Molar volume of liquid

Table 14.2 Densities and molar volumes of liquid and solid O2...

There may be more than a thousandfold increase in volume when liquids or solids react to form a gas. The molar volumes of gases are close to 25 L-mol 1 under normal conditions (room temperature and pressure), whereas liquids and solids occupy only about a few tens of milliliters per mole. The molar volume of liquid water, for instance, is only 18 mL-mol 1. In other words, 1 mol of gas molecules at 25°C and 1 atm occupies as much as 1000 times the volume of 1 mol of molecules in a typical liquid or solid. 

Most substances have a slightly smaller molar volume as a solid than as a liquid substances generally decrease in volume when they freeze. Water is the notable exception it expands (increases in molar volume) upon freezing. That is why closed containers holding water and other aqueous solutions will break in freezing weather. Although iron is much more dense overall than the compounds in Table 12-1, and its molar volumes are much less than those of benzene and carbon tetrachloride, iron still behaves normally. The molar volume of liquid iron is still greater than that of solid iron. 

Every segment in the polymer chain is solvated by two solvent molecules. Those molecules of solvents 1 and 3 in the solvated sheath which correspond to the bulk composition of 1 1 are disregarded. Only those molecules of solvent 1 in the solvated sheath in excess of this 1 1 ratio constitute what may be regarded as the complex with the polymer. In this particular example the value of is 1 mol of solvent-1 per mol of segment. If the molar volumes of liquid-1 and polymer segment were equal, the coefficient of selective adsorption could also be expressed here as 1 ml of liquid-1 per ml of monomer units. 

A problem with Equation (6.18) is the prefactor of the logarithmic term. Using the molar volume of liquid water, this factor is... 

Eor example, the molar volume of liquid H2O near the boiling point is about 18 cm", whereas that for water vapor is near 30,000 cm. ... 

Calado and Gomes de Azevedo (11) have measured the molar volume of liquid mixtures of ethane and ethene at 161.39 K. Their values are shown in Table 18.7. 

TABLE 18.7. Molar Volume of Liquid Mixtures of Ethane and Ethene at 161.39 K... 

Fedors, R. F., A Method for Estimating Both the Solubility Parameters and Molar Volumes of Liquids. Poly. Eng. Sci., 1974 14, 147-154. 

Water is highly unusual in that the density of water is greater than that of ice. We know that from a common observation ice floats on water. Therefore, at the melting point, the molar volume of liquid water is less than that of ice. As a result, high pressures can encourage ice to melt at a lower temperature, and the melting point of water decreases as the pressure is increased (see Section 5.14). 

In evaluating this exponential term (the Poynting correction), it is important to recognize that u is not the molar volume of i in the gas phase, but the molar volume of i dissolved in the membrane material, which is approximately equal to the molar volume of liquid i. 

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.

Estimate the specific molar volume of liquid benzene using the Rackett equation (3.72). 

Although the molar volumes of liquids can be calculated by means of generalized cubic equations of state, the results are not of high accuracy. However, generalized equations are available for the calculation of molar volumes of saturated liquids. 

A rigid vessel, filled to one-half its volume with liquid nitrogen at its normal boiling point (-195.8 C), is allowed to warm to 25°C. What pressure is developed The molar volume of liquid nitrogen at its normal boiling point is 34.7 cm3 mol-1. 

TABLE 4.4 Group contribution of CH2 to molar volume of liquids... 

It must be emphasised that Hoy is the only author who uses a "base value" in the calculation of Ft/ whereas he neglects a base value in V. It was mentioned earlier that Traube (1895) already proved that for the additive calculation of the molar volume of liquids a base value has to be used (see Chap. 4). 

Comparison of molar volumes of liquid nitrogen(l) + methane(2) predicted with the GvdW and the TBS equations of state with experimental data [10]. 

Af=mol. wt., and iV=Avogadro s number. Jouniauxi plotted the molar volumes of liquid metals against the temperature, and found that the curvatures of the plot are opposite in sign for monatomic and polyatomic metals. 

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