Molar volume of compound

The molar volume of compounds is the volume that one mole of compound will occupy at a particular temperature. It can be calculated by dividing the atomic weight, AW, of an element by its density. 

Jacob et al. used the method of characteristics to discuss the general properties of the system of mass balance equations in multicomponent preparative gas chromatography (GC) [34-36], assuming either a linear or a nonlinear isotherm. The GC problem is more complicated than the HPLC one because the gas mobile phase is much more compressible than a solution and the mobile phase velocity is very different inside and outside a high concentration band because the partial molar volumes of compounds are much larger in the gas mobile phase than in the condensed stationary phase (the sorption effect). They showed that the method of characteristics appHes to multicomponent systems as well as to single component... 

For benzene at 25°C this becomes AU = 33,900 - 8.314 (298) = 31,400 J mol". The molar volume of a compound is given by V° = (molecular weight)/ (density). For benzene at 25°C, this becomes V° = 78.0/0.879 = 88.7 cm mol". Tlie cohesive energy density is simply the ratio AUy/V°, but in evaluating this numerically, the question of units arises. By convention, these are usually expressed in calories per cubic centimeter, so we write... 

Studies of the molar volumes of perdeuteriated organic compounds might be expected to be informative about non-bonded intermolecular forces and their manifestations, and such studies might be considered to obviate the necessity of investigating steric isotope effects in reacting systems. The results from non-reacting systems could then be simply applied to the initial and transition states in order to account for a kinetic steric isotope effect. 

The molar volumes of CH4 and CD4 are known to differ in the expected direction in the condensed phases at low temperatures (Olusius and Weigand, 1940 Grigor and Steele, 1968). Such a difference would in principle originate in the movement of the molecule as a whole as well as in its carbon-hydrogen oscillations, but a macroscopically available compound would be expected to offer better possibilities for experimental investigation than poorly known transition states. 

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. 

Finally, it should be noted that the effect of the compressibility on the thermodymanics of solids is small even at relatively high pressures. The molar volume of magnetite, Fe3C>4, at 1000 K is 46.0 cm3 mol-1 and VAp at p = 1 GPa is 46 kJ mol-1 if the compressibility of the compound is neglected. Taking compressibility into account reduces this contribution to 45.88 kJ mol-1 [29],... 

A thermodynamic parameter (dV/dnB)T,F,n g which describes how the volume of component S in a multicomponent system depends on the change in its amount expressed in mol. Hpiland recently summarized the partial molar volumes of numerous biochemical compounds in aqueous solution. See Dalton s Law of Partial Pressures Concentrations Molecular Crowding... 

Molar volumes of organic compounds in the liquid state m3/kmol... 

Note that CiL is the inverse of the molar volume of the liquid compound, which we denote as viL. Substitution ofEqs. 3-17 and 3-18 into Eq. 3-16 yields ... 

Hence, if no experimental value for AuHi is available (i.e., from measurements of Ka( ) at different temperatures), it can be obtained from experimental (or estimated) AvapH, and Hfe values. Finally, we should note that Eq. 6-8 applies in a strict sense only if we express the amount of the compound in the gas and liquid phase as partial pressure and mole fraction, respectively. However, if we assume that the molar volume of the liquid, Vi, is not significantly affected by temperature changes, we may also apply Eq. 6-8 to describe the temperature dependence of K,n ( ) (Eq. 6-5) with a constant term that is given by constant + In Ve Furthermore, if we express the amount of the compound in the gas phase in molar concentrations (Eq. 6-6), then we have to add the term RTm to Aa< // where rav (in K) is the average temperature of the temperature range considered (see Section 3.4) ... 

It is seen, firstly, that the ratio of the thicknesses of the ApBq and ArBs layers depends upon (/) the values of the physical (diffusional) constants, (ii) the ratio of the molar volumes of the ApBq and ArBs compounds, (///) the stoichiometry of these compounds. ... 

The first term wt = (l+2rc)1/2 of the power series w defined in Eq. (6-10) plays a special role within the interaction model in that it represents a perfect gas phase. If Vo, pc, Tc and R represent the molar volume of a compound, the critical pressure and critical temperature of the system and the gas constant, then the product pcV0 is reduced to llw of the product RTC due to the interaction between the particles in the system. Taking into account an empty (free) volume fraction in the critical state, the critical molar volume is written as Vc = V(). Consequently, a dimensionless critical... 

---