Estimating the Density and Compressibility of Seawater to High Temperatures Using the Pitzer Equations

Abstract

The density and compressibility of seawater solutions from 0 to 95 °C have been examined using the Pitzer equations. The apparent molal volumes (X = V) and compressibilities (X = κ) are in the form

$$ X_{\phi } = \bar{X}^{0} + A_{X} I/(1.2 \, m)\ln (1 + 1.2 \, I^{0.5} ) + \, 2{\text{RT }}m \, (\beta^{(0)X} + \beta^{(1)X} g(y) + C^{X} m) $$

where $\bar{X}^{0}$ is the partial molal volume or compressibility, I is the ionic strength, m is the molality of sea salt, A_X is the Debye–Hückel slope for volume (X = V) or adiabatic compressibility (X = κ _s), and g(y) = (2/y ²)[1 − (1 + y) exp(−y)] where y = 2I ^0.5. The values of the partial molal volume and compressibility ($\bar{X}^{0}$) and Pitzer parameters (β ^(0)X, β ^(1)X and C ^X) are functions of temperature in the form

$$ Y^{X} = \sum_{i} a_{i} (T-T_{\text{R}} )^{i} $$

where a _i are adjustable parameters, T is the absolute temperature in Kelvin, and T _R = 298.15 K is the reference temperature. The standard errors of the seawater fits for the specific volumes and adiabatic compressibilities are 5.35E−06 cm³ g⁻¹ and 1.0E−09 bar⁻¹, respectively. These equations can be combined with similar equations for the osmotic coefficient, enthalpy and heat capacity to define the thermodynamic properties of sea salt to high temperatures at one atm. The Pitzer equations for the major components of seawater have been used to estimate the density and compressibility of seawater to 95 °C. The results are in reasonable agreement with the measured values (0.010E−03 g cm⁻³ for density and 0.050E−06 bar⁻¹ for compressibility) from 0 to 80 °C and salinities from 0 to 45 g kg⁻¹. The results make it possible to estimate the density and compressibility of all natural waters of known composition over a wide range of temperature and salinity.

Appendices

Appendix 1

See Table 6.

Table 6 The effect of temperature on $\bar{V}_{0}$ from the Pitzer equation for the major sea salts (Krumgalz et al. 2000)

Appendix 2

See Table 7.

Table 7 The effect of temperature on the Pitzer β ^(0)V parameter for the major sea salts (Krumgalz et al. 2000)

Appendix 3

See Table 8.

Table 8 The effect of temperature on the Pitzer β ^(1)V parameter for the major sea salts (Krumgalz et al. 2000)

Appendix 4

See Table 9.

Table 9 The effect of temperature on the Pitzer C ^V parameter for the major sea salts (Krumgalz et al. 2000)