CO2 and TIC calculator

Use this calculator to compute the carbon dioxide and total inorganic carbon concentration for fresh, saline and seawater using alkalinity and pH.

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	Salinity Range
	NaCl only saline water	5-45 ppK seawater	0-5 ppK fresh /seawater
Water pH				input
Temperature (°C)				input
Salinity (ppK)				input
Tot. alkalinity (mmol/L)				input
Atmos. pressure (mBar)				input

Dissolved CO2 (mg/L)				output
pCO2 (mm Hg)				output
pCO2 (µatm)				output
	Intermediate calculations
Water density (kg/L)				output
Abs. temperature (°K)				output
[H+] (mmol/L)				output
[OH-] (mmol/L)				output
KW	a	a	b	output
K0 (moles/L atm)				output
K1	c	e	g	output
K2	d	f	h	output
KB				output
Total boron (mmol/L)				output
B(OH)4- (mmol/L)				output
Carbonate alk. (mmol/L)				output
TIC (mmol/L)				output
α0				output
α1				output
α2				output
H2CO3* (mmol/L)				output
HCO3- (mmol/L)				output
CO3-- (mmol/L)				output

Reference Equations

Water density (kg/L) = (800*(1-(TEMP°C + 288.9414) / (508929.2* (TEMP°C+68.12963))*(TEMP°C-3.9863)^2)) + (0.824493 - 0.0040899*TEMP°C + 0.000076438*TEMP°C^2 -0.00000082467 *TEMP°C^3 + 0.0000000053675* TEMP°C^4) *SALINITY_PPK+ (-0.005724 + 0.0008227*TEMP°C - 0.0000016546*TEMP°C^2) *SALINITY_PPK^(3/2) + 0.00048314*SALINITY_PPK^2

Reference: McCutcheon, S.C., Martin, J.L, Barnwell, T.O. Jr. (1993). Water Quality. In: Maidment, D.R. (Editor). Handbook of Hydrology, McGraw-Hill, New York, U.S.A. (p. 11.3).

Absolute temperature (°K) = 273.15 + TEMP°C

[H+] =10^-pH

[OH-] = Kw/[H+]

Kw sea/salinewater = EXP^((148.9802 - 13847.26 /TEMP°K - 23.6521 * ln TEMP°K + ((-5.977 + 118.67/TEMP°K + 1.0495 * ln TEMP°K) * SALINITY^0.5 - 0.01615*SALINITY))

Reference: Millero, F.J., 1995. Geochim. Cosmochim. Acta 59, 661-677. eq 63.

Kw freshwater = EXP^(-4470.99/TEMP°K + 6.0875 - 0.01706*TEMP°K)

Reference: Harned, H.S., Owen, B.B. (1958). The Physical Chemistry of Electrolyte Solutions. 3rd ed. Van Nostrand Reinhold, New York, U.S.A.

K1 NaCl saline water = 10^-(35.2911 * SALINITY^0.5 + 0.8491 * SALINITY^1 - 0.32 * SALINITY^1.5 + 0.055 * SALINITY^2 - 1583.09 * SALINITY^0.5 /TEMP°K + -5.4366 * SALINITY^0.5 * ln TEMP°K + -114.3106 + 5773.67 / TEMP°K + 17.779524 * ln TEMP°K)

K2 NaCl saline water = 10^-(38.2746 * SALINITY^0.5 + 1.6057 * SALINITY^1 - 0.647 * SALINITY^1.5 + 0.113 * SALINITY^2 -1738.16 * SALINITY^0.5 / TEMP°K + -6.0346 * SALINITY^0.5 * ln TEMP°K + -83.2997 + 4821.38 / TEMP°K + 13.5962 * ln TEMP°K )

Reference for K1 & K2 NaCl saline water: Millero F., Huang F., Graham T. and Pierrot D. (2007) The dissociation of carbonic acid in NaCl solutions as a function of concentration and temperature, Geochim. Cosmochim. Acta, 71, 46-55.

NOTE: SALINITY IN UNITS OF mol/kg W for above NaCl K1 and K2.

K1 Seawater = EXP^(2.83655-(2307.1266/TEMP°K)-(1.5529413* ln TEMP°K) + ((-0.20760841-( 4.0484/TEMP°K)) *(TEMP°K^0.5)) + (0.08468345*TEMP°K)-(0.00654208*(TEMP°K^1.5)))

K2 Seawater = EXP^(-9.226508-( 3351.686/TEMP°K)-(0.2005743*(ln TEMP°K)))+((-0.106901773 - 23.9722/TEMP°K)*SALINITY^0.5) + 0.1130822*SALINITY-((0.00846934)*SALINITY^1.5))

Reference for K1 & K2 seawater: Roy, L.N., Vogel, K.M., Porter-Moore, C., Pearson, T., Good, C.E., Millero, F.J., Campbell, D.M. (1993). The dissociation constants of carbonic acid in seawater at salinities 5 to 45 and temperatures 0 to 45°C. Marine Chemistry 44:249-267, (also see errata in 1994 and 1996).

K1 Freshwater = EXP^(290.9097-14554.21/TEMP°K - 45.0575*ln TEMP°K +(-228.39774 + 9714.36839/TEMP°K + 34.485796*ln TEMP°K) *SALINITY^0.5 + (54.20871-2310.48919/TEMP°K - 8.19515*ln TEMP°K)*SALINITY^1 + (-3.969101 + 170.22169/TEMP°K + 0.603627*ln TEMP°K)*SALINITY^1.5) - 0.00258768* SALINITY^2)

K2 Freshwater = EXP^(207.6548-11843.79/TEMP°K - 33.6485*ln TEMP°K +(-167.69908+6551.35253/TEMP°K + 25.928788*ln TEMP°K)*SALINITY^0.5 + (39.75854-1566.13883/TEMP°K - 6.171951*ln TEMP°K)*SALINITY^1 + (-2.892532+116.270079/TEMP°K + 0.45788501*ln TEMP°K)*SALINITY^1.5 - 0.00613142*SALINITY^2)

Reference K1 & K2 freshwater: Millero, F.J., (1995). Thermodynamics of the carbon dioxide system in the oceans. Geochim. Cosmochim. Acta 59, 661-677.

KB = EXP^(-8966.9-2890.51*SALINITY^0.5 - 77.942*SALINITY^1 + 1.726*SALINITY^1.5 - 0.0993*SALINITY^2/ TEMP°K + 148.0248 + 137.194*SALINITY^0.5 + 1.62247*SALINITY^1 + -24.4344 - 25.085*SALINITY^0.5 - 0.2474*SALINITY^1 * ln TEMP°K + 0.053105*SALINITY^0.5* TEMP°K)

Reference: Dickson, A.G., 1990. Thermodynamics of the dissociation of boric acid in synthetic seawater from 273.15 to 318.15 K. Deep Sea Research A 37, 755-766.

NOTE: SALINITY IN UNITS OF mol/kg W for above KB equations.

Total Boron (TB, mmol/L, approximation based on salinity) = 0.000416*(SALINITY/35)*WATER_DENSITY

Reference: Millero, F.J. (1982). The thermodynamics of seawater at one atmosphere. Ocean Science and Engineering 7, 403-460.

B(OH)4- = TB*KB/([H+]+KB)

Reference: Millero, F.J. (1995). Thermodynamics of the carbon dioxide system in the oceans. Geochim. Cosmochim. Acta 59, 661-677.

Carbonate alkalinity = TOTAL_ALK - [OH-] - [B(OH)4-] + [H+]

Total inorganic carbon (TIC) = ([CARB_ALK] - [OH-] + [H+] )/ (α1 + 2*α2)

derived from: [Carb_alk] = [CO3--] + [HCO3-] + [OH-] - [H+], [HCO3-] = [TIC] * α1, [CO3--] = [TIC] * α2

α0 (proportion of TIC as H2CO3 & CO2) = (1+(K1/[H+]) + (K1*K2/[H+]^2))^-1

α1 (proportion of TIC as HCO3-) = (([H+]/K1)+1+(K2/[H+]))^-1

α2 (proportion of TIC as CO3--) = (([H+]^2/(K1*K2))+([H+]/K2)+1)^-1

Reference for α0, α1, α2: Stumm, W., Morgan, J.J. (1996). Aquatic chemistry: chemical equilibria and rates in natural waters. 3rd edition, Wiley-Interscience, New York, U.S.A. (p. 150).

K0 (Henry's solubility constant) = EXP^(-58.0931 + (90.5069*(100/TEMP°K)) + (22.294*(ln(TEMP°K/100))) + (SALINITY*(0.027766 + ((-0.025888)*(TEMP°K/100)) + ((0.0050578)*((TEMP°K/100)^2)))))

Reference: Weiss, R.F. (1974). Carbon dioxide in water and seawater: the solubility of a non-ideal gas. Marine Chemistry 3:203-215.

[H2CO3*] = [TIC]*α0 (H2CO3* represents CO2 + H2CO3, but >99% of H2CO3* is CO2)

[HCO3-] = [TIC]*α1

[CO3--] = [TIC]*α2

Dissolved CO2 (mg/L) = [ H2CO3*]*44

MW CO2=44

pCO2 (uatm) = ([H2CO3*]/K0)*1000000

pCO2 (mm Hg) = ([H2CO3*]/K0)/760