CARBCALC 5e, E. Boyle, MIT (Jan. 2005).

This spreadsheet is designed to calculate carbon system parameters given T, S, P, TotCO2, and Alkalinity inputs (boldface blue cells).

It is based on the Dickson and Millero (1987) recommended constants.

It uses the cubic [H+] simplification of the carbon system, which only applies in the range of natural seawater pH. (so it cannot be used to calculate at low and high pH values such as found in a titration).It uses the formula for the exact solution of the cubic equation to find the pH

This speadsheet is released for your convenience without any guarantees of accuracy. It is intended as a tool to get carbon system estimates, but it is not intended to be a slick professional-looking piece of software, nor is it intended to be an example of good spreadsheet programming. Many of the formulas were inherited from an old Apple II spreadsheet - so don't expect it to take advantage of modern spreadsheet features. It was devised using a Macintosh, and I don't know if everything will display properly on a PC. I have tried to get these calculations right, but I am not a professional carbonate chemist nor programmer, so bugs can always creep in. If you find a mistake, let me know and in time I will fix the problem in future versions. I am not willing to engage in extended discussions on how to use it or debates on the calculation scheme. - if it isn't obvious how to use it, then don't!

Don't modify any of the cells other than the boldface blue input cells. If you do, I cannot guarantee that the spreadsheet will continue to function properly.

You are free to redistribute this speadsheet without charge. The copyright notice below is intended to discourage attempts to sell this spreadsheet or modifications of it.

©2005 Ed Boyle, MIT

Instructions: (a) Enter values for T, S, P, Total CO2, and Alkalinity in cells B6,C6,E6,G6, and H6. Then recalculate (or set to auto-calculate). (b) The main CO2 system parameters are shown in cells B11-G11. Other properties (e.g. carbon isotope values) are estimated elsewhere.

This spreadsheet is designed to calculate carbon system parameters given T, S, P, TotCO2, and Alkalinity inputs (boldface blue cells).

It is based on the Dickson and Millero (1987) recommended constants.

It uses the cubic [H+] simplification of the carbon system, which only applies in the range of natural seawater pH. (so it cannot be used to calculate at low and high pH values such as found in a titration).It uses the formula for the exact solution of the cubic equation to find the pH

This speadsheet is released for your convenience without any guarantees of accuracy. It is intended as a tool to get carbon system estimates, but it is not intended to be a slick professional-looking piece of software, nor is it intended to be an example of good spreadsheet programming. Many of the formulas were inherited from an old Apple II spreadsheet - so don't expect it to take advantage of modern spreadsheet features. It was devised using a Macintosh, and I don't know if everything will display properly on a PC. I have tried to get these calculations right, but I am not a professional carbonate chemist nor programmer, so bugs can always creep in. If you find a mistake, let me know and in time I will fix the problem in future versions. I am not willing to engage in extended discussions on how to use it or debates on the calculation scheme.

Don't modify any of the cells other than the boldface blue input cells. If you do, I cannot guarantee that the spreadsheet will continue

The copyright notice below is intended to discourage attempts to sell this spreadsheet or modifications of it.

(a) Enter values for T, S, P, Total CO2, and Alkalinity in cells B6,C6,E6,G6, and H6. Then recalculate (or set to auto-calculate). (b) The main CO2 system parameters are shown in cells B11-G11. Other properties (e.g. carbon isotope values) are estimated elsewhere.

(a) Enter values for T, S, P, Total CO2, and Alkalinity in cells B6,C6,E6,G6, and H6. Then recalculate (or set to auto-calculate). (b) The main CO2 system parameters are shown in cells B11-G11. Other properties (e.g. carbon isotope values) are estimated elsewhere.

Page

Equations assume H+, OH-, and other weak acids are negligible compared to CO3=, HCO3-, and B(OH)4-

(mathematically, this spreadsheet only gives an answer when Alk>0 and Alk/CO2<2.2)

Sal, ppt T, deg C T, deg K D, m P, bar ( CO2, µmol/kg Alk, µeq/kg -------- -------- -------- -------- -------- ------------ -----------

34.700 27.000 300.15 0 1.0 1930 2290

pH pCO2O2(aq) CO3- CO3= Omega ------ ----- ------ ------ ----- ------

8.114 317 8.6 ### ### 6.467 calcite36 4.287 aragonite

frac. of tot CO2: 0.4% ### 13.8%

1a epsilon CO2(gas) rel. to CO2 (aq) 1.18 source: Zhang, Quay, Wilbur GCA 59:1071b epsilon CO2 (gas) rel. to HCO3- -6.97 source: Zhang, Quay, Wilbur GCA 59:1071c epsilon CO2 (gas) rel. to CO3= -5.82 source: Zhang, Quay, Wilbur GCA 59:1072 epsilon CO2(gas) rel. to CO2 (aq) -1.05 source: Vogel et al. 1970 (Z. phys. 230: 225) as computed by Mook et al. 19743 epsilon CO2 (gas) rel to HCO3- -7.70 source: Mook et al. 1974 (EPSL 22:169-176)4 epsilon CO2 (aq) rel. to HCO3- -8.75 source: Mook et al. 1974 (EPSL 22:169-176), by combining 2 and 35 epsilon CO2 (gas) rel. to CO3= -8.15 source: Lesniak and Sakai 1989 (EPSL 95:297-301)6 epsilon CO2 (gas) rel. to CaCO3 -9.31 source: Emrich et al. 1970 (EPSL 8:363-371) (but note they excluded their 20°C measurement)

Using 1a-c and 6 above: Pre-anth d13C of atm: -6.4 (280 ppmV) epsilon CO2(aq) rel to HCO3- -8.15 1990 d13C of atm: -7.8 (350 ppmV) epsilon CO3 rel to HCO3- -1.16 Glacial max d13C of atm: -6.9 to -7.1 (200 ppmV) epsilon CaCO3 rel to HCO3- 2.34

eq. d13C (rel. to tot CO2)gas CO2(aq) HCO3- CO3= CaCO3 (calcite)

-6.78 -7.95 0.20 -0.96 2.53If d13C tot CO2 = 0.4 , then:

eq. d13C (absolute)-6.38 -7.55 0.60 -0.56 2.93

ref: Basicly uses UNESCO (1987) recommendationsK1' and K2' [(T,1,S) ]from Dickson and Millero, 1987 Deep-Sea Res. 34:1733-1743using Hansson, Mehrbach, Harned and Owen pooled equations converted to hydrogen ion concentration Kb: Ref: Millero, 1979 using Hansson constant for borate Ksp: Mucci (1983) equations for solubility; with c Yand Millero (1979) expression for pressure depe cubic -5.292534E-22 #DIV/0!

setup -3.14318E-45 #DIV/0! Geochim. Cosmochim. Acta 43:651-666 ion solutions:

X37.6828641E-09 [H+] #DIV/0!8.1144768504 pH #DIV/0!0.0021883933 Carb Alk #DIV/0!0.0002669829 CO3= #DIV/0!0.0016544276 HCO3- #DIV/0!

8.5895364E-06 H2CO3 #DIV/0!0.0003174155 pCO2 #DIV/0!

101.6 B(OH)4-

Page

305.9 B(OH)3407.5 sumB

omega calcite 6.4666636817omega aragonit 4.2871828278

CO2-Alk-pCO2 table offset 10Alkalinity

offset= 317.415 2190 2200 2210 2220 223025 CO2 1800 249 241 233 225 217

1825 280 270 261 252 2431850 315 303 293 282 2721875 355 342 329 317 3061900 402 386 371 357 3441925 457 438 421 404 3881950 522 499 478 458 4401975 599 572 546 522 5002000 692 659 627 598 5712025 805 764 725 689 656

Page

Equations assume H+, OH-, and other weak acids are negligible compared to CO3=, HCO3-, and B(OH)4-

(mathematically, this spreadsheet only gives an answer when Alk>0 and Alk/CO2<2.2)

--------- --------- ----> ......... ......... ......... .......... ..lin... ...log.10pK(T,P=1,S=0) pK(T,P=1,S) K9 V9 pK(T,P,S)

Don't delete --> 6.340 5.8302 0.0007 22.053 5.83 1.48E-06 -5.830this section! 10.310 8.907 0.0028 16.443 8.91 1.24E-09 -8.907

9.220 8.594 0.0029 27.031 8.59 2.552E-09 -8.593

Don't delete --> 8.491 6.376 0.0018 34.439 6.38 4.216E-07 -6.375this section! 8.317 6.197 0.0018 31.639 6.20 6.359E-07 -6.197

13.929 13.109 ? ? 13.10902 7.78E-14 -13.109Don't delete --> ? ? 1.57 0.027061 -1.568this section!

source: Vogel et al. 1970 (Z. phys. 230: 225) as computed by Mook et al. 1974

source: Mook et al. 1974 (EPSL 22:169-176), by combining 2 and 3 source: Lesniak and Sakai 1989 (EPSL 95:297-301) source: Emrich et al. 1970 (EPSL 8:363-371) (but note they excluded their 20°C measurement)

Glacial max d13C of atm: -6.9 to -7.1 (200 ppmV)

Don't delete -->

this section!

using Hansson, Mehrbach, Harned and Owen pooled equations converted to hydrogen ion concentration Don't delete -->this section!

Don't delete -->this section!

Don't delete -->this section!

Don't delete -->this section!

Don't delete -->--------- ------------------ --------- --------- --------- --------- --------- --------- ---------

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->2240 2250 2260

210 204 197235 227 220263 254 246295 285 275331 319 308373 359 346422 405 390479 459 441546 522 500626 597 571

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......... ............. ......... ......... .........e:

K_1 2.71828 K_2 K_B

Ks_calc Ks_arag

K_wSetup solution to cubic equation:

B/CO2 Alk/CO2

sumB/CO2 Alk/CO20.2111 1.18653

### #DIV/0!-4.798E-24 A0 #DIV/0!-1.585E-15 A1 #DIV/0!2.785E-07 A2 #DIV/0!1.1865285 A3 #DIV/0!

Q-6.57E-15 #DIV/0!

--------- --------- --------- ------------- --------- ---------

a_0

avgs and typ values

Page 9

CO2 AlkGlobal Ocean Avg. (@S=34.7) 2260 2375Warm surface waters (Pre-Anth 1920 2290Cold surface waters 2140 2310

Revision 5b assumes that Adkins has correctly identified the following errors:1. Temperature dependance of epsilon HCO3-gas is 0.141 in Zhang et al. (1995) but Ed has 0.1141 in spreadsheet2. In the equation for pK1_TP1S the linear salinity dependance should be 0.0068 not 0.006683. P dependence (column Q) of K_1 and K_2 need to have negative sign and factor of ln(10) added

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June 20, 1999: change to create CarbCalc.5c

X-Sender: tmarchitto@mail.whoi.eduMime-Version: 1.0To: eaboyle@MIT.EDUFrom: tmarchitto@whoi.edu (Tom Marchitto)Subject: CaCO3 solubility calculationDate: Sat, 19 Jun 1999 16:26:49 -0400

Hi Ed,

While converting your carbonate spreadsheet to Matlab, I think I foun `small error in the Ksp(calcite) calculation (at least in the version of thespreadsheet I have). Depending on how it's corrected, it changes[CO3]sat'n(calcite) by up to a few umol/kg.

The error arises from a typo in UNESCO (1987). They give Mucci's (1983)equation as:log(Kspar/Kspcal)=0.0385+63.974/Tbut Mucci gives it as:log(Kspar/Kspcal)=-0.0385+63.974/T

In your spreadsheet, you effectively corrected this error by subtracting afudge factor of 0.1 from pKsp_cal_(t,p1,s), to force a value of 6.35 at 25Cand S=35, which was given by UNESCO as "preferred".

The correct equation (with the "-") gives a value of 6.37, same as whatMucci got, and within error of the preferred 6.35 +/-0.02. With no fudgefactor, [CO3]sat'n changes by a few umol/kg. If a new fudge factor of -0.02is used, there is less than 1 umol/kg change.

The old fudge factors for both calcite (-0.1) and aragonite (-0.01) werejustified because the calcite pKsp value was so far off (by 0.1). But withthe correct Mucci equation, I'd argue that fudge factors are not required(both pKsp values at 25C and S=35 are only off by 0.02, within error of thepreferred).

Let me know what you think when you get a chance.

Tom

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Jan. 21, 2000change to CarbCalc.5d XL

Mar 9, 1999:Yair says:While looking into the problem I noticed that your file need a minorcorrection for R. It should be 83.143 rather than 82.05 when using pressurein bars

Jan. 21, 2000: verfied that 1 bar = 0.9869 atmthis would correspond to R=83.139 for bar units (not exactly what Yair proposes, but very close)But rather than changing R, I chose to convert pressure to atm. instead.

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change to CarbCalc.5e XLadded in Revelle Factor calculation

1. Temperature dependance of epsilon HCO3-gas is 0.141 in Zhang et al. (1995) but Ed has 0.1141 in spreadsheet2. In the equation for pK1_TP1S the linear salinity dependance should be 0.0068 not 0.006683. P dependence (column Q) of K_1 and K_2 need to have negative sign and factor of ln(10) added

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this would correspond to R=83.139 for bar units (not exactly what Yair proposes, but very close)

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