH4NO3(s),Lower TLower KpLower equilibrium values of the NH3 and HNO3 gas-phase concentrations Lower T shift the equilibrium of the system toward the aerosol ph

32、ase, increasing the aerosol mass of NH4NO3(fig 9.20),9.4 Thermodynamics of Atmospheric Aerosol Systems,9.4 Thermodynamics of Atmospheric Aerosol Systems,NH3(g)+HNO3(g)NH4+NO3-(9.92),Ambient RHDRHLiquid(826 M) Strongly non-idealneed activity coefficient Equilibrium condition Estimate K(T)Need “m”Need

33、 aerosol water content Fig 9.21 depicts the results of such a computation.(The product of the mixing ratios of ammonia and nitric acid over solution as a function of RH),9.4 Thermodynamics of Atmospheric Aerosol Systems,Water activity=RH One needs to relate the tendency of the aerosol components to

34、absorb moisture(RH) W: the mass of aerosol water(kg of water/m3 of air) Ci:the aqueous-phase concentration of electrolyte i (moles/m3 of air) mi,o(aw):the molality(mol/kg) of a single-component aqueous solution of electrolyte i (water activity, aw=RH/100)查表計算,Aerosol water content (ZSR relationship,

35、 Zdanovskii-Stokes-Robinson relationship),9.4 Thermodynamics of Atmospheric Aerosol Systems,NH3(g)+HNO3(g)NH4+NO3-(9.92),Y=1no (NH4)2SO4, 隨RH增加，濃度乘積快速減少，可知主要以aerosol phase為主。Water會使NH4NO3溶解，並使其在aerosol phase量增加。,9.4 Thermodynamics of Atmospheric Aerosol Systems,NH3(g)+HNO3(g)NH4+NO3-(9.92),Input RH,

36、 T, TN, TA,可知gas phase-aerosol phase平衡組成 TN=HNO3(g)+NO3- TA=NH3(g)+NH4+ Kp/(RT)2TNTA: no NH4NO3 TNTAKp/(RT)2: NH4NO3 formation Equilibrium Kp/(RT)2=NH3(g)eHNO3(g)e,NH4NO3e=0.5(TA+TN-(TA+TN)2-4(TATN-Kp/(RT)2)0.5 NH3(g)=TA-NH3NO3e HNO3(g)=TN-NH3NO3e,9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water S

37、ystem,Gas Phase: NH3,HNO3,H2SO4,H2O Solid Phase:NH4HSO4, (NH4)2SO4, NH4NO3, (NH4)SO42NH4NO3, (NH4)2SO4 3NH4NO3,(NH4)3H(SO4)2 Aqueous Phase:NH4+,H+,HSO4-,SO42-,NO3-,H2O Two observations 1.Sulfuric acid possesses an extremely low vapor pressure(僅在aerosol) 2.(NH4)2SO4 solid or aqueous is the preferred

38、form of sulfate Two regime Fig 9.23,9.4 Thermodynamics of Atmospheric Aerosol Systems,9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water System,9.4 Thermodynamics of Atmospheric Aerosol Systems,Low NH3 : SO42- and HSO4- As NH3 increase: NH4NO3 become important Aerosol water content : nonlinear(與其電解質組成變