Table 6-2: Thermodynamic and Kinetic Constants

Table 6-2: Thermodynamic and kinetic constants –formulae and references

Quantity

Units

Name

Formula

Constants

Reference

Solubilities

CO₂

mol kg^-1atm^-1

k₀

exp [A / t_k +B+Cln (t_k /100) +s (D +Et_k +Ft_k²)]

A 9345.17, B-60.2409, C 23.3585,
D 0.023517, E -2.3656e-4, F 4.7036e-7

Weiss 1974

O₂

exp[A + B / t_k + C ln (t_k/100) +s (D + E t_k +F t_k²) ] * p / (R * 273 * 1035)

A -58.3877, B 85.8079, C 23.8439,
D -0.034892, E 1.5568e-4, F -1.9387e-7

Weiss 1970

SF₆

exp[A +B / t_k +C ln (t_k) +D s ] * p / (R *273 *1035)

A -520.606, B 25060, C 75.701, D -0.0117

Wanninkhof 1991

CO₂

dimensionless

a

k₀ R t_k (1 / 103.5) (see Section 4.3)

R 8.3145

Acid Dissociation Constants

carbonic 1^st

mol kg^-1

k₁

exp [A / t_k + B + C ln (t_k) + (D / t_k + E) s^0.5 + F s + G s^1.5 + ln (1-0.001005 s)]

A -2307.1366, B 2.83655, C -1.5529413,
D -4.0484, E -0.20760841,

F 0.08468345, G -0.00654208

Roy 1993

carbonic 2^nd

k₂

exp [A / t_k + B + C ln (t_k) + (D / t_k + E) s^0.5 + F s + G s^1.5 + ln (1-0.001005 s)]

A -3351.6106, B -9.226508, C -0.2005743, D -23.9722, E -0.106901773,

F 0.1130822, G -0.00846934

water

k_w

exp [A / t_k +B +C ln (t_k) + (D / t_k +E +F ln (t_k)) s^0.5 + G s]

A -13847.26, B 148.96502, C -23.6521,
D 118.67, E -5.977, F 1.0495, G -0.01615

Millero 1995

boric

kb

exp [(A + B s^0.5 +C s + D s^1.5 +E s²) / t_k + F + G s^0.5+ H s + (I + J s^0.5 + K s) ln (t_k) + L s^0.5t_k]

A -8966.9, B -2890.53, C -77.942, D 1.728, E -0.0996, F 148.0248, G 137.1942,

H 1.62142, I -24.4344, J -25.085,
K -0.2474, L 0.053105

Dickson 1990

phosphoric 1^st

kp₁

exp [A/t_k +B +C ln(t_k) +(D/t_k +E) s^0.5 +( F/t_k +G) s ]

A -4576.752, B 115.525, C -18.453,
D -106.736, E 0.69171, F -0.65643,
G -0.01844

Millero 1995

phosphoric 2^nd

kp₂

exp [A/t_k +B +C ln(t_k) +(D/t_k +E) s^0.5 +( F/t_k +G) s ]

A -8814.715, B 172.0883, C -27.927,
D -160.340, E 1.3566, F 0.37335,
G -0.05778

phosphoric 3^rd

kp₃

exp [A/t_k +B +(C/t_k +D) s^0.5 + ( E/t_k +F) s ]

A -3070.75, B -18.141, C 17.27039,
D 2.81197, E -44.99486, F -0.09984

Reaction rates

CO₂ +H₂O

mol kg^-1 s^-1

kCO₂

exp [A + B/t_k + C ln (t_k)]

A 1246.98, B -61900, C -183

Johnson 1982

CO₂ +OH^-
(* K_w)

s^-1

k_OHK_w

exp [A +B s^0.5+ C / t_k + D ln (t_k)]

A -930.13, B 1.1e-7, C 3.1e4, D 140.9

Schmidt numbers

CO₂

sc

A + B t +C t² + D t³

A 2073.1, B -125.62, C 3.6276, D 0.043219 (for S=35 only)

Wanninkhof 1992

O₂

A + B t + C t² + D t³

A 1953.4, B -128.00, C 3.9918, D -0.050091 (for S=35 only)

Wanninkhof 1992

SF₆

A + B t + C t² + D t³

A 3531.6, B -231.4, C 7.2168, D -0.090558 (for S=35 only)

diffusivity of CO₂

m² s^-1

D

1e-4 A exp (Ea / RT)

A 0.05019, Ea 19510, R 8.3145
(for S=35 only)

Jahne 1987b

Quantity		Units	Name	Formula	Constants	Reference
Solubilities	CO₂	mol kg^-1atm^-1	k₀	exp [A / t_k +B+Cln (t_k /100) +s (D +Et_k +Ft_k²)]	A 9345.17, B-60.2409, C 23.3585, D 0.023517, E -2.3656e-4, F 4.7036e-7	Weiss 1974
	O₂			exp[A + B / t_k + C ln (t_k/100) +s (D + E t_k +F t_k²) ] * p / (R * 273 * 1035)	A -58.3877, B 85.8079, C 23.8439, D -0.034892, E 1.5568e-4, F -1.9387e-7	Weiss 1970
	SF₆			exp[A +B / t_k +C ln (t_k) +D s ] * p / (R 273 1035)	A -520.606, B 25060, C 75.701, D -0.0117	Wanninkhof 1991
	CO₂	dimensionless	a	k₀ R t_k (1 / 103.5) (see Section 4.3)	R 8.3145
Acid Dissociation Constants	carbonic 1^st	mol kg^-1	k₁	exp [A / t_k + B + C ln (t_k) + (D / t_k + E) s^0.5 + F s + G s^1.5 + ln (1-0.001005 s)]	A -2307.1366, B 2.83655, C -1.5529413, D -4.0484, E -0.20760841, F 0.08468345, G -0.00654208	Roy 1993
	carbonic 2^nd		k₂	exp [A / t_k + B + C ln (t_k) + (D / t_k + E) s^0.5 + F s + G s^1.5 + ln (1-0.001005 s)]	A -3351.6106, B -9.226508, C -0.2005743, D -23.9722, E -0.106901773, F 0.1130822, G -0.00846934	Roy 1993
	water		k_w	exp [A / t_k +B +C ln (t_k) + (D / t_k +E +F ln (t_k)) s^0.5 + G s]	A -13847.26, B 148.96502, C -23.6521, D 118.67, E -5.977, F 1.0495, G -0.01615	Millero 1995
	boric		kb	exp [(A + B s^0.5 +C s + D s^1.5 +E s²) / t_k + F + G s^0.5+ H s + (I + J s^0.5 + K s) ln (t_k) + L s^0.5t_k]	A -8966.9, B -2890.53, C -77.942, D 1.728, E -0.0996, F 148.0248, G 137.1942, H 1.62142, I -24.4344, J -25.085, K -0.2474, L 0.053105	Dickson 1990
	phosphoric 1^st		kp₁	exp [A/t_k +B +C ln(t_k) +(D/t_k +E) s^0.5 +( F/t_k +G) s ]	A -4576.752, B 115.525, C -18.453, D -106.736, E 0.69171, F -0.65643, G -0.01844	Millero 1995
	phosphoric 2^nd		kp₂	exp [A/t_k +B +C ln(t_k) +(D/t_k +E) s^0.5 +( F/t_k +G) s ]	A -8814.715, B 172.0883, C -27.927, D -160.340, E 1.3566, F 0.37335, G -0.05778
	phosphoric 3^rd		kp₃	exp [A/t_k +B +(C/t_k +D) s^0.5 + ( E/t_k +F) s ]	A -3070.75, B -18.141, C 17.27039, D 2.81197, E -44.99486, F -0.09984
Reaction rates	CO₂ +H₂O	mol kg^-1 s^-1	kCO₂	exp [A + B/t_k + C ln (t_k)]	A 1246.98, B -61900, C -183	Johnson 1982
Reaction rates	CO₂ +OH^- (* K_w)	s^-1	k_OHK_w	exp [A +B s^0.5+ C / t_k + D ln (t_k)]	A -930.13, B 1.1e-7, C 3.1e4, D 140.9	Johnson 1982
Schmidt numbers	CO₂		sc	A + B t +C t² + D t³	A 2073.1, B -125.62, C 3.6276, D 0.043219 (for S=35 only)	Wanninkhof 1992
	O₂			A + B t + C t² + D t³	A 1953.4, B -128.00, C 3.9918, D -0.050091 (for S=35 only)	Wanninkhof 1992
	SF₆			A + B t + C t² + D t³	A 3531.6, B -231.4, C 7.2168, D -0.090558 (for S=35 only)	Wanninkhof 1992
diffusivity of CO₂		m² s^-1	D	1e-4 A exp (Ea / RT)	A 0.05019, Ea 19510, R 8.3145 (for S=35 only)	Jahne 1987b