The Apparent Molal Volume and Compressibility of Seawater Fit to the Pitzer Equations

Abstract

The density and compressibility of seawater salt solutions for ionic strengths 0to 0.8 m, temperatures 0–40°C, and applied pressure 0 to 1000 barare fitted tothe Pitzer equations. The apparent molal volumes and compressibilities (Xφ) arefitted to equations of the form

$$X_\phi = \mathop {X^0 }\limits^ + A_X I/(1.2m)\ln (1 + 1.2I^{0.5} ) + 2 RT m(\beta ^{(0)X} + \beta ^{(1)X} g(y) + m C^X )$$

where I is the ionic strength, m is the molality of seasalt, A _X is the Debye—Hückelslope for the volume (X = V) or compressibility(X = κ) and g(y) = (2/y ²)[1 − (1 + y)exp(x)] where y = 2I ^0.5. The Pitzer parameters β^(0)X,β^(1)X, and C ^Xare fitted to functions of temperature and pressure in the form

$$Y^{\text{x}} = \Sigma _{\text{i}} \Sigma _{\text{j}} a_{{\text{ij}}} (T - T_{\text{R}} )^{\text{i}} P^{\text{j}} $$

where a _ij are adjustable parameters, Y ^X is the Pitzer parameter, T is the temperaturein K, T _R = 298.15 K, and P is the applied pressure in bars (P = 0 at 1 atm or1.013 bar). The standard deviations of the seawater fits are 8.3×10⁻⁶ cm³-g⁻¹for the specific volumes, 0.0007×10⁻⁶ bar⁻¹ for the compressibilities, and0.63×10⁻⁶ K⁻¹ for the thermal expansibilities. At 25°C, the measured densitiesof seawater are compared to the calculated values using Pitzer coefficients forthe major sea salts. The results agree with the measured values to within 45×10⁻⁶g-cm⁻³.