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
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
9.1 Thermodynamics Principles
Chemical Potential
藉由熱力學觀念討論Gas-Phase、
Aqueous Phase、Solid Phase三相平衡
SOLID=LIQUID
Chemical Potential =f(T, P, ni)

ni:the moles of species i
•9.1.3 Conditions for Chemical Equilibrium
自發性反應趨向減少Gibbs free energy之方向進行
G  0
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
• 9.2.3 Deliquescence of
Multicomponent Aerosols
• 9.2.4 Crystallization of Single and
Multicomponent Salts
9.2 Aerosol Liquid Water Content
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 , fig 9.4
9.2 Aerosol Liquid Water Content
9.2 Aerosol Liquid Water Content
DRH、Deliquescence、 Crystallization ：與G相關
Deliquescence and Crystallization
Deliquescence
 當RH<DRH,，Solid之Gibbs free energy較低，
因而致使 (NH4)2SO4以Solid存在
 當RH>DRH，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 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
Water Activity
H 2O( g )  H 2O( aq)
 H O( g )   H O
2

0
H 2O
9.2.1 Chemical Potential of Water
in Atmospheric Particles
2 ( aq)
 RT ln pw  
*
H 2O
 RT ln  w (9.61)
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)
*
0
0
 H O   H O  RT ln pw (9.62)
2
2
(9.61) 、(9.62)可得
pw RH
w  0 
pw 100
Water Activity
9.2.1 Chemical Potential of Water
in Atmospheric Particles
pw RH
w  0 
pw 100
由於Pw/Pw0即為相對濕度(0~1)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
DRH
  ws
100
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會隨溫度改變(推導)、(應用)
H 2O( g )  H 2O( aq)
H 2O( aq)  nSs   nS( aq)
 H s
DRH T   DRH 298 exp 
 R
 1

1 
T
 A T  298   B ln 298  C T  298 

 

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 Dependence of the DRH
H 2O( g )  H 2O( aq) (a)
H 2O( aq)  nSs   nS( aq) b 
(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
H  nH s  H v
溶液中水蒸氣於此溫度之變化=>Clausius-Clapeyron equation
d ln pw
d ln pw H v
H s
H



n
(9.67)
2
2
2
dT
RT
dT
RT
RT
純水
d ln pw0 H v

dT
RT 2
(9.68)
0
pw：溫度T
時之飽和蒸汽壓
Temperature Dependence of the DRH(續)


結合(9.67) 、(9.68)
d ln pw / pw0
H s
 n
dT
RT 2
代入DRH關係式
H s
d ln DRH / 100
 n
dT
RT 2
代入n=A+BT+CT2，積分範圍T0~T
 DRH T   
 H s
  
ln 
 DRH T0   
 R
T0=298 K
 1 1 

T





A


B
ln

C
T

T
 
0 

T0
  T T0 


 H s
DRH T   DRH 298 exp 
 R
 1

1 
T
 A T  298   B ln 298  C T  298 

 

9.2.3 Deliquescence of
Multicomponent Aerosols
多成分氣膠(Multicomponent 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
Mixed-salt
KCl
NaCl
DRH
72.7%
84.2%
75.3%
混合鹽類之DRH較
低
9.2.3 Deliquescence of Multicomponent Aerosols
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)
n1d1  n 2d 2  n w d w  0
n1、n2、nw：the numbers of moles of electrolytes of 1,
2, and water
 1、2、w：chemical potential

9.2.3 Deliquescence of Multicomponent Aerosols
推導雙電解質造成之DRH改變
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d1=0。 electrolyte 2和H2O之化學潛
能 n 2dln  2  n w dln  w  0
n 2 M w m2

nw
1000
m2: the molality of electrolyte 2
Mw: the molecular weight of water
1000
m 2 dln  2 
dln  w  0
nw
9.2.3 Deliquescence of Multicomponent Aerosols
推導雙電解質造成之DRH改變
積分m’2=0~m2
 w m 2 
M w m m '2 d 2 m '2  '
ln
dm 2
'
'

0
 w 0
1000
 2 m 2  dm 2
Wexler and Seinfeld(1991) d 2  0
dm 2
2
 w m2    w m2  0
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
9.2.3 Deliquescence of Multicomponent Aerosols
NH4NO3 and NH4Cl
303 K
DRH
NH4Cl(only) 77.4%
NH4NO3(only) 61.8%
1
3
2
5
4
7
6
兩電解質混合後，
潮解點相對濕度會
降低，最低達51%。
9.2.3 Deliquescence of Multicomponent Aerosols
NH4NO3 and NH4Cl
Solid
Aqueous
1
-
NO3-,NH4+,Cl-
2
NH4Cl
NO3-,NH4+,Cl-
3
-
NO3-,NH4+,Cl-
4
NH4Cl
NO3-,NH4+,Cl-
5
-
NO3-,NH4+,Cl-
6
NH4NO3
NO3-,NH4+,Cl-
1
3
2
5 6
4
7
7 NH4ClNH4NO3，RH<DRH*(51%)
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 evaporation and condensation
RH
51%*
60%
70%
71%
xNH4NO3
0.811
0.73
0.42
-
xNH4Cl
0.189
0.27
0.58
-
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 lines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
X(Ammomia) Y(Sulfate)
1
1
DRH
80%
Solid
(NH2)4SO4
9.2.4 Crystallization 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 Effect
• 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
G  Gdrpolet  G pure
water
G  N1 gv  ngl  4Rp2  NT gv
G  n( gl  gv )  4Rp2
n
4R 3p
3vl
G 
4R 3p
3vl
( g l  g v )  4R p2
dp
pA p
p
g l  g v   kT ln A0
pA
pA
g l  g v  kT  0
4R 3p kT
G  
ln S  4R p2
3vl vl
Species A、radius Rp、n molecules
NT: total number of 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
k
(gl-gv) (9-13) dG   SdT  Vdp   i dni
i 1
at T, dni=0
dg=vdp or dg=(vl-vv)dp
vv>>vl， dg=-vvdp
vv=kT/p
9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Effect
Gibbs free change for
formation of a droplet
The behavior of G as a function of Rp
G
0
Rp
S<1 Both terms are positive
G increase with Rp
S>1
Surface tension Small Rp:
Surface tension term dominates
Large Rp:
Bulk free energy dominates
Bulk free energy
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。
 2M 

p A  p exp 
 RT l Rp 
0
A
4R 3p kT
G  
ln S  4R p2
3vl vl
The Kelvin effect
Gmaximum G* at Rp=Rp*
the equilibrium at this point is metastable
G
0)
0
S:Saturation
ratio(p
/p
A
A
Rp
:surface tension
2vl
R 
kT ln S
*
p
 2vl 

p A  p exp 
 kTRp 
0
A
 2M 

p A  p exp 
 RT l Rp 
0
A
or
M:the molecular weight of the substance
l:the liquid-phase density
9.3 Equilibrium Vapor Pressure Over a Curved Surface: The Kelvin Effect
The Kelvin Effect
 2M 

p A  p exp 
 RT l Rp 
0
A
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
3~6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
成長區
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
蒸發區
 2M 

p A  p A0 exp 
 RT l Rp 
CONTENTS
• 9.4 Thermodynamics of Atmospheric
Aerosol Systems
• 9.4.1 The H2SO4-H2O system
• 9.4.2 The Sulfuric Acid-AmmoniaWater System
• 9.4.3 The Ammonia-Nitric Acid-Water
System
• 9.4.4 The Ammonia-Nitric AcidSulfuric Acid-Water System
• 9.4.5 Other Inorganic Aerosol Species
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.1 The H2SO4-H2O system
H2SO4-hydroscopic, extremely low RH
9.4.1 The H2SO4-H2O system
Dp/Dp0:particle growth factor
Dpoln(pH2SO4/p0H2SO4):Kelvin effect parameter
How to use fig 9.13(1 m H2SO4-H2O droplet)
RH
50%(negligible Kelvin
effect)
90%(negligible
Kelvin effect)
H2SO4 Conc.
42.5%
18%
Density()
1.32
1.1
B. P.
115 C
100 C
76 dyn/cm
73 dyn/cm
11 N
4N
0.55 g/cm3 of solution
0.2 g/cm3 of solution
1.48
2.12
1/1.48=0.68 m
2.12/1.48=1.43 m
Kelvin effect parameter
11.310-4 m
9.210-4 m
ln(pH2SO4/p0H2SO4)
11.310-4/0.68=16.6210-4
9.210-4/1.43= 6.410-4
1.0017
1.0006
Surface tension()
Normality
Mass concentration(xH2SO4)
Particle growth factor(Dp/Dp0)
pure H2SO4
(p
/p0
)
9.4.1 The H2SO4-H2O system
The saturation vapor pressure of pure sulfuric acid, p0H2SO4
p0H2SO4=1.31.010-8 atm(1310 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
RH>50%，[H2SO4]<40% by mass，xH2SO4<0.1(T=20 C)，
H2SO4 equilibrium vapor pressure<10-12 mmHg。
[H2SO4]gas<[SO42-]aerosol
9.4.1 The H2SO4-H2O system
The effect on the composition of atmospheric H2SO4-H2O
droplets.
Particle size>1 m，negligible Kelvin effect
For smaller particles the H2SO4 mole fraction in the droplet is
highly dependent on particle size.
The water concentration increases as the RH increase.
9.4.1 The H2SO4-H2O system
The composition of atmospheric H2SO4-H2O droplets
H 2 SO4( g )  H 2 SO4( aq)
H 2 SO4( g )  H   HSO4
The vapor pressure of H2SO4(g) is zero over atmospheric
particles
The whole systembisulfate dissociation reaction
HSO4  H   SO42
Keq(298
K)=1.0110-2(mol/kg)
1.0110
The molar ratio of HSO4- to SO42-
2
mHSO
4
mSO2
4
The ratio is proportional to [H+]
[H+],pH,[HSO4-]
mol / kg  
 99
 H2
 H2

, SO42
mH  mSO2
4
 HSO mHSO

4

, SO42
 HSO

4
mH 

4
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.2 The Sulfuric Acid-Ammonia-Water System
T, RH, NH3, H2SO4, determine the aerosol composition
30%, 298 K, 10 g/m3 H2SO4
[NH3]/[H2SO4]
<0.5
H2SO4 dominate
0.5~1.25
NH4HSO4 dominate
1.25~1.5
(NH4)3H(SO4)2 dominate
2
(NH4)2SO4 dominate
>2
NH3, it does not change
the aerosol composition
[NH3],[H2SO4],H2O , total mass 
0.5 1 1.25
2
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.2 The Sulfuric Acid-Ammonia-Water System
75%, 298 K, 10 g/m3 H2SO4
[NH3]/[H2SO4]
<0.5
H2SO4 dominate
0.5~1. 5
HSO4- dominate
High NH3
SO42- dominate
DRHNH4HSO4
40%
DRH(NH4)3H(SO4)2
69%
DRH(NH4)2SO4
80%
Molar ratio=2, form (NH4)2SO4, loss water
Liquid phaseSolid Phase
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.2 The Sulfuric Acid-Ammonia-Water System
NH3/H2SO4 molar ratio<0.5
Exist primarily as H2SO4 solution
0.5< NH3/H2SO4 molar ratio<1.5
Consist mainly as HSO4NH3/H2SO4 molar ratio=2
Consist mainly as (NH4)2SO4
NH3/H2SO4 molar ratio>2
Ammonia also exist in the gas phase
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.3 The Ammonia-Nitric Acid-Water System
NH3(g)+HNO3(g)NH4NO3(s)
Condition:high NH3、high HNO3、lowSO422 Cases for NH4NO3


Ambient RH<DRHSolid
Ambient RH>DRHLiquid
9.4 Thermodynamics of Atmospheric Aerosol Systems
NH3(g)+HNO3(g)NH4NO3(s)
T(K)
DRH
Ambient RH<DRHSolid
298
61.8%
ln DRH  
288
67%
723.7
 1.6954
T
Equilibrium condition (chemical potential of ideal gases and solids)
 NH   HNO   NH
3
3
4 NO3
*
0
0
  NH




NO
NH
HNO
4
3
3
3
exp 

RT


  K p T   p NH pHNO
3
3


Kp(ppb2): estimated by van’t Hoff equation, shown as fig9.19, it is
sensitive to T change
ln Kp  84.6 
24220
 T 
 6.1ln 

T
 298 
9.4 Thermodynamics of Atmospheric Aerosol Systems
NH3(g)+HNO3(g)NH4NO3(s)
Lower TLower KpLower equilibrium values of the NH3
and HNO3 gas-phase concentrations
Lower T shift the equilibrium of the system toward the aerosol
phase, increasing the aerosol mass of NH4NO3(fig 9.20)
9.4 Thermodynamics of Atmospheric Aerosol Systems
NH3(g)+HNO3(g)NH4++NO3-(9.92)
Ambient RH>DRHLiquid(8~26 M)
Strongly non-idealneed activity coefficient
Equilibrium condition
 NH   HNO 
3
0
0


  NH




  
HNO
NO3
NH 4
3
3

exp

RT

K 9.92 
2
 NH
4 NO3
mNH  mNO 
4
pHNO3 p NH 3
3
3
 NH   NO
  NH   NO  mNH  mNO 
4
3
4
3


pHNO3 pNH 3


4

3
2
 NH
4 NO3
  NH   NO 
4
3


 298 
 298  298  
K9.92  4 1017 exp 64.7
 1  11.511  ln 


T
T
T







Estimate K(T)Need “m”Need 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
Aerosol water content
(ZSR relationship, Zdanovskii-Stokes-Robinson relationship)
Water activity=RH
One needs to relate the tendency of the aerosol components to absorb
moisture(RH)
C
 
i
W 
i mi, o aw
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
9.4 Thermodynamics of Atmospheric Aerosol Systems
NH3(g)+HNO3(g)NH4++NO3-(9.92)
K p   HNO3 NH 3
Y=1no (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, T, [TN], [TA],可知gas
phase-aerosol phase平衡組成
[TN]=[HNO3(g)]+[NO3-]
[TA]=[NH3(g)]+[NH4+]
Kp/(RT)2[TN][TA]: no NH4NO3
[TN][TA]Kp/(RT)2: NH4NO3
formation
Equilibrium
Kp/(RT)2=[NH3(g)]e[HNO3(g)]e
[NH4NO3]e=0.5([TA]+[TN]-[([TA]+[TN])2-4([TA][TN]-Kp/(RT)2)]0.5
[NH3(g)]=[TA]-[NH3NO3]e
[HNO3(g)]=[TN]-[NH3NO3]e
Kp 
2
 NH
4 NO3
mNH  mNO 
K 9.92
4
3
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water System
Gas Phase: NH3,HNO3,H2SO4,H2O
Solid Phase:NH4HSO4, (NH4)2SO4, NH4NO3,
(NH4)SO4·2NH4NO3, (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 form of sulfate
Two regime
Ammonia
Fig 9.23
SO42- form
NH4NO3
Poor
[TA]<2[TS]
HSO4-
No
Rich
[TA]>2[TS]
SO42-
Yes
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water System
Low [NH3] : SO42- and HSO4As NH3 increase: NH4NO3 become important
Aerosol water content : nonlinear(與其電解質組成變化有關)
nonlinear
Low NH3
High NH3
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.4 The Ammonia-Nitric Acid- Sulfuric Acid-Water System
sulfatereplacement by nitrate(HNO3 and
NH3 react)
sulfateNO3- , and NH4+, water, total
mass
The reduction of the mass is nonlinear
減少20 g SO42-/m3(from 30 to 10 g/m3)
Dry aerosol mass 減少12.9 g/m3
只會增加10 g NO3-/m3
僅會減少2.9 g NH4+/m3
9.4 Thermodynamics of Atmospheric Aerosol Systems
9.4.5 Other Inorganic
Aerosol Species
加入其他物種(Cl-、Na+)之熱力學計算
NaCl(s)+HNO3(g)NaNO3(s)+HCl(g)
2NaCl(s)+H2SO4(s) Na2SO4(s)+2HCl(g)
NaCl(s)+H2SO4(s) NaHSO4(s)+HCl(g)
Aerosol water content
Suppose a solution contains 6 moles H+/m3, 6 moles
Na+/m3, 7 moles Cl-/m3, 5 moles NO3-/m3
The 4 ions can combine in many ways to form electrolytes: HNO3, HCl,
NaNO3, NaCl.
Mass-balance
CH+,m=CHNO3,m+CHCl,m CNa+,m=CNaNO3,m+CNaCl,m
CCl+,m=CHCl,m+CNaCl,m CNO3-,m=CHNO3,m+CNaNO3,m
Result
Case
C
C
C
C
HCl,m
Cw 
HNO3,m
NaCl,m
NaNO3,m
1
6
0
1
5
2
4
2
3
3
3
1
5
6
0
1000  C NaCl ,m C NaNO3 ,m CHNO3 ,m CHCl ,m 




mw  mHCl ,m mNaNO3 ,m mHNO3 ,m mHCl ,m 
mk ,a  Y0,k  Y1,k aw  Y2,k aw2  Y3,k aw3     
Y0,k,Y1,k,Y2,k: polynomial coefficients(table)
Aerosol water content
RPM input: TOTSO4, TOTNH3, TOTNO3
1. 分配: Temp, gas phase and aerosol phase
TOTSO4皆為aqueous phase
2. Composition
1. SO42->2NH4+: all NH4+(NH4)2SO4、H2SO4、HNO3
2. 2NH4+>SO42-: (NH4)2SO4、NH4NO3、HNO3
3. Aerosol water content
依個別計算所得之物種莫爾濃度(in air)配合大氣相對溼度，
計算其相對吸水量，相加後即得氣膠含水量。
W 
i
Mi
mio a w 
mi 0 (aw )  Y0,i  Y1,i aw  Y2,i aw2  Y3,i aw3    
Y’s 為 polynomial coefficients(如表)
計算含水率之重要參數(298.15 K)
mi 0 (aw )  Y0,i  Y1,i aw  Y2,i aw2  Y3,i aw3    
Y
(NH4)2SO4
37% R.H.; 29.0 m
1.1065495×102
HNO3
0% R.H.; 22.6 m
2.306844303×101
H+/HSO40% R.H.; 30.4 m
3.0391387536×101
NH4NO3
62% R.H.; 28 m
3.983916445×103
(NH4)2SO4
37% R.H.; 29.0 m
1.1065495×102
2H+/SO420% R.H.; 30.4 m
3.0391387536×101
-3.6759197×102
-3.563608869×101
-1.8995055929×102
1.153123266×104
-3.6759197×102
-1.8995058929×102
5.0462934×102
-6.210577919×101
9.7428231047×102
-2.13956707×105
5.0462934×102
9.7428231047×102
-3.1543839×102
5.510176187×102
-3.1680155761×103
7.926990533×105
-3.1543839×102
-3.1680155761×103
6.770824×101
-1.460055286×103
6.1400925314×103
-1.407853405×106
6.770824×101
6.1400925314×103
1.894467542×103
-6.9116348199×103
1.351250086×106
-6.9116348119×103
-1.220611402×103
4.1631475226×103
-6.770046794×106
4.1631475226×103
3.098597737×102
-1.0383424491×103
1.393507324×105
-1.0383424491×103
0
Y
1
Y
2
Y
3
Y
4
Y
5
Y
6
Y
7