Energetic property of magma degassing: a thermodynamic model
Shigeru Yamashita
Institute for Study of the Earth’s Interior, Okayama University, Misasa, Tottori 682-0193,
Japan (e-mail: shigeru@misasa.okayama-u.ac.jp)
Knowledge of the latent heat of water dissolution in silicate melts is of importance forunderstanding the energetic property of magma degassing. I present here athermodynamically based model for computing the latent heat of water dissolution in rhyolite
melt. Fundamental assumption in the model developed here is that hydrous rhyolite melt canbe treated as the system H2O molecules (melt) – OH groups (melt) – O (melt), and that thesethree quasi-chemical components mixes ideally. The melt –water vapor equilibrium isexpressed by the following two reactions: H2O (vapor) = H2O molecule (melt)(heterogeneous reaction) and H2O molecule (melt) + O (melt) = 2 OH (melt) (homogeneousreaction). Yamashita (1999) found that under the same assumption, all previously publishedsolubility data for water in rhyolite melts are reproduced over a wide range of temperaturefrom ~700 to 1200 degree C at pressure to 100 MPa. His non-linear multiple regression forthe solubility dataset converged upon the standard enthalpy of heterogeneous reaction = -25.3± 4.8 kJ / mol water at (1bar, T), the standard enthalpy of homogeneous reaction = 25.8 ±11.8 kJ / mol water at (P, T), and the standard entropy of homogeneous reaction = 6.0 ± 8.7 J/ mol water per K at (P, T). In this study, these optimum parameters were used to estimate thelatent heat of water dissolution in rhyolite melts along the water solubility surface. Theresults demonstrate that at pressure between ~20 MPa and 0.1 MPa, the latent heat of water
dissolution monotonously decreases with decreasing water content (hence with decreasing
H2O vapor pressure), where the absolute value is negative (Fig. 1). This monotonous
decrease arises from a great change in the enthalpic contribution of homogeneous reaction tothe latent heat of water dissolution; the fraction of water that has been converted to OH
groups by homogeneous reaction approaches unity as water content decreases, which thereby
yields the maximum enthalpic contribution of homogeneous reaction. As homogeneous
reaction is endothermic (as is indicated by positive sign of the standard enthalpy), whereas
heterogeneous reaction is exothermic, the latent heat of water dissolution decreases as watercontent in the melt decreases. At pressure above ~20 MPa, a cancellation of these two
enthalpic contributions occurs. The latent heat of water dissolution roughly levels out overthe pressure range ~20 MPa to 100 MPa as a result of this cancellation (Fig. 1). The latent
heat of water dissolution estimated at 850 degree C is approximately –7 kJ / mol water at 20MPa, and practically zero at 0.1 MPa. Although standard error of estimation is large (up to ±6kJ), the present results help in evaluating the energetic property of magma degassing undergeologically relevant conditions. A numerical calculation for the conservation of energy in arising water-saturated rhyolite magma (that is, when the exsolved H2O is sustained in themelt as vapor bubbles) suggests that at pressures below 100 MP, the latent heat of water
dissolution causes a temperature drop of only <10 degree C (Fig. 2).
References:Burnham C.W. & Davis N.F. (1974). Amer. J. Sci. 274, 902-940.
Holloway J.R. (1977). In: Fraser D.G. (ed.) Thermodynamics of Geology, pp161-181.
Lange R.A. & Navrotsky A. (1992). Contrib. Mineral. Petrol. 110, 311-320.
Ochs F.A. & Lange R.A. (1997). Contrib. Mineral. Petrol. 129, 155-165.
Sahagian D.L. & Proussevitch A.A. (1996). J. Volcanol. Geotherm. Res. 74, 19-38.
Yamashita S. (1999). J. Petrol. 40, 1497-1507.

H2O vapor pressure (MPa)Figure 1. Latent heat of water dissolution in rhyolite melts modeled along the watersolubility surface. Data labeled by S&P represent earlier thermodynamic model proposed foralbite melt by Sahagian and Proussevitch (1996). The absolute values of the latent heat ofwater dissolution by the S&P model are substantially greater than those obtained by thepresent model at relatively low pressure. Such a large discrepancy probably stems from that
the S&P model depends on the Burnham and Davis (1974)’s activity-temperature relation
for water dissolved in albite melt, which needs to be revised at pressure below 200 MPa(Yamashita, 1999).

Figure 2. Energetic conservation for degassing in a rising water-saturated rhyolite magma asa function of initial water content of the melt. The energy conservation eqaurion was
numerically integrated from the initial water saturation depth to the magma fragmentation
depth based on the latent heat of water dissolution in rhyolite melt (this study), the heat
capacity of rhyolite melt (Lange & Navrotsky, 1992) and available equation of state (hydrousrhyolite melt, Ochs & Lange, 1997; H2O vapor, Holloway, 1977).