CO 2 and the carbonate system. 1/45

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1 CO 2 and the carbonate system 1/45

The Atmospheric CO 2 -Climate Connection From: http://www.google.ca/imgres?imgurl=http:/ /www.

2 The Atmospheric CO 2 -Climate Connection From: / From: Ruddiman, html#alternative 2/45

3 The Atmospheric CO 2 -Climate Connection Rising atmospheric CO 2 From: cdiac.ess-dive.lbl.gov & 3/45

4 The Atmospheric CO 2 -Climate Connection History of global surface temperature since 1880 Rising global temperature From: climate.gov 4/45

5 Greenhouse Effect Incoming solar radiation Outgoing thermal radiation Gases Reflected thermal radiation (greenhouse effect) Marine Physical Chemistry Land Ocean 5/45

6 Sources and Sinks of CO Pg Biological activity/respiration Volcanic activity Fires Cement production Metamorphism/weathering CaCO 3 + SiO 2 CaSiO 3 + CO Pg ATMOSPHERE -1.8 Pg? +1.6 Pg ~37% -2.0 Pg LAND OCEAN Pg = petagram = grams 6/45

7 Carbon reservoirs Reservoir Size (Gt C/Pg C) Atmosphere 750 Forests 610 Soils 1,580 Surface Ocean 1,020 Deep Ocean 38,100 Coal 4,000 Oil 500 Natural Gas 500 7/45

8 Carbon reservoirs Atm GasForest Oil Coal Soils Surface Ocean Deep Ocean The kinetic processes of gas exchange and transport at the air-sea interface operate on a time scale of about one year, but the exchange time with the deep ocean is on the order of a thousand years. Hence, the ocean as a whole has not equilibrated in response to the increased atmospheric PCO 2. 8/45

9 Sources and Sinks of CO 2 SOURCES Deforestation Fossil Fuel SINKS Terrestial Forests Atmosphere Oceans 9/45

10 Global Carbon Cycle STOCKS (Gt C) FLOWS (Gt C y -1 ) Fossil Fuel ATMOSPHERE Weathering Forestry LAND 639 RIVER SURFACE OCEAN SOIL DIC DIC 0.45 DOC?? Pycnocline 32 Plankton 5-27 DEEP WATERS DIC POC 7-9 POC 4.7 PIC 0.75 DOC 1198 PIC 0.15 POC 0.04 SEDIMENTS POC PIC /45

11 Weathering Reactions CO 2 dissolved in water produces carbonic acid H 2 O + CO 2 H 2 CO 3 H 2 CO 3 H + + HCO 3 H + + CaCO 3 Ca 2+ + HCO 3 H 2 O + CO 2 + CaCO 3 Ca HCO 3 10 KAlSi 3 O H 2 CO H 2 O 5 Al 2 (OH) 4 Si 2 O H 4 SiO HCO K + 11/45

Carbonate Reactions Carbon dioxide dissolved in water produces carbonic acid which, in turn, dissociates into bicarbonate and carbonate ions,

12 Carbonate Reactions Carbon dioxide dissolved in water produces carbonic acid which, in turn, dissociates into bicarbonate and carbonate ions, releasing H + to the solution. CO 2(g) CO 2(aq) (1) H 2 O + CO 2(aq) H 2 CO 3 (2) slow H 2 CO 3 H + + HCO 3 (3) fast HCO 3 H + + CO 2-3 (4) fast 12/45

Carbonic acid reaction equilibria The equilibrium constants for each of these reactions can be defined in terms of the ratio of the activity of the products to the reactants such as: K o 0 = a(h 2 CO

13 Carbonic acid reaction equilibria The equilibrium constants for each of these reactions can be defined in terms of the ratio of the activity of the products to the reactants such as: K o 0 = a(h 2 CO 3 * )/ a(h 2 O) fco 2 = [H 2 CO 3* ] γ(h 2 CO 3* )/ PCO 2 = at 25 o C ( ) From the latter equation, you can easily appreciate how an increase in PCO 2 in the atmosphere due to fossil fuel burning will lead to an uptake by the oceans K o 1 = a(hco 3 - ) a(h + )/ a(h 2 CO 3* ) = [HCO 3- ] γ(hco 3- ) a(h + )/ [H 2 CO 3* ] γ(h 2 CO 3* ) = at 25 o C (4.45 x 10-7 ) The two constants defined above are called composite constants because they are defined in terms of the activity of the sum of : H 2 CO 3 + CO 2 (sol'n) = H 2 CO 3 * (H 2 CO 3 / H 2 CO 3* = 0.003) 13/45

14 Carbonic acid reaction equilibria Finally, K o 2 = a(h+ ) a(co 3 2- )/ a(hco 3- ) = [CO 3 2- ] γ(co 3 2- ) a(h + )/ [HCO 3- ] γ(hco 3- ) = at 25 o C (4.68 x ) 14/45

15 Carbonic acid species as a function of ph (H + ) (OH - )/(H 2 O) = /45

16 Carbonic acid species as a function of ph FRACTION CO 2 HCO 3 CO ph ph 16/45

$previously, we can describe each species in terms of ph and C T, so that: C T = α 0 C T + α 1 C T + α 2 C T where α i is the relative fraction of each$ species in solution or the ionization factor or degree of protolysis, and α 0 + α 1 + α 2 = 1.

species in solution or the ionization factor or degree of protolysis, and α 0 + α 1 + α 2 = 1.

17 Carbonic acid species as a function of ph C T, DIC, TCO 2 or ΣCO 2 = [H 2 CO 3* ] + [HCO 3- ] + [CO 3 2- ] Using the equilibrium constants defined previously, we can describe each species in terms of ph and C T, so that: C T = α 0 C T + α 1 C T + α 2 C T where α i is the relative fraction of each species in solution or the ionization factor or degree of protolysis, and α 0 + α 1 + α 2 = 1. The subscript refers to the number of protons lost from the most protonated species. α 0 = 1/(1 + K 1 /[H + ] + K 1 K 2 /[H + ] 2 ) α 1 = 1/([H + ]/K K 2 /[H + ]) α 2 = 1/([H + ] 2 /K 1 K 2 + [H + ]/K 2 + 1) 17/45

Equilibrium constants K o 0 = a(h 2 CO 3 * )/ a(h 2 O) fco 2 = [H 2 CO 3* ] γ(h 2 CO 3* )/ PCO 2 = 10-1.47 (0.

18 Equilibrium constants K o 0 = a(h 2 CO 3 * )/ a(h 2 O) fco 2 = [H 2 CO 3* ] γ(h 2 CO 3* )/ PCO 2 = ( ) at 25 o C and 1 atm K o 1 = a(hco 3 - ) a(h + )/ a(h 2 CO 3* ) = [HCO 3- ] γ(hco 3- ) a(h + )/ [H 2 CO 3* ] γ(h 2 CO 3* ) = at 25 o C (4.45 x 10-7 ) K o 2 = a(co 3 2- ) a(h + )/ a(hco 3- ) = [CO 3 2- ] γ(co 3 2- ) a(h + )/ [HCO 3- ] γ(hco 3- ) = at 25 o C (4.68 x ) Under the infinite dilution convention, when the ionic strength (I = 0.5 Σ [i] Z i2 ) is close to zero (or Σ[i] 0), the ion activity coefficients of the carbonic acid species are close to 1. lim γ T (i) = 1 or lim a i = [i] I 0 I 0 18/45

Debye-Hückel Theory log γ i = AZ 2 i I 1/2 /(1 + a i BI 1/2 ) where A and B are constants that depend only on the temperature and dielectric constant of the system.

19 Debye-Hückel Theory log γ i = AZ 2 i I 1/2 /(1 + a i BI 1/2 ) where A and B are constants that depend only on the temperature and dielectric constant of the system. For water at 25 o C and 1 atm total pressure. A = x 10 6 (εt) 2/3 = mol -1/2 L 1/2 and B = x 10 8 /(εt) 1/2 = x 10 8 cm -1 mol -1/2 L 1/2 ε is the dielectric constant of water (a measure of its capacity to hold charges in solution). Pure water has the highest dielectric constant of all liquids. a i = adjustable size parameter (in angstroms or 10-8 cm) which corresponds roughly to the distance of closest approach between the centre of adjacent ions or the radius of the hydrated ion 19/45

20 Single ion activity coefficients calculated from the Debye-Hückel Equation The Debye-Hückel equation predicts that activity coefficients decrease continuously with ionic strength. The model is reasonably accurate to an ionic strength of 0.1 m. 20/45

Davies Equation For higher ionic strengths, the Debye-Hückel equation was modified by adding a term which takes into account non-coulombic interactions and the increase of γ with I.

21 Davies Equation For higher ionic strengths, the Debye-Hückel equation was modified by adding a term which takes into account non-coulombic interactions and the increase of γ with I. log γ i = AZ 2 i (I1/2 /1+BaI 1/2 ) +bi where b is a general constant ( ) or a specific constant for each individual ion i. This expression is known as the Davies equation. This equation yields reasonably accurate estimates of the individual ion activity coefficients for solutions of ionic strengths up to 0.5 m but is not suitable for seawater or solutions of higher ionic strength. 21/45

22 Ion-pairing model Mg 2+ + SO 4 2- MgSO 4 o K o (MgSO 4o ) = (MgSO 4o ) = [MgSO 4o ] γ(mgso 4o ) (Mg 2+ ) (SO 4 2- ) [Mg 2+ ] F [SO 4 2- ] F γ F (Mg 2+ ) γ F (SO 4 2- ) = K * (MgSO 4o ) γ(mgso 4o ) γ F (Mg 2+ ) γ F (SO 2-4 ) where (Mg 2+ ) = [Mg 2+ ] T γ T (Mg 2+ ) = [Mg 2+ ] F γ F (Mg 2+ ) from which γ T (Mg 2+ ) = [Mg 2+ ] F γ F (Mg 2+ ) [Mg 2+ ] T D-H The ion-pairing model assumes that short-range electrostatic interactions can be represented by the formation of ion-pairs. The ion-pairing model fails at I > 1 m because it does not take into account interactions between ions of like charge (++, --) and interactions between more than two ions (+-+, -+-). 22/45

23 Specific interaction or Pitzer model ln γ M = D.H. + M-X + M-N + M-N-X MX = M-Cl + M-SO 4 + M-HCO 3 + M-N = M-Na, M-Mg, M-Ca M-N-X = M-Na-Cl, M-Na-SO 4, /45

24 Specific interaction or Pitzer model 24/45

25 Range of application of various activity coefficient models log γm 2+ γm 2+ 25/45

26 Apparent and stoichiometric equilibrium constants K * 0 = [H 2 CO 3 * ]/PCO 2 = f(t, P, S) K 1 = [HCO 3 - ] a(h + )/ [H 2 CO 3* ] or K * 1 = [HCO 3 - ] [H + ]/ [H 2 CO 3* ] K 2 = [CO 3 2- ] a(h + )/ [HCO 3- ] or K * 2 = [CO 3 2- ] [H + ]/ [HCO 3- ] They are called apparent or stoichiometric constants because they are defined in terms of concentrations and, for K 1 and K 2, an operational system, ph. Hence, the absolute value of the first and second carbonic acid dissociation constants are a function of the definition of the operational system used to measure ph or the ph scale. 26/45

ph scales and conventions NIST (NBS)-scale defined on the infinite dilution convention lim γ T (i) = 1 or lim a i = [i] I 0 I 0 for which the apparent constants determined by Merhbach et al.

γ T (H + ) = 1 when Σ[j] = constant and [H + ] 0 [H + ]* = [H + ] F + [HSO 4- ]= [H + ] F { 1 + [SO 4 2- ] T /K(HSO 4- )} Hanson (1973) Deep-Sea Res. 20: 479-491.

27 ph scales and conventions NIST (NBS)-scale defined on the infinite dilution convention lim γ T (i) = 1 or lim a i = [i] I 0 I 0 for which the apparent constants determined by Merhbach et al. (1973) L&O 18: Total hydrogen ion concentration (Hansson TRIS bufferscale) defined on the constant ionic medium convention. γ T (H + ) = 1 when Σ[j] = constant and [H + ] 0 [H + ]* = [H + ] F + [HSO 4- ]= [H + ] F { 1 + [SO 4 2- ] T /K(HSO 4- )} Hanson (1973) Deep-Sea Res. 20: The Seawater scale defined on the constant ionic medium convention. [H + ] sws = [H + ] F + [HSO 4- ] + [HF ] = [H + ] F { 1 + [SO 4 2- ] T /K(HSO 4- ) + [F - ] T /K(HF )} Dickson and Millero (1987) Deep-Sea Res. 34: The free hydrogen ion concentration scale defined on the constant ionic medium convention. [H + ] F = [H + ] T / (1 + [HSO 4- ] + [HF ]) = [H + ] T / { 1 + [SO 4 2- ] T /K(HSO 4- ) + [F - ] T /K(HF )} Khoo et al. (1977) Analytical Chemistry 49: /45

28 Interaction of water with H + (H 3 O + ) H + + H 2 O H 3 O + ; ΔG = 0 or H + = H 3 O + = H 9 O /45

ph measurements in seawater Sorensen (1909) proposed an electrochemical procedure for the determination of the hydrogen ion concentration which he dubbed the hydrogen ion exponent : p S H = -log [H +

29 ph measurements in seawater Sorensen (1909) proposed an electrochemical procedure for the determination of the hydrogen ion concentration which he dubbed the hydrogen ion exponent : p S H = -log [H + ] where [H + ] = α [HCl] and α is the degree of ionization of HCl in NaCl-HCl solutions The electrochemical potential (EMF) between solutions of various H + concentrations was measured with a set of electrodes. Pt: H 2 (g: 1 atm, sol n x) salt bridge Pt: H 2 (g: 1 atm, 1N HCl) Pt: H 2 (g: 1 atm, sol n x) salt bridge 0.1N Hg 2 Cl 2 /Hg (calomel) By definition, the potential at the Pt: H 2 (g: 1 atm, 1 N HCl) electrode is null: 2H + + 2é H 2 (g) ΔG o = 0, E ho = 0 volt E h (calomel) = volt 29/45

ph measurements in seawater As modern formulations of thermodynamic concepts and theories of

cell is related directly to the activity rather than concentrations.

Eventually, it was recognized that the activity of a single ion plays no real part in the EMF of a

30 ph measurements in seawater As modern formulations of thermodynamic concepts and theories of electrolyte solutions were developed, it was shown that the electromotive force (EMF) of a galvanic cell is related directly to the activity rather than concentrations. Hence, in 1924, Sorensen and Linderstrom-Lang proposed a new acidity unit: p(h + ) = - log (H + ) Eventually, it was recognized that the activity of a single ion plays no real part in the EMF of a galvanic cell Nevertheless, there remained a need to have a reproducible ph scale based on a convenient method to characterize acid-base reactions. 30/45

Reference electrode: H + /H 2, Hg 2 Cl 2 /Hg or AgCl/Ag

31 Operational definition of ph Reference electrode Concentrated KCl sol n Test solution electrode reversible to hydrogen ion Reference electrode: H + /H 2, Hg 2 Cl 2 /Hg or AgCl/Ag Hydrogen ion reversible electrode: H + /H 2, glass electrode 31/45

32 Typical commercial reference & glass electrodes The potential of the reference electrode is set by the redox potential of the redox couple under standard state. The glass electrode membrane works as a cation exchanger with a high specificity for H +. 32/45

33 Combination ph glass electrode 33/45

Practical definition of ph Ag/AgCl test solution electrode reversible to hydrogen ion In the absence of a salt bride (liquid junction), the reaction for the cell can be written as: 0.

34 Practical definition of ph Ag/AgCl test solution electrode reversible to hydrogen ion In the absence of a salt bride (liquid junction), the reaction for the cell can be written as: 0.5H 2 (g) + AgCl(s) H + + Ag(s) + Cl - for which: K 0 = (H + ) (Ag(s)) (Cl - ) (H + ) (Cl - ) at PH 2 (g) = 1 atm P 0.5 H 2 (g) (AgCl(s)) V Ag electrode Remember that: E o h = - ΔG /F = ln K o eq * RTF-1 E = E 0 + RT/F ln (H + ) (Cl - ) E = E 0 + ln 10 RT/F log (H + ) (Cl - ) -log (H + ) = ph = (E 0 E)/(ln 10 RT/F) + log (Cl - ) AgCl ph = (E 0 E)/(ln 10 RT/F) when (Cl - ) = 1 34/45

35 Conventional and operational definitions of ph The use of a glass electrode and salt bridge adds to the problem. Ag/AgCl KCl sol n test solution electrode reversible to hydrogen ion E = E 0 + RT/F ln (H + ) (Cl - ) + E j where E j is the liquid junction potential between the two half-cells. This potential is generated by the difference in composition between the solutions on both sides of the salt bridge. E = {E 0 + RT/F ln (Cl - ) + E j } + RT/F ln (H + ) = E 0 + RT/F ln (H + ) = conventional definition where the value of E 0 and (H + ) depend on the value assigned to each other. In the operational definition, ph of a solution X is related to the ph assigned to a standard (S): ph(x) = ph(s) + [EX - ES/(RT ln 10/F)] 35/45

Operational definition of ph In the operational definition, ph of a solution X is related to the ph assigned to a standard (S): ph(x) = ph(s) + [EX - ES/(RT ln 10/F)] But more formally, ph(x) = ph(s)

36 Operational definition of ph In the operational definition, ph of a solution X is related to the ph assigned to a standard (S): ph(x) = ph(s) + [EX - ES/(RT ln 10/F)] But more formally, ph(x) = ph(s) + [EX - ES/(RT ln 10/F)] + [E o X - E 0 S/(RT ln 10/F)] According to the conventional definition, ph(x) is equivalent to the activity of the proton in solution if: a) E o X - E 0 S = 0 b) ph(s) is defined as log(h + ) S where (H + ) S has been conventionally assigned. If (H + ) S is defined under the infinite dilution convention, the ph measured in a high ionic strength solution, like seawater, is not a measure of the H + concentration since γ(h + ) < 1, nor is it a true representation of the proton activity since E o X - E 0 S 0. 36/45

37 NIST-traceable buffer solutions (infinite dilution convention) but the use of apparent constants has two additional drawbacks: 1) The value of E o X - E 0 S is dependent on the electrode(s) 2) The electrodes require long equilibration times because of ionic shock 37/45

ph scales defined on the constant ionic medium convention Total hydrogen ion concentration (Ingemar Hansson, 1973: TRIS buffer in artificial seawater) defined on the constant ionic medium convention.

38 ph scales defined on the constant ionic medium convention Total hydrogen ion concentration (Ingemar Hansson, 1973: TRIS buffer in artificial seawater) defined on the constant ionic medium convention. γ T (H + ) = 1 when Σ[j] = constant and [H + ] 0 [H + ]* = [H + ] F + [HSO 4- ]= [H + ] F { 1 + [SO 4 2- ] T /K(HSO 4- )} Hence, ph = -log [H + ] since γ T (H + ) = 1, ionic shock is minimized and E o X - E 0 S 0. Nevertheless, buffer solutions of various salinities must be prepared and used to calibrate the electrodes if samples display large salinity variations. The Seawater scale defined on the constant medium convention. [H + ] sws = [H + ] F + [HSO 4- ] + [HF ] = [H + ] F { 1 + [SO 4 2- ] T /K(HSO 4- ) + [F - ] T /K(HF )} The free hydrogen ion concentration scale defined on the constant medium convention. [H + ] F = [H + ] T / (1 + [HSO 4- ] + [HF ]) = [H + ] T / { 1 + [SO 4 2- ] T /K(HSO 4- ) + [F - ] T /K(HF )} 38/45

39 The Hansson or seawater ph scale TRIS = tris-(hydroxymethyl)-aminomethane 39/45

40 The seawater ph scale 40/45

41 Spectrophotometric ph measurements 41/45

Spectrophotometric ph measurements The acid dissociation of a color indicator is characterized by the following reaction: HL H + + L - (ex: for phenol red, HL yellow L - red + H + ) for which: K* =

42 Spectrophotometric ph measurements The acid dissociation of a color indicator is characterized by the following reaction: HL H + + L - (ex: for phenol red, HL yellow L - red + H + ) for which: K* = [H + ] [L - ]/[HL] and, hence [H + ] = ([HL]/[L - ]) K* or ph = pk* + log ([L - ]/[HL]) The ratio, [L - ]/[HL], can be determined colorimetrically by measuring the optical absorbance at two wavelengths, typically the wavelengths of maximum specific absorbance of the protonated and deprotonated indicator. The principle is based on the application of Beer s law: λa = λ ε b C Where: λ A = absorbance at wavelength λ λε = molar absorptivity b = path length of the cell C = molar concentration of the indicator 42/45

43 Spectrophotometric ph measurements We know the total amount of indicator added to a sample (C T = [HL] + [L - ]) λat = λ AHL + λ AL - = λ εhl b [HL] + λ εl - b [L - ] λat = λ εhl [HL] + λ εl - [L - ] = λ εhl [HL] + λ εl - [HL] [H + ] -1 K* = λ εhl + λ εl - [H + ] -1 K* C T b [HL] + [L - ] [HL] + [HL] [H + ] -1 K* 1 + [H + ] -1 K* λεhl and λ εl - are measured from known concentrations of the indicator at high and low ph where the indicator is either fully protonated or fully deprotonated. If the absorbance measurements are made at two wavelengths: λ1 and λ2 2A/ 1 A = ( 2 εhl + 2 εl - [H + ] -1 K*)/( 1 εhl + 1 εl - [H + ] -1 K*) = R R 1 εhl + + R 1 εl - [H + ] -1 K* = 2 εhl + 2 εl - [H + ] -1 K* Dividing by 1 εhl, R ( 1 εhl/ 1 εhl) + R ( 1 εl - / 1 εhl) [H + ] -1 K* = ( 2 εhl/ 1 εhl) + ( 2 εl - / 1 εhl) [H + ] -1 K* R - ( 2 εhl/ 1 εhl) = [( 2 εl - / 1 εhl) R ( 1 εl - / 1 εhl)] [H + ] -1 K* 43/45

44 Spectrophotometric ph measurements R - ( 2 εhl/ 1 εhl) = [( 2 εl - / 1 εhl) R ( 1 εl - / 1 εhl)] [H + ] -1 K* R - ( 2 εhl/ 1 εhl) = [H + ] -1 K* [( 2 εl - / 1 εhl) R ( 1 εl - / 1 εhl)] log R - ( 2 εhl/ 1 εhl) = ph - pk* [( 2 εl - / 1 εhl) R ( 1 εl - / 1 εhl)] ph = pk* + log R - ( 2 εhl/ 1 εhl) = [( 2 εl - / 1 εhl) R ( 1 εl - / 1 εhl)] The values of K* and λ ε must also be determined at various T and S but the ratios of the molar absorptivities ( 1 εl - / 1 εhl) are not very sensitive to T. The method is capable of ± precision w/o calibration or w/calibration. 44/45

45 Choice of color indicators 45/45

ph of natural waters

ph of natural waters Na 2 CO 3 10H 2 O (natron) 2 Na + + CO 3 + 10H 2 O 4FeS 2 + 15O 2 + 14H 2 O 4 Fe(OH) 3 + 16H + + 8SO 4 4NaAlSi 3 O 8 + 11H 2 O 4Na + + 4OH - + Al 4 Si 4 O 10 (OH) 8 + 8Si(OH) 4 In