Molar volume of solid

Figure 13.3. A P- V-T surface for a one-component system in which the substance contracts on freezing, such as water. Here Tj represents an isotherm below the triple-point temperature, 72 represents an isotherm between the triple-point temperature and the critical temperature, is the critical temperature, and represents an isotherm above the triple-point temperature. Points g, h, and i represent the molar volumes of sohd, hquid, and vapor, respectively, in equilibrium at the triple-point temperature. Points e and d represent the molar volumes of solid and liquid, respectively, in equihbrium at temperature T2 and the corresponding equilibrium pressure. Points c and b represent the molar volumes of hquid and vapor, respectively, in equilibrium at temperature and the corresponding equihbrium pressure. From F. W. Sears and G. L. Sahnger, Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. 3rd ed., Addison-Wesley, Reading, MA, 1975, p. 31.

For geologic purposes, the dependence of the equilibrium constant K on temperature is the most important property (4). In principle, isotope fractionation factors for isotope exchange reactions are also slightly pressure-dependent because isotopic substitution makes a minute change in the molar volume of solids and liquids. Experimental studies up to 20kbar by Clayton et al. (1975) have shown that the pressure dependence for oxygen is, however, less than the limit of analytical detection. Thus, as far as it is known today, the pressure dependence seems with the exception of hydrogen to be of no importance for crustal and upper mantle environments (but see Polyakov and Kharlashina 1994). 

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Thus, if the partial molar volume of solute in aqueous solution is greater than the molar volume of solid solute, an increase in pressure will increase the chemical potential of solute in solution relative to that in the solid phase solute will then leave the solution phase until a lower, equilibrium solubility is attained. Conversely, if the partial molar volume in the solution is less than that in the solid, the solubility will increase with pressure. 

For example, near 0°C, ice has a density of 0.92 g cm thus, the molar volume of solid water under these conditions is... 

The need to include solid structural property variations in the single-pellet models was illustrated by the high-temperature results from the two examples cited above. In those cases, the structural property variations were attributed to sintering of the solid product and/or reactant. Structural property variations may also occur at lower temperatures where sintering would not be expected because of the differences in molar volumes of solid reactant and product. 

If instead of using the molar volume of solid sucrose we took the partial molar volume of sucrose in aqueous solution, the result would be effectively the same. The weakest point in this treatment is the assumption that Stokes law should be obeyed by such a small particle as a sucrose molecule. The approximation should be better for colloidal particles, but then there is the problem of determining their mass. Compare problem 13. 

AHs = enthalpy of sublimation of solid Vy = molar volume of vapor Vs = molar volume of solid... 

Fri] Thermodynamic calculation Recalculation of molar volumes of solid and liquid phases and their variation with composition and temperature... 

Given that the molar volume of liquid carbon dioxide at —37 C is 39.9 mL/mol and the molar volume of solid carbon dioxide at — 79 C is 28.2 ml. /mol, calculate the density of carbon dioxide at each set of conditions. If carbon dioxide were to act as an ideal gas, what would be its density at 5 0°C When one compares each value for density to the state of the carbon dioxide, which phase change results in the greater change in density ... 

Figure 1. Geometric changes of cylindrical pore because of the large molar volume of solid product...

At the normal melting temperature, 83.78 K, the molar volume of solid argon is 0.0246 Lmol and that of... 

EXAMPLE 4.11 Temperature Correction for Molar Volume of Solid Cu Determine the molar volume of copper at 500°C from the data in Table 4.4. SOLUTION We can rewrite Equation (4.32) as foUows Separation of variables leads to ... 

Solving for the molar volume of solid in state 2, and plugging in values from Table 4.4, we get ... 

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