Volume, liquid molar

T were eliminated beyond that point, the vapor-phase correction, as calculated here, is inadequate and the liquid molar volume is no longer constant with pressure. 

Subroutine MVOLM. MVOLM calculates the liquid molar volume at a given temperature using the modified Rackett equation... 

Spencer and Danner, 1972). This equation has been further modified by O Connell for reduced temperatures greater than 0.75. The saturated-liquid molar volume is given by the equation... 

ZRA - PACKET PARAMETER FOR SATURATED LIQUID MOLAR VOLUME CORRELATION... 

SATURATED LIQUID MOLAR VOLUME, CC/GR-MOLE ZERO PRESS REF FUGACITY IF 1VAP.LE.2 OR VA OR PRESS IP lVAP.f O.3 K-FAC TOR... 

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

Standard-state fugacities at zero pressure are evaluated using the Equation (A-2) for both condensable and noncondensable components. The Rackett Equation (B-2) is evaluated to determine the liquid molar volumes as a function of temperature. Standard-state fugacities at system temperature and pressure are given by the product of the standard-state fugacity at zero pressure and the Poynting correction shown in Equation (4-1). Double precision is advisable. 

VIP(I) Vector (length 20) of saturated liquid molar volumes (cm / mole) for condensable components for noncondensable components Vip(i) = 0 (I = 1,N). 

Xi j = mole fraction of component or / in the liquid mixture V I = liquid molar volume of pure component or / at temperature T, mVkmol... 

Chen-Chen Their correlation was based on diffusion measurements of 50 combinations of conditions with 3 to 4 replicates each and exhibited an average error of 6 percent. In this correlation, = Vg/[0.9724 (V, /g -I- 0.04765)] and = the liquid molar volume at the... 

Table 13-1, based on the binary-system activity-coefficient-eqnation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...

TABLE 13-4 Antoine Vapor-Pressure Constants and Liquid Molar Volume ... 

Species Antoine constantsf Applicable temperature region, C liquid molar volume, cmV g-mol... 

Scatchard and Hildebrand defined the cohesive energy density coh-ii of a liquid 1 as the negative molar configurational energy divided by its liquid molar volume, V, ... 

Solubility parameters and liquid molar volumes for various solvents and polymers (25°C)... 

Solubility parameters are generally tabulated, together with the corresponding liquid molar volumes, only at 25°C. Although solubility parameters are themselves temperature-dependent, the combination of quantities in Eq. 70 is not. Differentiating Eq. 70 with respect to temperature gives — the excess entropy, a quantity which has been assumed to be zero in accord with the definition of a regular solution. Thus only data at 25°C are needed. Solubility parameters may be... 

Solubility Parameters and Liquid Molar Volumes in the Chao-Seader Correlation... 

For components near or above their critical temperatures, the liquid volume t>j was evaluated by extrapolation with respect to temperature. For supercritical components, the fugacity f° was also evaluated by extrapolation the effect of pressure was found from the Poynting relation using the previously extrapolated liquid molar volumes. 

Since the liquid molar volume is always larger than that of solid [48,49], Ap/AT < 0 if... 

Vb = liquid molar volume at the normal boiling point, can be found fr molecular contributions. 

Constantinou, L., R. Gani, and J. P. O Connell, "Estimation of the acentric factor and the liquid molar volume at 298K through a new group contribution method". Fluid Phase Equilibria 103, 11, (1995). 

The parameters were optimised to represent the critical data p and T, the vapour pressure from room temperature up to the critical point and the saturated vapour and liquid molar volumes. Account was also taken of the representation of the binary systems H20-CH. to C.H.q. Initially the method of Powell... 

Fig. 13.2 Vapor pressures (PV,T) and liquid molar volumes (Vm,T) along the orthobaric LV equilibrium line for reference isotopomer pairs, showing their distinctly different behaviors (schematic). The thicker lines label the heavier isotopomers. The curves begin at the triple points and end at the critical points (except for He which has no triple point under orthobaric conditions). Not to scale, isotopic differences are exaggerated (Reprinted from Van Hook, W. A., Rebelo, L. P. N. and Wolfsberg, M., Fluid Phase Equilib. 257, 35 (2007), copyright 2007, with permission from Elsevier)...

Cross-sectional areas from the liquid molar volume... 

Figure 18.9 Molecular diffusion coefficients in air, Dla, at 25°C for different molecules plotted as a function of (a) their liquid molar volume, V(, (calculated as ratio of molar mass M, to liquid density, p,L), and (b) their molar mass, Mh Data from references reviewed by Fuller et al. (1966) plotted on double-logarithmic scale.

Calculate D,a from the empirical relation to (liquid) molar volume Vt. From Fig. 18.9a follows ... 

Peneloux et al. [35] have introduced a clever method of improving the saturated liquid molar volume predictions of a cubic equation of state, by translating the calculated volumes without efffecting the prediction of phase equilibrium. The volume-translation parameter is chosen to give the correct saturated liquid volume at some temperature, usually at a reduced temperature Tr = T/Tc = 0.7, which is near the normal boiling point. It is possible to improve the liquid density predictions further by making the translation parameter temperature dependent. 

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