R. Feistel et al.: Oceanographic application and numerical implementation of TEOS-IO: Part 1 
641 
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Ocean Sci., 6, 633-677, 2010 
and the relative chemical potential, p, 
P = 
dg s _ 
dS A 
= si 
T, P 
(3.10) 
The list of properties derived from g s (S A , T, P) is given in 
Table S4. Partial derivatives with respect to the three inde 
pendent variables are written as subscripts where the sub 
script of 5a is omitted for simplicity. 
Details on the definition of osmotic and activity coeffi 
cients are given by Falkenhagen et al. (1971), Millero and 
Leung (1976), Ewing et al. (1994), Lehmann et al. (1996), 
IUPAC (1997), Feistel and Marion (2007) and Feistel (2008). 
The mean practical activity coefficient In y of sea salt 
(S4.1) can be computed from the activity potential 0 (S4.2) 
as (Feistel and Marion, 2007) 
The zero-salinity limit is lim 0=1. 
S A ^0 
The saline excess chemical potential p ws , Eq. (S4.3), is 
the difference between the chemical potentials of water in 
seawater and of pure water, 
Ip ws (Sa, T, P) = fiw(S A , T, P) - /¿ w (0, T, P) = - mRT(p. 
(3.16) 
The zero-salinity limit is lim u ws =0. 
S A ^0 
The activity of water a w , Eq. (S4.3), is related to the os 
motic coefficient by 
aw = ex P (— mMw0) = exp 
¿¿ ws 
RwT 
(3.17) 
y /9 (m0)\ 
y id V 3m ) TP 
(3.11) 
Flere, m=5A/[(l — 5a) xMs] is the molality (moles of 
salt per kg of water) implemented in the library as 
sal_molality_si, and y ld =l kg mol -1 is the asymptotic 
value of y at infinite dilution. Ms=31.4038218 g mol -1 is 
the mean molar mass of sea salt with Reference Composi 
tion (Millero et al., 2008), R=8.314472Jmol _1 K _1 is the 
molar gas constant and (1—5a) is the mass fraction of wa 
ter in seawater. The zero-salinity limit of Eq. (3.11) is 
lim In (y/K ld )= 0. 
Sa^>-0 
The activity potential 0(5a, T, P), Eq. (S4.2), describes 
the ion-ion interactions and consists of higher salinity powers 
O (if) of the saline part of the Gibbs function (Eq. 2.2) in 
the form (Feistel and Marion, 2007) 
g S (S A ,T,P) = S Ag2 (T,P) (3.12) 
+ S A R S T Jin + 0 (5 A , T, P) 
Flere, Rs=^/Afs=264.7599Jkg -1 K _1 is the specific gas 
constant of sea salt. The activity potential is related to the 
osmotic coefficient 0 and the activity coefficient In y by 
0 = 1 - 0 + In -^. (3.13) 
The zero-salinity limit is lim 0=0. The activity potential 
Sa^>-0 
vanishes for ideal solutions. 
The osmotic coefficient 0 , Eq. (S4.11), expresses the ac 
tivity coefficient of water and can be computed from the ac 
tivity potential 0, Eq. (S4.2), as 
0=1 +m( d 1 P) ■ (3.14) 
V ) t,p 
It is related to the chemical potential of pure water, g w 
(Sect. 4), and the chemical potential of water in seawater, 
pw, by (Feistel and Marion, 2007) 
fL W (S A ,T,P) =g W (r,P) -mRT(t>(S A ,T,P). (3.15) 
Flere, Mw=18.015268 gmol 1 is the molar mass of water 
(IAPWS, 2008b) and R W =R/M W =461.523 64 Jkg“ 1 K“ 1 is 
the specific gas constant of water. The zero-salinity limit is 
lim aw=l- At low vapour pressures, aw equals the relative 
S A ^0 
humidity of sea air (Feistel et ah, 2010a). 
The relative chemical potential p, Eq. (S4.5), describes the 
change of the Gibbs energy of a seawater parcel if at constant 
temperature and pressure a small mass fraction of water is re 
placed by salt. Its zero-salinity limit possesses a logarithmic 
singularity, lim u=RsT In S A . 
S A ^0 
The dilution coefficient D, Eq. (S4.6), describes the 
change of salinity in relation to freezing or evaporation pro 
cesses, (Feistel and Flagen, 1998; Feistel et al., 2010a), as 
e.g. in Eqs. (A28), (4.44) or (A38). The zero-salinity limit 
(Raoult’s law) is lim D=R$T. The chemical coefficient 
S A ^0 
(S4.6), Ds=S a D, is used for the description of sea air (Feis 
tel et al., 2010a). 
The specific enthalpy, entropy and volume of sea salt, 
Eqs. (S4.12)-(S4.14), provide the enthalpy, entropy and vol 
ume per mass of sea-salt particles dissolved in water. The 
zero-salinity limits are lim h$=g2(T, P) — T (dg2/dT) P , 
Sa^>-0 
lim r)s — — Rs In 5a and lim vs=(dg2/dP) T . The loga- 
Sa^O Sa^>-0 
rithmic singularity of entropy reflects the empirical fact that 
rigorous purification of a mixture, i.e., complete desalination, 
is impossible by thermodynamic processes. 
Mixing enthalpy, entropy and volume, Eqs. (S4.12)- 
(S4.14), provide the change of enthalpy, entropy or specific 
volume if two seawater samples with absolute salinities 5i, 
S2 and mass fractions w\,W2 are mixed at constant tempera 
ture and pressure. If the mixing occurs adiabatically at con 
stant pressure, the enthalpy remains constant while entropy 
is produced and the temperature changes. Since such effects 
do not occur in ideal solutions, the related quantities can 
be computed from the activity potential 0 (5a, T, P) alone 
(Feistel and Marion, 2007). They disappear at infinite dilu 
tion.