Molar volume of water

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

What is the molar volume of water under each of the following conditions ... 

Plot an appropriate volume unit vs. mole fraction of acetic acid. Determine the partial molar volumes of water and acetic acid at X2 = 0, 1, and several intermediate compositions (at least three). Plot V and V2 as a function of. Y2. 

Here, Mn, is the molecular weight of the polymer chains prepared under identical conditions but in the absence of the crosslinking agent, u is the specific volume of the polymer and V is the molar volume of water. 

This is a complete expression but we can simplify it further, especially in the case of dilute solutions ln(x, ) = ln(l — xB) —xB, where xB is the mole fraction of the dissolved molecules. One further simplification is to take the total volume of the cell to be the number of moles of water, , multiplied by the molar volume of water, to give nwVm = V. Now we can derive a simple expression for the osmotic pressure ... 

There are apparently two sources of this effect. The molar volume of water changes relatively little as a result of the presence of a small quantity of dissolved octanol, however the quantity of dissolved water in the octanol is considerable, causing a reduction in molar volume of the octanol phase. The result is that even if activity coefficients are unaffected, log S0/Sw will be about 0.1 units less than that of log KoW. Effectively, the octanol phase swells as a result of the presence of water, and the concentration is reduced. In addition, when log KqW exceeds 4.0 there is an apparent effect on the activity coefficients which causes log (SQ/SW) to increase. This increase can amount to about one log unit when log Kow is about 8. A relatively simple correlation based on the analysis by Beyer et al. (2002) (but differing from their correlation) is that... 

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

A = +14 cm3 mol-1 for both the forward and the reverse reaction. That this AV value is markedly less than the partial molar volumes of water and of ammonia (25 and 18 cm3 mol-1, respectively) indicates limiting dissociative (D) activation (133), as do the A values of close to +70JK-1mol-1 in both directions. Overall, the current situation with regard to thermal substitution at pentacyanoferrates(II) appears to be that an I,i mechanism can also operate for reactions of [Fe(CN)5(H20)]3-, whereas the D mechanism operates for all other [Fe(CN)5L]" complexes (134). 

If we consider water molecules to be spheres of radius 138 pm, then the molar volume of water in a closest-packed array 3 -1... 

For all hydrates, the second term on the right dominates Equation 3.10, and the first and last terms effectively cancel, because the molar volume of water is within 15% of that of hydrates. The Natarajan et al. driving force of [(/fxp//fq) - 1] is the first term in an infinite series expansion of the second term [In (/fxp//fq) in Equation 3.10—acceptable when O/fV 1 -3]. 

We define the molar volume of the standard hydrates of si and sll as the molar volumes of methane and propane hydrate, respectively. The molar volume of these hydrates, and therefore of the standard states, is well-characterized via diffraction data (Tse, 1990 Huo, 2002). Ballard proposed the following expression for the molar volume of water in hydrates ... 

Here, E, is the current utilization, / is the membrane permselectivity, T is the transport number, n is the number of cell pairs in the stack, Vw is the partial molar volume of water, and C is the concentration, a, c, s and w refer to anion, cation, solution and water, respectively, and the superscripts cm, am, c, and d refer to cation-exchange membrane, anion-exchange membrane, concentrate and diluate. 

The critical molar volume of water is VCtB = 57.1E-6 m3 mob1. With these values Vc,ab = (81.6E-6+57.1E-6)/2 = 69.35E-6 m3mol 1. Together with TcA and Eq. (6-18) the calculated values in Table 6-3 for the diffusion coefficients of water in air were obtained. 

Using the Avogadro number, the Boltzmann constant, and the molar volume of water (M/p = 0.01807 m3/kg), we have... 

Vs are the partial molar volumes of water and salt, respectively. t// is the electric potential and I the electric current. Here, Jv,and Js represent the virtual flows. Experimentally, Jv is determined by measuring the change in volume of one or both compartments at opposite surfaces of the membranes. Equation (10.84) yields a set of three-flow linear phenomenological equations of conductance type... 

The molar volume of water in the natural state is 18 cm moE but if water molecules are close-packed in the liquid state, this volume would become only 12cm mor, a reduction of 33%. Thus, the volume available for the effects of electrical constriction by ions on water molecules is as much as 6 cm mol". ... 

---