271
The Carbonate System
which is related to the thermodynamic value K 2 by
K 2 = K 2 *γ H γ CO 3 /γ HCO 3
(7.59)
where the activity coefficients are total values that include the effect of ionic interactions.
The values of K 2 * in seawater can be determined from (S = 0 to 45 and t = 0 to 50°C; Millero
et al., 2006)
ln K 2 * = ln K 2 + A S 0.5 + B S + C S 2
(7.60)
A = 22.444 + 797.294/T – 3.558 ln T
B = 0.148 – 26.687/T
C = 0.000369
where the thermodynamic value ln K 2 is given by
ln K 2 = 207.6548 – 11843.79/T – 33.6485 ln T
(7.61)
The effect of pressure (p, bar) on K 1 * and K 2 * can be estimated from
ln(K P i / K 0 i ) = –(ΔV i / RT) P + 0.5ΔK i P 2
(7.62)
where
–ΔV 1 = 25.50 + 0.151(S – 34.8) – 0.1271(T – 273.15)
(7.63)
–103ΔK 1 = 3.08 + 0.578(S – 34.8) – 0.0877(T – 273.15)
(7.64)
–ΔV 2 = 15.82 – 0.321(S – 34.8) + 0.0219(T – 273.15)
(7.65)
–103ΔK 2 = –1.13 + 0.314(S – 34.8) + 0.1475(T – 273.15)
(7.66)
Since boric acid makes up one of the major constituents of seawater, it is necessary to
consider its ionization:
HB = H + + B –
(7.67)
where HB = B(OH) 3 and B– = B(OH) 4– . The dissociation constant is defined by
K* HB = [H + ] T [B–] T /[HB] T
(7.68)
The values of pK KB * in seawater can be calculated from (Dickson, 1990)
ln K HB * = ln K HB + B S 0.5 + C S + D S 1.5 + ln (1 – S 0.001005)
(7.69)
A = –167.69908 + 6551.35253/T + 25.928788 ln T
B = 39.75854 – 1566.13883/T – 6.171951 ln T