200
F. Millero . D. Pierrot
2. The interaction parameters of M with the major anions (a) in the solution
(2 Lam.(BMa + BeMa) are determined from binary solutions of Ma (e.g. NaCl).
3. The interaction parameters of M with the major cations (c) (Leme2 ~e) are determined from ternary solutions (Ma + ca) (e.g. NaCI-MgCI2).
4. The triplet interaction parameters of M with the major cations and anions
(LemeLama P Mea and LaLa'mama' Paa'M) are determined from ternary solutions
(Ma + ca).
5. The media terms for the major components (Z~R + ZMS) are determined from binary solutions of the major components of the solution.
6. The higher order electrical terms (Leme2E~e + Z~Rl + Z~R2) for the interactions
of ions of different charge (Mg-Na) are a function of ionic strength.
As shown elsewhere (Millero 1982) for the trace components (H+, Cu 2 +, etc.) of the
solution, only the major cation interaction parameters (2, 3, 4) are needed to make
reasonable estimates of the "trace" activity coefficients (Millero 1982). The trace components of the solution do not contribute significantly to the media terms. Although
this simplifies the estimation of the activity coefficients of trace constituents, many
trace constituents form strong interactions with the major (SO~-) and minor components (OH-, CO~-, etc.) and cannot be accounted for using reasonable values for the
interaction parameters. To correct for these strong interactions, one must consider the
formation of an ion pair between the cation and anion. This leads to parameters for
the ion pairs that are model dependent.
At a given temperature, the model requires the interaction terms f3'k., 13k, 13k.,
and ctx for all the major electrolytes (MX) that make up the solution. These parameters account for the binary interactions of the individual components of each electrolyte (M-M, X-X, and MX) in the mixture (Pitzer and Mayorga 1973,1974). The values of f3~, 13k, 13k., c4' MX for the major components of natural waters are available at
25°C and are tabulated elsewhere (Pitzer 1991). The Pitzer activity coefficient parameters for a number of electrolytes important in natural systems (HCI, NaCI, KCI, NaOH,
MgCl2, CaCl2, Na2S04' K2S04, MgS04, CaS04) are known (M011er 1988; Greenberg and
M011er 1989; Spencer et al. 1990; Pabalan and Pitzer 1987) over a wide range of temperatures (0 to 250°C) and have been fitted to equations of a form (Pabalan and Pitzer
1987; M011er 1988; Greenberg and M011er 1989) such as:
P(T) = al + ai1/ T -1/ TR) + a3ln(T / TR) + a4(T - TR) + asO·.,z - T~)
(8.19)
Pis f3'k., 13k, or C"MX and TR is a reference temperature (298.15 K) and ai are adjustable parameters given elsewhere (Millero and Pierrot 1998). Data over a more limited temperature range (0 to 50°C) (Simonson et al. 1987a,b, 1988) are fitted to equations of the form:
f3'k.(T) = a + b(T - T R ) + c(T - TR)2
(8.20)
One can make reasonable estimates of activity coefficients over smaller ranges
of temperature (0 to 50°C) by using heat capacity (Criss and Millero 1996,1999)
and enthalpy (Silvester and Pitzer 1978) data at 25°C (Millero 1979a). The
F. Millero . D. Pierrot
2. The interaction parameters of M with the major anions (a) in the solution
(2 Lam.(BMa + BeMa) are determined from binary solutions of Ma (e.g. NaCl).
3. The interaction parameters of M with the major cations (c) (Leme2 ~e) are determined from ternary solutions (Ma + ca) (e.g. NaCI-MgCI2).
4. The triplet interaction parameters of M with the major cations and anions
(LemeLama P Mea and LaLa'mama' Paa'M) are determined from ternary solutions
(Ma + ca).
5. The media terms for the major components (Z~R + ZMS) are determined from binary solutions of the major components of the solution.
6. The higher order electrical terms (Leme2E~e + Z~Rl + Z~R2) for the interactions
of ions of different charge (Mg-Na) are a function of ionic strength.
As shown elsewhere (Millero 1982) for the trace components (H+, Cu 2 +, etc.) of the
solution, only the major cation interaction parameters (2, 3, 4) are needed to make
reasonable estimates of the "trace" activity coefficients (Millero 1982). The trace components of the solution do not contribute significantly to the media terms. Although
this simplifies the estimation of the activity coefficients of trace constituents, many
trace constituents form strong interactions with the major (SO~-) and minor components (OH-, CO~-, etc.) and cannot be accounted for using reasonable values for the
interaction parameters. To correct for these strong interactions, one must consider the
formation of an ion pair between the cation and anion. This leads to parameters for
the ion pairs that are model dependent.
At a given temperature, the model requires the interaction terms f3'k., 13k, 13k.,
and ctx for all the major electrolytes (MX) that make up the solution. These parameters account for the binary interactions of the individual components of each electrolyte (M-M, X-X, and MX) in the mixture (Pitzer and Mayorga 1973,1974). The values of f3~, 13k, 13k., c4' MX for the major components of natural waters are available at
25°C and are tabulated elsewhere (Pitzer 1991). The Pitzer activity coefficient parameters for a number of electrolytes important in natural systems (HCI, NaCI, KCI, NaOH,
MgCl2, CaCl2, Na2S04' K2S04, MgS04, CaS04) are known (M011er 1988; Greenberg and
M011er 1989; Spencer et al. 1990; Pabalan and Pitzer 1987) over a wide range of temperatures (0 to 250°C) and have been fitted to equations of a form (Pabalan and Pitzer
1987; M011er 1988; Greenberg and M011er 1989) such as:
P(T) = al + ai1/ T -1/ TR) + a3ln(T / TR) + a4(T - TR) + asO·.,z - T~)
(8.19)
Pis f3'k., 13k, or C"MX and TR is a reference temperature (298.15 K) and ai are adjustable parameters given elsewhere (Millero and Pierrot 1998). Data over a more limited temperature range (0 to 50°C) (Simonson et al. 1987a,b, 1988) are fitted to equations of the form:
f3'k.(T) = a + b(T - T R ) + c(T - TR)2
(8.20)
One can make reasonable estimates of activity coefficients over smaller ranges
of temperature (0 to 50°C) by using heat capacity (Criss and Millero 1996,1999)
and enthalpy (Silvester and Pitzer 1978) data at 25°C (Millero 1979a). The