CO2 SoluBility

7/18/2019 CO2 SoluBility

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CARBON IN LAKES

I. The CO2 carbonate system

A. Sources and Sinks o CO2

!" Sources

a" atmos#here $ %%% ##m b" res#iration

c" combustion

i. natura&

ii industria&

d" so&ution

2" Sinks

a" #hotosynthesis

b" biomass

c" sedimentation ' #reci#itation

B. So&ubi&ity in the CO2 system

!" CO2 ( $!)2" So&ution *ure +ater , #- ./ 0 -enry1s &a+ , 2/oC % mmo& &0!

3!45 m(&0!6

C. Chemistry o CO2

!" -ydration o CO2 (

CO2 7 -2O -2CO%

-2CO% -CO%0 7 -7

-CO% CO%8 7 -7

2" re&ations +ith #-

-i(h #- CO%8 dominates

9id ran(e #- -CO%

0

dominatesLo+ #- -2CO% :CO2; dominates

%" Eects o Ca&cium <and 9a(nesium"

Ca<-CO%"2 CaCO% 7 CO2 7 -2O

Buerin( ca#acity

A&ka&inity

II. Bio&o(ica& =actors in&uencin( Carbon in &akes

A. *hotosynthesis

!" *hotosynthesis and #-

2" Carbon &imitationB. Res#iration

!" Res#iration and #-

2" BO>

C. Or(anic Carbon

!" Losses

2" Sinks

!



Carbon dioxide in water equilibrium

1. Introduction

Carbon dioxide does dissolve in water, however the system is somewhat complex [1].

First the CO2 dissolves according to:

1! CO2 g! CO2 l!

"t room temperat#re, the sol#bility o$ carbon dioxide is abo#t %& cm' o$ CO2 per 1&& ml watercl(cg ) &.*!.

"ny water+sol#ble gas becomes more sol#ble as the temperat#re decreases, d#e to the

thermodynamics o$ the reaction: "- l! "- g!. he entropy change, ∆-, o$ this reaction

is positive beca#se the gas molec#les are less constrained than the gas molec#les in

sol#tion. he change in Free energy o$ reaction with an increase in temperat#re is +/∆-. his

e$$ect is partic#larly large $or gases li0e CO2 that #ndergo speci$ic reactions with water.

#ilibri#m is established between the dissolved CO2 and 32CO', carbonic acid.

2! CO2 l! 4 32O l! 32CO' l!

his reaction is 0inetically slow. "t e#ilibri#m, only a small $raction ca. &.2 + 15! o$ thedissolved CO2 is act#ally converted to 32CO'. 6ost o$ the CO2 remains as solvated molec#larCO2. "s e#ation:

[ ]

[ ]%

2

%2 !/..! −≈=l

r

CO

CO H K

7n $act, the p8a most reported $or carbonic acid p8a1 ) 9.'! is not really the tr#e p8a o$carbonic acid. ;ather, it is the p8a o$ the e#ilibri#m mixt#re o$ CO2 l! and carbonic acid.Carbonic acid is act#ally a m#ch stronger acid than this, with a tr#e p8a1 val#e o$ '.<*.3owever these val#es are also temperat#re dependent.

Carbonic acid is a wea0 acid that dissociates in two steps[2].

'! 32CO' 4 32O 3'O4 4 3CO'

+ p8a1 2< =C! ) 9.'

>! 3CO'

+ 4 32O 3'O4 4 CO'

2+ p8a2 2< =C! ) 1&.2<

?ote that these carbonate anions can interact with the cations present in the water to $orminsol#ble carbonates. For instance, i$ Ca24 is present limestone, CaCO' is $ormed and i$ 6g24

is present 6gCO' is $ormed. he $ormation o$ these deposits is an additional driving $orce thatcan p#ll the e#ilibri#m more to the right res#lting in acidi$ication o$ the water [2].

<! Ca24 4 CO'2+ CaCO' - ) >.%9 x 1&+% - ) sol#bility constant!

9! 6g24 4 CO'

2+ 6gCO' - ) 9.*2 x 1&+9

he above presented more schematically:

4 32O 4 32O 4 32O 4 Ca24

CO2g! CO2 l! 32CO' 3CO'+

CO'2+

CaCO'

4 3'O4 4 3'O

4

?ote that the reverse is also tr#e and that the scheme represents the sol#bility o$ CaCO' in anacidic sol#tion res#lting in the liberation o$ CO2 in the atmosphere.

2



2. Deriving [H2CO3]

7$ we ass#me CO2 is a simple gas we can apply 3enry@s law that describes the e#ilibri#mbetween vapor and li#id. h#s:

pCO2 ) 8 . xCO2

where pCO2 is the partial press#re o$ the gas in the b#l0 atmosphere Aa!, 8 is a constant Aa!and xCO2 is the e#ilibri#m mole $raction o$ sol#te in li#id phase.

he sol#bility o$ CO2 is temperat#re dependent, as shown in able 1: -ol#bility o$ CO2 at apartial press#re $or CO2 o$ 1 bar abs ['] .

Table 1: Solubility of CO2 at a partial pressure for CO2 of 1 bar abs[3].

emperat#re oC! & 1& 2& '& >& <& *& 1&&

-ol#bilitycm' CO2(g water!

1.* 1.' &.** &.9< &.<2 &.>' &.2% &.29

F#rthermore, as stated above, CO2 reacts with the water on dissol#tion and there$ore onewo#ld expect that 3enry@s law has to be modi$ied.

3owever, according to Carrol and 6ather [>] a $orm o$ 3enry@s law can be #sed $or modelingthe sol#bility o$ carbon dioxide in water $or press#res #p to abo#t 1&& 6Aa, as can be seen inFig#re 1: 3enryBs Constant $or Carbon ioxide in Dater + $rom Carroll et al. [>] .

Figure 1: Henry's Constant for Carbon Dioi!e in "ater # fro$ Carroll et al. [%]

%



hey concl#de that the 8richevs0y+8asarnovs0y #ation, which can be derived $rom 3enry@sEaw, can be #sed to model the system CO2+32O at temperat#res below 1&& oC.

h#s in the range o$ interest, 2&+'< =C, the 3enry coe$$icient $or CO2 in water goes $rom 1<& +2&& 6Aa(mole $raction

"pplying the above to the conditions #nder investigation:emperat#re range: 2& '< =CAress#re range: *& %& bar CO2 concentration in gas phase: 1.'+1. mol5

he partial press#re o$ CO2 in the gas phase is there$ore in the range:1.'(1&& G *& G &.1 ) &.1&> 6Aa1.(1&& G %& G &.1 ) &.1<' 6Aa

"pplying 3enry@s Eaw we calc#late a CO2 mole $raction in water in the range:xlow ) &.1&> ( 2&& ) &.&&&<2xhigh ) &.1<' ( 1<& ) &.&&1&2

Converting mole $ractions to concentrations: "t 2& =C the molar density o$ water ) %%*.21(1*.&2 ) <<.'% mol(l "t '< =C the molar density o$ water ) %%>.'(1*.&2 ) <<.1* mol(l

h#s the CO2 concentration range in water #nder these conditions is:clow ) &.&&&<2 G <<.1* ) &.&2% mol(lchigh ) &.&&1&2 G <<.'% ) &.&<9 mol(l

3. Calculating the H[!]

he basic e#ations needed to calc#late the p3 are derived $rom e#ation '! and >!.

?ote: x ) [3'O4] and y ) [O3+]

he protolysis constants:

63

63

"63

63

63

63<

63

63

%

2

%2

2

%

%22

%

%2

%!

−

−

−−−

=

≈

+

≈=

HCO

CO x K

CO

HCO x

CO H CO

HCO x

CO H

HCO x K

a

l

a

"ss#ming the initial concentration o$ carbonic acid ) c then we derive the ste#chiometricrelation:

c ) [32CO'] 4 [3CO'+] 4 [CO'

2+] he water constant: x.y ) 8w and p8w )1>

he electro ne#trality e#ation:2[CO'

2+] 4 [3CO'+] 4 y ) x

De now have < e#ations and < #n0nowns.From the e#ilibri#m constants we derive

2

2

%

%6363

a K

CO x HCO

−− =

?



and

2!

2

%

2

%2

6363

aa K K

CO xCO H

−

=

-#bstit#ting these into the ste#chiometric relation we derive:

2!!

2

!%

2!!

2

2!2

%

2!

2

2

2

%

2

%

2

2

%

2!

2

%

2

.

..63

.

.63

!63636363

aaa

a

aaa

aa

aaaaaa

K K x K x

c x K HCO

K K x K x

c K K CO

K K

x

K

xCOCO

K

CO x

K K

CO xc

++=

++=

⇒

++=++=

−

−

−−

−−

hese e#ations can be #sed to calc#late in which p3 area which CO 2 species dominates as

can be seen in Fig#re 2: p3 and CO2 species.

H"CO2 equilibra

&.&

&.1

&.2

&.'

&.>

&.<

&.9

&.

&.*

&.%

1.&

& 1 2 ' > < 9 * % 1& 11 12 1' 1>

H

c # m

o l " l $

[3CO'+]

[CO' 2+]

[32CO'])[CO2]l

Figure 2: pH an! CO2 spe&ies

-#bstit#ting these into the electro ne#trality e#ation:

x y K K x K x

x K K K c

x y K K x K x

c x K

K K x K x

c K K

aaa

aaa

aaa

a

aaa

aa

=+

++

+

⇒=+

++

+

++

2!!

2

!2!

2!!

2

!

2!!

2

2!

.

..2.

.

..

.

.2

Combining the above with 8w)x.y we derive a > th degree e#ation in x:

@



x x

K

K K x K x

x K K K c w

aaa

aaa=+

++

+

2!!

2

!2!

.

..2.

Compare:

2!!

2

!2!

.

..2

aaa

aaa

K K x K x

x K K K

+++

with

2!2!

2

2!2!

2

2

!

!

..

...2

aaaa

aaaa

a

a

a

a

K K x K x K x

x K x K K K

x K

K

x K

K

+++

++⇒

+

+

+

7$ 8a1 HH 8a2 then 8a1.x HH 8a2.x and we can consider the e#ations e#al and derive $or theelectro ne#trality e#ation:

x x

K c x K

K c x K

K w

a

a

a

a =++

++ 2

2

!

!

stimating the di$$erence between 8a and x can help simpli$ying the e#ation even $#rther.

F#rthermore: p3 ) +log x.

"pplying the e#ations derived above to the CO2 concentrations calc#lated we calc#late byapplying that i$ 8a II x a valid approach i$ the p3 is ca. > we can write:

waawaa K c K c K x x

x

K c

x

K c

x

K ++=⇒=++ 2!

2! .

h#s with the CO2 concentration range in water calc#lated above we calc#late $or the p3range:

clow ) &.&2% mol(l p3 ) '.%<

chigh ) &.&<9 mol(l p3 ) '.*1

Jeri$ication has been done #sing the basic e#ation1 via a n#meric sol#tion in excelemploying the goal see0 $#nction. he same p3 val#es as derived above are $o#nd.

7t is possible to re$ine the res#lt even $#rther. he dissociation constant is also depending onthe temperat#re o$ the sol#tion.

Table 2: Disso&iation &onstant ( 1)* of &arboni& a&i! at +arious te$peratures[2].

emperat#re oC! & < 1& 1< 2& 2< '& '< >& >< <&

81".1& 2.9> '.&> '.>> '.*1 >.19 >.>< >.1 >.%& <.&> <.1' <.1%

! By transormin( the basic euation

( ) /2.

..2.

2!!

2

!2!2!

%

!

?

2!!

2

!2!

=−−−−−++

⇒=+

++

+

waawaaaawaaa

w

aaa

aaa

K K K x K K xc K c K K K K K x K x

x

x

K

K K x K x

x K K K c

4



3owever, as can be seen in able 2: issociation constant 81"! o$ carbonic acid at vario#stemperat#res [2] ., the p8a1 does not change eno#gh to in$l#ence the p3 signi$icantly.

%. &''ect o' in(oluble carbonate( 'ormation #deo(it($ on H

Formation o$ scale! deposits will in$l#ence the p3 o$ sol#tion is an indicator $or a p3 above 9+. he sol#bility o$ CaCO' as a $#nction o$ the p3 can be described by:

"!<63663332!

2

2

22

%

2

aaa K K

x

K

xS CaCOCaS ++=⇒= +−+

"t lower p3@s the sol#bility o$ the carbonate increases signi$icantly as can be seen in Fig#re ':-ol#bility o$ CaCO' as a $#nction o$ p3.

)olubilit* o' CaCO3 a( a 'unction o' H

&

1&&&

2&&&

'&&&

>&&&

<&&&

9&&&

&&&

1 2 ' > < 9H

[ C a 2 + ] # m o l " l $

Figure 3: Solubility of CaCO3 as a fun&tion of pH

h#s the absence o$ scaling in combination with relatively high Ca24 and(or 6g24 concentrations can be an indicator $or a p3 o$ the water below 9.

!. Conclu(ion

"t the conditions #nder investigation, a press#re range o$ *&+%& bar, a temperat#re range o$2&'< =C and a CO2 gas phase concentration range o$ 1.'+1. mol5 the p3 o$ the water isca. >.

,. -e'erence(

[1] ;obert C. ;eid, Kohn 6. Ara#snitL, and Mrice . Aoling, The Properties of Gases &Liquids, > ed. Moston: 6craw+3ill, 1%*.

[2] avid ;. Eide, CRC Handbook of Chemistry and Physics, 1 ed. Moca ;aton, "nn "rbor, Moston: C;C Aress, 1%%&+1%%1.

['] Ahysical and ngineering ata, Kan#ary 1%* ed. he 3ag#e: -hell 7nternationaleAetrole#m 6aatschappiN MJ, 1%*.

[>] Kohn K. Carroll and "lan . 6ather, he -ystem Carbon ioxide+Dater and the8richevs0y+8asarnovs0y #ation, Ko#rnal o$ -ol#tion Chemistry, vol. 21, pp. 9&+921, 1%%2.



[<] . den Moe$, heoretische grondslagen van de analyse in waterige oplossingen, >ed. "msterdam(Mr#ssel: lsevier, 1%.

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CO2 SoluBility