26
F. J. Millero
properties of sea water (Millero 1973a,b, 1975, 1982; Millero and Lepple 1973; Millero
and Poisson 1981):
p = pO + Lion-water + Lion-ion interactions
(1.43)
Thus, any physical property of sea water at a given ionic strength is equal to the property of pure water plus a term related to the weighted ion-water and ion-ion interactions.
The second term is completely additive for the components of an electrolyte mixture.
These equations have been used to estimate the properties of sea water (Millero
1973a,b, 1974, 1975, 1978; Millero and Lepple 1973; Millero et al.1977), seas (Millero 1978;
Millero and Chetirkin 1980; Millero et al.1982), lakes (Effler et al.1986; Millero 2000a),
rivers (Millero 1975; Millero et al. 1976c, 1978); estuaries (Millero 1975; Millero and
Kremling 1976; Millero et al. 1976a,c) and brines (Millero et al.1982). This includes the
estimates of sound speeds (Millero et al. 1977), heat capacities (Millero et al. 1973a),
enthalpies (Millero 1974), freezing points (Millero 1974), densities (Millero 1975),
expansibilities (Millero 1973b), and compressibilites (Millero 1973b). Examples of the
estimates of the densities and compressibilities of sea water using this simple additivity method are shown in Table 1.3. The calculated values are in good agreement with
the measured values. At higher ionic strengths, the estimates are not as good. This is
shown in more detail for the density comparisons of Red Sea Brine waters in Table 104These larger errors at higher ionic strengths are related to excess mixing parameters
due to the interactions of ions of the same sign (Na + _Mg2+, cr -soh. These excessmixing properties can be studied by mixing two electrolyte solutions at a constant ionic
strength. For the mixing of the major sea salts, there are six possible mixtures that can
be represented by the so-called cross square diagram Fig. 1.22)
The mixing of the salts around the sides of this diagram has either a common cation or anion during mixing. A number of studies by Young et al. (1957) have shown
the excess mixing properties MEx follow some simple rules. They are:
1. The values of MEx in dilute solutions are not very large and can be assumed to be
zero. This leads to the additivity of I/J or Young's first rule.
2. The values of MEx for mixtures with a common anion or cation are not strongly affected by the common ion. For example, the MEx for mixing NaCI and KCI is nearly
the same as mixing NaBr and KBr.
MEiNaCI-KCI) = MEx(NaBr-KBr)
(1.44)
Since this mixing process is largely related to cation-cation and anion-anion interactions, this means that as a first approximation, plus-plus and minus-minus interactions are independent of the other ions in the solutions.
3. The third rule is called the cross square rule and is given by:
LD=LX
(1.45)
which states the sum of the excess mixing properties around the sides of the diagram given above is equal to the sum of the excess properties of the cross mixtures.
For the major sea salts, this gives:
F. J. Millero
properties of sea water (Millero 1973a,b, 1975, 1982; Millero and Lepple 1973; Millero
and Poisson 1981):
p = pO + Lion-water + Lion-ion interactions
(1.43)
Thus, any physical property of sea water at a given ionic strength is equal to the property of pure water plus a term related to the weighted ion-water and ion-ion interactions.
The second term is completely additive for the components of an electrolyte mixture.
These equations have been used to estimate the properties of sea water (Millero
1973a,b, 1974, 1975, 1978; Millero and Lepple 1973; Millero et al.1977), seas (Millero 1978;
Millero and Chetirkin 1980; Millero et al.1982), lakes (Effler et al.1986; Millero 2000a),
rivers (Millero 1975; Millero et al. 1976c, 1978); estuaries (Millero 1975; Millero and
Kremling 1976; Millero et al. 1976a,c) and brines (Millero et al.1982). This includes the
estimates of sound speeds (Millero et al. 1977), heat capacities (Millero et al. 1973a),
enthalpies (Millero 1974), freezing points (Millero 1974), densities (Millero 1975),
expansibilities (Millero 1973b), and compressibilites (Millero 1973b). Examples of the
estimates of the densities and compressibilities of sea water using this simple additivity method are shown in Table 1.3. The calculated values are in good agreement with
the measured values. At higher ionic strengths, the estimates are not as good. This is
shown in more detail for the density comparisons of Red Sea Brine waters in Table 104These larger errors at higher ionic strengths are related to excess mixing parameters
due to the interactions of ions of the same sign (Na + _Mg2+, cr -soh. These excessmixing properties can be studied by mixing two electrolyte solutions at a constant ionic
strength. For the mixing of the major sea salts, there are six possible mixtures that can
be represented by the so-called cross square diagram Fig. 1.22)
The mixing of the salts around the sides of this diagram has either a common cation or anion during mixing. A number of studies by Young et al. (1957) have shown
the excess mixing properties MEx follow some simple rules. They are:
1. The values of MEx in dilute solutions are not very large and can be assumed to be
zero. This leads to the additivity of I/J or Young's first rule.
2. The values of MEx for mixtures with a common anion or cation are not strongly affected by the common ion. For example, the MEx for mixing NaCI and KCI is nearly
the same as mixing NaBr and KBr.
MEiNaCI-KCI) = MEx(NaBr-KBr)
(1.44)
Since this mixing process is largely related to cation-cation and anion-anion interactions, this means that as a first approximation, plus-plus and minus-minus interactions are independent of the other ions in the solutions.
3. The third rule is called the cross square rule and is given by:
LD=LX
(1.45)
which states the sum of the excess mixing properties around the sides of the diagram given above is equal to the sum of the excess properties of the cross mixtures.
For the major sea salts, this gives: