Presentation Slides for
Chapter 19of
Fundamentals of Atmospheric Modeling 2nd Edition
Mark Z. JacobsonDepartment of Civil & Environmental Engineering
Stanford UniversityStanford, CA [email protected]
March 31, 2005
S(IV) and S(VI) Families
S
OO
O
S
HO OH
O
S
HO O
O
S
O O
S
O
OH
O OH
S
O
OH
O O
S
O
O
O O
Sulfurous acidH2SO3(aq)
Bisulfite ionHSO3
-
Sulfite ionSO3
2-
Sulfuric acidH2SO4(g,aq)
Bisulfate ionHSO4
-
Sulfate ionSO4
2-
S(IV) Family
Sulfur dioxideSO2(g,aq)
S(VI) Family Table 19.1
Mechanisms of Converting S(IV) to S(VI)
Why is this important?It allows sulfuric acid to enter or form within cloud drops and aerosol particles, increasing their acidity
Mechanisms1. Gas-phase oxidation of SO2(g) to H2SO4(g) followed by condensation of H2SO4(g)
2. Dissolution of SO2(g) into liquid water to form H2SO3(aq) followed by aqueous chemical conversion of H2SO3(aq) and its dissociation products to H2SO4(aq) and its dissociation products.
Gas-Phase Oxidation of S(IV)Gas-phase oxidation of sulfur dioxide to sulfuric acid (19.1)
+ OH(g), M + H2
O (g)
Sulfur
dioxide gas
Bisulfite Sulfur
trioxide
Sulfuric
acid gas
+ O2
(g)
HO2
(g)
SO2
(g) HSO3
(g) SO3
(g) H2
SO4
(g)
Condensation and dissociation of sulfuric acid (19.1)
Bisulfate ion
H2
SO4
(aq) H+
+ HSO4
-
2H+
+ SO4
2-
Sulfate ionAqueous
sulfuric acid
H2
SO4
(g)
Sulfuric
acid gas
S(IV) Dissolution/Aqueous Oxidation
Dissolution of sulfur dioxide (19.3)
Dissociation of dissolved sulfur dioxideAt pH of 2-7, most S(IV) dissociates to HSO3
- (19.4)
S O2
(g) S O2
(aq)
Dissolved
sulfur dioxide
Sulfur
dioxide gas
SO2
(aq) + H2
O(aq) H2
SO3
(aq) H+
+ HSO3
-
Dissolved
sulfur
dioxide
Liquid
water
Sulfurous
acid
Hydrogen
ion
Bisulfite
ion
2H+
+ SO3
2-
Hydrogen
ion
Sulfite
ion
Aqueous Oxidation of S(IV)Oxidation of S(IV) by hydrogen peroxide (19.5)
If [H2O2(aq)] > [S(IV)]S(IV) is consumed within tens of minutes
If [S(IV)] > [H2O2(aq)]H2O2(aq) is consumed within minutes
SO4
2-
+ H2
O(aq) + 2H+
Bisulfite
ion
HSO3
-
+ H2
O2
(aq) + H+
Hydrogen
peroxide (aq)
Sulfate
ion
Hydrogen Peroxide Sources/SinksSources of hydrogen peroxide (19.8, 19.9)
Sinks of hydrogen peroxide (19.6, 19.7)
H2
O2
(g) H2
O2
(aq)
Hydrogen
peroxide
Hydroperoxy
radical
HO2
(aq) + O2
-
+ H2
O(aq) H2
O2
(aq) + O2
(aq) + OH-
Peroxy
ion
Hydroxide
ion
H2
O2
(aq) + h ν 2OH(aq)
H2
O2
(aq) + OH(aq) H2
O(aq) + HO2
(aq)
Aqueous Oxidation of S(IV)Oxidation by ozone, important when pH > 6 (19.11)
Oxidation by hydroxyl radical, important when pH ≈ 5 (19.12)
SO3
2-
+ O3
(aq) SO4
2-
+ O2
(aq)
Sulfite
ion
Dissolved
ozone
Sulfate
ion
Dissolved
oxygen
SO5
-
+ H2
O(aq)
Bisulfite
ion
Peroxysulfate
ion
HSO3
-
+ OH(aq) + O2
(aq)
Aqueous Oxidation of S(IV)Oxidation by oxygen, catalyzed by peroxysulfate ion (19.13)
Oxidation by the peroxymonosulfate ion (19.14)
Dissolved
oxygen
Bisulfite
ion
Peroxymonosulfate
ion
HSO3
-
+ O2
(aq)
SO5
-
HSO5
-
2SO4
2-
+ 3H+
Bisulfite
ion
Sulfate
ion
HSO3
-
+ HSO5
-
+ H+
Aqueous Oxidation of S(IV)Oxidation by oxygen, catalyzed by Fe(III)=Fe3+ (19.15)
Oxidation by oxygen, catalyzed by Mn(II) = Mn2+ (19.16)
Sulfite ion Sulfate ion
Fe(III)
SO4
2-
+ H2
O2
(aq)SO3
2-
+ H2
O(aq) + O2
(aq)
Bisulfite ion Sulfate ion
Mn(II)
SO4
2-
+ H2
O2
(aq) + H+
HSO3
-
+ H2
O(aq) + O2
(aq)
Aqueous Oxidation of S(IV)Oxidation by formaldehyde (19.19)
Formaldehyde equilibrates with methylene glycol (19.17)
SO3
2-
+ HCHO(aq)
Sulfite
ion
Formald
-ehyde
HMSA
HOCH2
SO3
-
+ OH-
H2
C(OH)2
(aq)
Formaldehyde
HCHO(aq) + H2
O(aq)
Methylene glycol
Aqueous Oxidation of S(IV)Oxidation by dichloride ion (19.24)
Dichloride ion equilibrates with chlorine atom,ion (19.21)
Dichloride
ion
Peroxysulfate
ion
Bisulfite
ion
HSO3
-
+ Cl2
-
+ O2
(aq) SO5
-
+ 2Cl-
+ H+
Chlorine
atom
Chloride
ion
Dichloride
ion
Cl(aq) + Cl-
Cl2
-
Cloud Conversion of S(IV) to S(VI)
Fig. 19.1
Change in S(VI) content when SO2(g) dissolved and (a) did not and (b) did react in a cloud. The conversion took < 10 minutes
0
5
10
15
20
25
30
35
40
0 0.5 1 1.5 2
Summed concentration (
μ
g μ
-3
)
Tiμe froμ start (h)
H
2
O 0.0001 (a aνd b)
SO
4
2-
(a)
HSO
4
-
(b)
HSO
3
-
(b)
HSO
4
-
(a)
SO
4
2-
(b)
×
Sum
med
con
cent
ratio
ns (μ
g m
-3)
Diffusion Within a DropCharacteristic time for aqueous diffusion in cloud drop (19.25)
Example 19.1:di = 30 μm
---> tad,q = 0.011 sdi = 10 μm
---> tad,q = 0.0013 s
Reaction times for O3(aq), NO3(aq), OH(aq), Cl(aq), SO4- CO3
-, and Cl2- are shorter than are diffusion transport times
τad,q = ri2
π2Daq,q
Diffusion Within a DropTime rate of change of concentration of species q in size bin i as a function
of radius during diffusion (19.26)
Boundary condition At drop center, ∂cq,i,r/ ∂ r = 0
dcq,i,rdt
⎛ ⎝ ⎜ ⎞
⎠ ⎟ ad,aq
=Daq,q1r2
∂∂r r2
∂cq,i,r∂r
⎛ ⎝ ⎜
⎞ ⎠ ⎟ +Pc,q,i,r −Lc,q,i,r
Aqueous Chemistry With GrowthAqueous reactions stiffer than gas reactionsAqueous reactions solved in more size bins than gas reactionsAqueous concentrations coupled to growth and equilibrium --> Either time split aqueous chemistry from other processes with a small splitting time step or solve aqueous chemistry together with other processes
Change in aerosol composition (19.27)
Corresponding conservation of gas equation (19.28)
dcq,i,tdt
⎛ ⎝ ⎜ ⎞
⎠ ⎟ ge,eq,aq
=dcq,i,t
dt⎛ ⎝ ⎜ ⎞
⎠ ⎟ ge
+dcq,i,t
dt⎛ ⎝ ⎜ ⎞
⎠ ⎟ eq
+dcq,i,t
dt⎛ ⎝ ⎜ ⎞
⎠ ⎟ aq
dCq,tdt =−
dcq,i,tdt
⎛ ⎝ ⎜ ⎞
⎠ ⎟ gei=1
NB∑
Aqueous Chemistry Families
(19.29)-(19.35)
cS IV( ),i =cSO2 aq( ),i +cHSO3−,i +cSO32−,icS VI( ),i =cH2SO4 aq( ),i +cHSO4−,i +cSO42−,i
cHO2,T ,i =cHO2 aq( ),i +cO2−,icCO2,T ,i =cCO2 aq( ),i +cHCO3−,i +cCO32−,i
Used for one type of numerical solution to aqueous chemistry
cHCHOT ,i =cHCHOaq( ),i +cH2C OH( )2,icHCOOHT ,i =cHCOOH aq( ),i +cHCOO- ,i
cCH3COOHT ,i =cCH3COOH aq( ),i +cCH3COO-,i
Growth/Aqueous Chemistry ODEsChange in S(IV) due to aqueous chemistry (19.43)
Chemical production and loss terms (19.45)
Gas conservation equation (19.53)
dcS IV( ),i,tdt =kS IV( ),i,t−h CSO2 g( ),t − ′ S S IV( ),i,t−h
cS IV( ),i,t′ H S IV( ),i,t−h
⎛ ⎝ ⎜ ⎜
⎞ ⎠ ⎟ ⎟
+Pc,S IV( ),i,t −Lc,S IV( ),i,t
Pc,q,i,t = Rc,nP (l,q),tl=1
Nprod,q∑ Lc,q,i,t = Rc,nL (l,q),t
l=1
Nloss,q∑
dCSO2 g( ),tdt =− kS IV( ),i,t−h CSO2 g( ),t − ′ S S IV( ),i,t−h
cS IV( ),i,t′ H S IV( ),i,t−h
⎡ ⎣ ⎢ ⎢
⎤ ⎦ ⎥ ⎥ i=1
NB∑
Growth/Aqueous Chemistry ODEsDimensionless effective Henry’s constant (19.44)
Dimensionless Henry’s constant (19.37)
′ H S IV( ),i,t−h = ′ H SO2 aq( ),icS IV( ),i,t
cSO2 aq( ),i,t
=mvcw,i,t−hR*THSO2 1+K1,S IV( )mH+,i,t−h
+K1,S IV( )K2,S IV( )
mH+,i,t−h2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
′ H SO2 aq( ),i =mvcwR*THSO2
Growth/Aqueous Chemistry ODEsRatio of S(IV) to SO2(aq) (19.38)
First and second dissociation constants of S(IV) (19.39)
(19.40)
cS IV( ),i,tcSO2 aq( ),i,t
= 1+K1,S IV( )mH+,i,t−h
+K1,S IV( )K2,S IV( )
mH+,i,t−h2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
K1,S IV( ) =mH+,imHSO3−,iγi,H+ HSO3−
2
mSO2 aq( ),i
K2,S IV( ) =mH+,imSO32−,iγi,H+ SO32−
2
mHSO3−,iγi,H+ HSO3−2
Chemical Loss TermConsider aqueous reactions of family (19.46 - 7)
S IV( )+H2O2 aq( )+H+ ⏐ → ⏐ S VI( )+2H++H2O aq( )
S IV( )+HO2,T ⏐ → ⏐ S VI( )+OH aq( )+2H+
HSO3−+H2O2 aq( ) +H+
HSO3−+HO2 aq( )SO32−+HO2 aq( )
HSO3−+O2−
SO32−+O2−
These represent individual aqueous reactions (19.48-52)
Chemical Loss Termand their equilibrium partitioning (19.53-4)
SO2 aq( )+H2O aq( )⇔ H++HSO3−⇔ 2H++SO32−
HO2 aq( ) ⇔ H++O2−
Chemical Loss TermFamily loss rate (19.55)
Rate coefficient for S(VI)+H2O2(aq)+H+ (19.56)
Mole fraction of S(IV) partitioned to HSO4- (19.57)
Lc,S IV( ),i,t =kacS IV( ),i,tcH2O2,i,tcH+,i,t +kbcS IV( ),i,tcHO2,T ,i,t
ka =ka,1α1,S IV( )
α1,S IV( ) =mH+,i,t−hK1,S IV( )
mH+,i,t−h2 +mH+,i,t−hK1,S IV( ) +K1,S IV( )K2,S IV( )
Chemical Loss TermRate coefficient for S(VI)+HO2(aq) (19.58)
Mole fraction of S(IV) partitioned to SO42- (19.59)
Mole fraction of HO2,T partitioned to HO2(aq) and O2- (19.60-1)
kb = kb,1α1,S IV( ) +kb,2α2,S IV( )[ ]α0,HO2,T+kb,3α1,S IV( ) +kb,4α2,S IV( )[ ]α1,HO2,T
α2,S IV( ) =K1,S IV( )K2,S IV( )
mH+,i,t−h2 +mH+,i,t−hK1,S IV( ) +K1,S IV( )K2,S IV( )
α1,HO2,T =K1,HO2,T
mH+,i,t−h +K1,HO2,T
α0,HO2,T = mH+,i,t−hmH+,i,t−h +K1,HO2,T
Table 19.2
Dissolution/chemistry of 10 gases to 16 size bins, 11 species per bin.
Effect of Sparse-Matrix Reductions When Solving Growth/Aqueous ODEs
Without With Quantity Reductions ReductionsOrder of matrix 186 186Initial fill-in 34,596 1226Final fill-in 34,596 2164 Decomp. 1 2,127,685 6333Decomp. 2 17,205 1005Backsub. 1 17,205 1005 Backsub. 2 17,205 973
