Inorganic carbon in the ocean: Basics

IntroductionEquilibrium and Measurement

Biogeochemical Processes and the CO2 system-- organic matter formation / destruction-- CaCO3 precipitation / dissolution

Why study carbonate in the ocean?(stating the obvious)

Life on earth is carbon-based!

pH is a key master variable for many processes - and carbonateequilibria play an important role in determining ocean pH

HCO3- is the 3rd most concentrated anion in the ocean

The marine carbon cycle is a key factor in determining the fate ofanthropogenic CO2

…

And if the pursuit of knowledge isn’t enough:MC&G students: I guarantee you’ll have a carbonate question

on your general exam!

Carbon cycling in the ocean(an overview)

Land

Atmosphere

Ocean

CO2

CO2 + H2O ⇔ H2CO3

H2CO3* ⇔ H+ + HCO3

−

HCO3− ⇔ H+ + CO3

2−

CO2 ⇒ Corg

Ca2+ + CO32− ⇒ CaCO3(s)

Corg ⇒ CO2

CaCO3(s) ⇒ Ca2+ + CO32−

Corg ⇒ CO2

CaCO3(s) ⇒ Ca2+ + CO32−

sediments

HCO3-

Earth surface carbon cycle - Time Scales

Increasing…

Surface ocean~ atmosphere

Deep ocean :large reservoir!

Largest reservoir:long time scales

Sundquist, 1993

Atmosphere420 18 ka590 A.D. 1750750 A.D. 1990

1

10

100

1,000

10,000

100,000

1,000,000

Foss

il fu

els 4

,000

Terrestrialbiosphere

560

Active Soils1,100

Old Soils500

Ocean Surface 900

Deep Ocean36,400

Reactive Marine Sediments3,000

90,000,000Earth's Crust

6 1 to 3 60 2 to 3 70

0.6 0.4

0.2 0.2

Tim

e re

quire

d to

affe

ct a

tmos

pher

e (y

ears

)

Earth Surface Carbon Cycle - Time Scales

Figure by MIT OCW.

Dissolved Carbonate Equilibria

ΣCO2 = H2CO3*[ ]+ HCO3

−[ ]+ CO32−[ ]

K1 =H+[ ]HCO3

−[ ]H2CO3

*[ ]

K2 =H+[ ]CO3

2−[ ]HCO3

−[ ]

K1, K2 known…

-- 3 equations, 5 unknowns…

Specify (or measure) 2 things - ∑CO2, pH … to get :

2.0x10-3

1.5

1.0

0.5

0.0

Conce

ntr

atio

n (

mole

s/kg

)

1210864pH = - log(H

+)

HCO3-

CO32-H2CO3*

Seawater pH

10-8

10-7

10-6

10-5

10-4

10-3

10-2

Conce

ntr

atio

n (

mole

s/kg

)

1210864pH = - log(H

+)

HCO3-

CO32-H2CO3*

Seawater pH

K1 =H+[ ]HCO3

−[ ]H2CO3

*[ ] ----> log K1{ }= log H+{ }+ logHCO3

−[ ]H2CO3

*[ ]⎧ ⎨ ⎪

⎩ ⎪

⎫ ⎬ ⎪

⎭ ⎪

Speciation as ƒ(pH) on log-log plot:A “Bjerrum” Plot

Are ∑CO2 and pH an ideal pair to measure?Sometimes, but note:

Water mass ApHA

∑CO2A

Water mass BpHB

∑CO2B

50 : 50 mix of A and B

∑CO2(mix)=0.5*∑CO2(A) + 0.5*∑CO2(B)

** Not true for pH !! **

How about a quantity that is related to the major ion composition?

The charge balance in seawater:

An apparent excess of positive charge of ~ 2.2 mmol / kg

What are the missing anions?

Cations

Na+

K+

Mg2+

Sr2+

Ca2+

[ci] [ci][qi] [qi]

Total

467.8

53.3

10.3

9.9

0.1

467.8

106.5

20.6

9.9

0.2

605.0

Anions

Cl-

F-

Br-SO4

2-

Total

545.5 545.5

28.2

0.8

0.1

56.4

0.8

0.1

602.8

Concentrations, [ci] (mmol kg-1), and charge concentrations, [qi] = zi [ci] (mmol kg-1),of conservative ions in seawater at S = 35.

.

. .

..

Figure by MIT OCW.

The Alkalinity

The missing anions: HCO3-, CO3

2-, B(OH)4-

The conjugate bases of the weak acids,H2CO3 and B(OH)3

HA ⇒ H+ + A−

acid conjugatebase

Alkalinity (mol/kg) = the amount of strong acid that must be added to a1 kg (sea)water sample to make its pH equal to that of the second equivalence point of the dissolved CO2 system, pH = 4.3

Total Alkalinity: seawater, pH = 8

“Practical Alkalinity”:

PA = HCO3

−⎡ ⎣ ⎢

⎤ ⎦ ⎥ + 2 CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥ + B OH( )4

−⎡

⎣ ⎢

⎤

⎦ ⎥ + OH−⎡

⎣ ⎢ ⎤ ⎦ ⎥ − H+⎡

⎣ ⎢ ⎤⎦⎥

20001770

1600

1200

800

400

0

Con

trib

utio

n to

PA

(µm

ol k

g-1 )

[HCO3]-

Σ = PA = 2300 µmol kg-1

438

866 -0.01

2[CO3 ]-2 [B(OH)4]-

[OH ]- -[H+]

Figure by MIT OCW.

What does the definition mean?

10-14

10

-12

10

-10

10

-8

10

-6

10

-4

Conce

ntr

atio

n (

mol/

kg)

12108642pH

H2CO3 HCO3-

CO32-

B(OH)3B(OH)4

-

Bjerrum Plotfor seawater

pH = 8

The titration of seawater with a strong acid (HCl)

8

7

6

5

4

3

pH

1.00.80.60.40.20.0Va (ml HCl added)

A titration of seawaterwith HCl

Start

8

7

6

5

4

3

pH

0.80.60.40.20.0Va (ml HCl added)

pH

dpH / dVa

titration endpoint atinflection of pH vs Va curve

10-14

10

-12

10-10

10

-8

10-6

10-4

Conce

ntr

atio

n (

mol/

kg)

12108642pH

H2CO3 HCO3-

CO32-

B(OH)3B(OH)4

-

Bjerrum Plotfor seawater

10-12

10

-10

10

-8

10

-6

10

-4

10

-2

Conce

ntr

atio

n (

mol/

l)

12108642pH

2*[CO32-] + [HCO3

-] + [B(OH)4-] + [OH-]

H+

The H+ at which

alkalinity --> 0

At the titration endpoint,

H+[ ]= 2 CO32−[ ]+ HCO3

−[ ]+ B OH( )4−[ ]+ OH−[ ]

That is, the endpointIs the point at whichAlk = 0

So: the moles of acidadded to reach theendpoint = Alk

Concentrations during the titration:

TA = HCO3

−⎡ ⎣ ⎢

⎤ ⎦ ⎥ + 2 CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥ + B OH( )4

−⎡

⎣ ⎢

⎤

⎦ ⎥ + OH−⎡

⎣ ⎢ ⎤ ⎦ ⎥ − H+⎡

⎣ ⎢ ⎤⎦⎥

Alkalinity: A precise definitionDickson, 1981 ; 19994

“The total alkalinity of a natural water is thus defined as the number of moles of hydrogen ionequivalent to the excess of proton acceptors (bases formed from weak acids with a dissociation constant K <= 10-4.5 at 25°C and zero ionic strength) over proton donors (acidswith K > 10-4.5) in one kilogram of sample.”

Remember:

(1) predominant speciesat pH = 4.5 does not contribute to Alkalinity

(2) How do you estimate pK for an acid from this diagram?

-1

-1.5

-2

-3

-4

-4

-5

-6-6

-7

-8

-2.5

-3.5

-4.5

-5.5

-6.5

-7.5

2 4 6 8 10 12

H+

SO42-

CO2

NH3

B(OH)3

2-CO3

2-HPO43-PO4

OH-

F-HF

pH

2 4 6 8 10 12pH

-HCO3

-HSO4B(OH)4

-

H3SiO4-

H2PO4-

H3PO4

H4SiO4

NH4+

Log

[con

cent

ratio

n (m

ol k

g-1)]

Log

[con

cent

ratio

n (m

ol k

g-1)]

Figure by MIT OCW.

Alkalinity

So we have:Carbonate Alkalinity: CA = [HCO3

-] + 2[CO32-]

“Water Alkalinity” = [OH-] - [H+]

“Borate Alkalinity” = [B(OH)4-]

For most applications, can use:

Alk = [HCO3-] + 2[CO3

2-] + [OH-] - [H+] + [B(OH)4-]

But in some applications, you need to add minor contributors, such as

NH3, PO43-, HPO4

2-, H3SiO4-, HS- , …

•Remember, when you titrate a seawater sample to the 2nd CO2 endpoint,The result is “Titration Alkalinity”, which includes all conjugate bases of weakAcids in the sample. The approximation in the Alk expression above is theNeglect of the contribution of minor constituents to the result.

Measurements: Summary

∑CO2

(i) Titration + curve fitting(ii) Acidify ; strip CO2 ; Measure CO2 by gas chromatography,Coulometry, IR analyzer

Calibration: reference seawater (Dickson)

± 2 µmol/kg

Alkalinity (i) Titration + curve fitting(ii) Gran titration

Calibration: reference seawater (Dickson)

± 2 µmol/kg

pH (i) Electrochemical measurement(ii) pH-sensitive dyes

Calibration: buffers for seawater

±0.002 pH units

The “more-than-I-ever-wanted-to-know” section :pH scales

(1) Laboratory chemistry: the NBS pH scale

pH = − logaH + ** Defined relative to low-ionic strength buffers --abandoned for measurements in seawater

(2) Seawater: An analysis of “[H+]” in seawater yields[H+]free + [HSO4

-] + [HF]

[HF] is small; in order to determine [H+]free, need to know K for HSO4

- dissociation WELL.

“They” have decided it is better to define a new pH scale:

The “Total pH scale” :

HT+ = H +⎡

⎣ ⎢ ⎤ ⎦ ⎥ free

+ HSO4−⎡

⎣ ⎢ ⎤ ⎦ ⎥

Or the “seawater pH scale” :

HT+ = H +⎡

⎣ ⎢ ⎤ ⎦ ⎥ free

+ HSO4−⎡

⎣ ⎢ ⎤ ⎦ ⎥ + HF[ ]

pH scales, cont.

So that:

(1) pH measurements are reported on the pHT scale(2) equilibrium constants are reported on the pHT scale

Can convert between the scales with KHSO4 and KHF

**The difference between pHsws and pHT is ~ 0.01 unit ~ 2% at pH 8The difference between pHNBS and pHT is ~ 0.1 unit ~ 20% at pH 8

The precision of good pH measurements is ~ 0.002 pH units

On equilibrium constantsfor calculations in seawater

Consider the reaction: HCO3− ⇔ H + +CO3

2−

In an “ ideal” solution: K =H +⎡

⎣ ⎢ ⎤ ⎦ ⎥ CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥

HCO3−⎡

⎣ ⎢ ⎤ ⎦ ⎥

In an “ideal” solution, all concentrations --> 0, so there are no ion-ion or ion-solvent interactions.

In a real solution, these interactions are important, so…

On equilibrium constantsfor calculations in seawater

Consider the reaction: HCO3− ⇔ H + +CO3

2−

In an “ ideal” solution: K =H +⎡

⎣ ⎢ ⎤ ⎦ ⎥ CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥

HCO3−⎡

⎣ ⎢ ⎤ ⎦ ⎥

In an “ideal” solution, all concentrations --> 0, so there are no ion-ion or ion-solvent interactions.

In a real solution: K =γ H + γCO3

2− H +⎡ ⎣ ⎢

⎤ ⎦ ⎥ CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥

γ HCO3− HCO3

−[ ]

The γ are “activity coefficients”, and are generally <1 forions in solution because of electrostatic interactions between ions and between and ions and solvent .In addition, some ions (esp. CO3

2-

) form complexes with other ions in seawater.

Equilibrium constants for calculations in seawater

For a solution with the ionic strength of seawater (I = ∑ci zi2 ~ 0.7), it is difficult to

calculate the γ values. Therefore:“Constant ionic medium” equilibrium constants are used. They are:

-- measured in solutions with the same proportions of major ions as seawater

-- measured as functions of T and S-- pressure dependence is calculated from thermodynamic data

So:

K '=H +⎡

⎣ ⎢ ⎤ ⎦ ⎥ T

CO32−⎡

⎣ ⎢ ⎤ ⎦ ⎥ T

HCO3−⎡

⎣ ⎢ ⎤ ⎦ ⎥ T

The “T” denote “total” concentrations, including complexes…And remember, for H+, the “T” denotes the “total”pH scale.

These “seawater” constants areavailable from the literature as ƒ(T,S,P)

Working with the carbonate system in seawater

ΣCO2 = H2CO3*⎡

⎣ ⎢ ⎤ ⎦ ⎥ + HCO3

−⎡ ⎣ ⎢

⎤ ⎦ ⎥ + CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥

Alk = HCO3−⎡

⎣ ⎢ ⎤ ⎦ ⎥ + 2 CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥ + B OH( )4

−⎡

⎣ ⎢

⎤

⎦ ⎥ + OH−⎡

⎣ ⎢ ⎤ ⎦ ⎥ − H+⎡

⎣ ⎢ ⎤ ⎦ ⎥ ± minor components

TB = B OH( )3[ ]+ B OH( )4−⎡

⎣ ⎢

⎤

⎦ ⎥ = cons tant × Salinity

K1 =H+⎡

⎣ ⎢ ⎤ ⎦ ⎥ HCO3

−⎡ ⎣ ⎢

⎤ ⎦ ⎥

H2CO3*⎡

⎣ ⎢ ⎤ ⎦ ⎥

K2 =H+⎡

⎣ ⎢ ⎤ ⎦ ⎥ CO3

2−⎡ ⎣ ⎢

⎤ ⎦ ⎥

HCO3−⎡

⎣ ⎢ ⎤ ⎦ ⎥

KB =H+⎡

⎣ ⎢ ⎤ ⎦ ⎥ B OH( )4

−⎡

⎣ ⎢

⎤

⎦ ⎥

B OH( )3[ ] KW = H+⎡

⎣ ⎢ ⎤ ⎦ ⎥ OH−⎡ ⎣ ⎢

⎤ ⎦ ⎥

Measure ∑CO2, Alk, S ==>7 equations in 7 unknowns

==> you can solve for speciation!

Useful approximations for back-of-the-envelopecalculations

At seawater pH,

∑CO2 ~ [HCO3-] + [CO3

2-]

Alk ~ [HCO3-] + 2 [CO3

2-]

And

[CO32-] ~ Alk - ∑CO2

10-14

10

-12

10

-10

10

-8

10

-6

10

-4

Conce

ntr

atio

n (

mol/

kg)

12108642pH

H2CO3 HCO3-

CO32-

B(OH)3B(OH)4

-

Bjerrum Plotfor seawater

pH = 8

The effect of biogeochemical processes on ∑CO2 and Alk

(1) The incorporation of CO2 into organic matter (I.e., production of o.m.)

CO2 --> “Corg” + O2

∆∑CO2 = -1∆Alk = 0

… and a small (usually negligible) increase in Alk due to NO3- assimilation, ∆Alk = (16/106))* mol Corg formed

(2) The precipitation of CaCO3

Ca2+ + CO32- --> CaCO3

∆∑CO2 = -1∆Alk = -2

How do these processes affect the ability of the ocean to take up CO2 from the atmosphere? Taking into account Henry’s law relating [CO2] in the water to the PCO2 in equilibrium withthe water,

CO2[ ]= KH PCO2System approaches equilibrium afterPerturbation: lower ocean [CO2] -->ocean absorbs CO2

Contours of [CO2] vs. Alk and ∑CO2

2450

2400

2350

2300

2250

Tot

al A

lkal

inity

230022502200215021002050TCO2

90

80 70

60

50

50

40

30

30 20

20

20

10

form Corg

form CaCO3

o.m. formation:decrease [CO2]

CaCO3 pptn:increase [CO2]

Biogeochemical processes and the carbonate system

How do decomposition and dissolution processes affect the carbonate system?

(3) Organic matter dissolution… reverses (1),Corg + O2 --> CO2 + …

∆∑CO2 = +1∆Alk = 0

(and, as before, there’s a small drop in Alk due to NH3 oxidation to NO3-)

(4) CaCO3 dissolution… reverses (2),CaCO3 --> Ca2+ + CO3

2-

∆∑CO2 = +1∆Alk = + 2

How do these processes affect the [CO32-] of seawater as it “ages” during its transit through the

deep sea?

Contours of [CO32-]

2450

2400

2350

2300

2250

Tot

al A

lkal

inity

230022502200215021002050TCO2

280 260

240

220

200 180

160

140 120

120 100

100

80

80

60

40

Contours of [CO32-]

Dissolve CaCO3

oxidize Corg

Oxidize o.m.:decrease [CO3

2-]

Dissolve CaCO3:increase [CO3

2-]

Question: what can you use this contour plot for if you have actual data?

0

12

3

45

6

7

DEP

TH (k

M)

Geosecs North Atlantic North of Equator

1.9 2.0 2.1 2.2 2.3 2.4

TCO2 (10-3 M/kG)

0

1

2

3

4

5

672.20 2.25 2.30 2.35 2.40 2.45 2.50

Talk (10-3 EO/KG)

DEP

TH (k

M)

Geosecs North Atlantic North of Equator

0

1

23

4

5

6

7

DEP

TH (k

M)

Geosecs North Atlantic North of Equator

1000 200 300CO3= (10-6 M/kG)

0

1

2

3

4

5

6

7

DEP

TH (k

M)

Geosecs North Pacific North of Equator

1000 200 300

CO3= (10-6 M/kG)

0

1

2

3

4

5

6

7

DEP

TH (k

M)

Geosecs North Pacific North of Equator

2.32.22.12.01.9 2.4

TCO2 (10-3 M/kG)

0

1

2

3

4

5

6

7

DEP

TH (k

M)

Geosecs North Pacific North of Equator

2.20 2.25 2.30 2.35 2.40 2.45 2.50

Talk (10-3 EO/kG)

OBSERVATION

NORTH ATLANTIC NORTH PACIFIC

Alk

TCO2

CO32-

Figure by MIT OCW.

Using data and theory to calculate relative ratesof organic matter oxidation and carbonate dissolution

see Broecker and Peng, Tracers in the Sea

North Indian andPacific Bottom Waters

1 Mole CaCO3

1 Mole ORG C

1 Mole CaCO3

4 Moles ORG C

15∆ALK∆ΣCO2

= =12

12 105

2 - .93

15∆ALK∆ΣCO2

∆ΣCO2N (µmol/kg)

ALK

N (µ

eq/k

g)

= =15

45 105x 2- .29

Antarctic SurfaceWater

Temperate SurfaceWater

Antarctic DeepWaters

North Atlantic DeepWater (2.5 oC)

x

2500

2450

2350

22501900 2000 2100 2200 2300 2400 2500

2400

2300

DeepWater

Surface Water

WSBWCPDWNIBWNPBWNADW

ANTARCTICS.INDIANS.PACIFICN.PACIFICS.ATLANTICN.ATLANTIC

Figure by MIT OCW.

And…

We’ve shown how biogeochemical processes affect ∑CO2 and Alk in the ocean…We’ve started to show how distributions of ∑CO2 and Alk can be usedTo learn about biogeochemical processes…

We’ve not discussed the biological and chemical processes that control

formation and decomposition of organic matter

formation and dissolution of CaCO3

Those discussions will follow…