Organic solvents’ Van der Waals volume in the book "Handbook of organic solvent properties, ISBN 0 340 64578 4" are very small, such as the Van der Waals' volume for methanol is 1.43. Is it correct? (Many papers reported the value for methanol is about 35 Angstrom^3)
The molar volume, symbol Vm,[1] is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ). It has the SI unit cubic metres per mole (m3/mol),[1] although it is more practical to use the units cubic decimetres per mole (dm3/mol) for gases and cubic centimetres per mole (cm3/mol) for liquids and solids.
The molar volume of a substance can be found by measuring its molar mass and density then applying the relation
Methanol as an example:
Molar mass: 32.04 g/mol
Density: 791.80 kg/m³
Vm = M/ρ
32.04/791800 x 1000000= 40.46 dm3/mol.
If you want to get the number in Angstrom unit, you should divide the above result by Avogadro number and then convert the unit of dm3 to Angstrom.
this is the way to calculate a molecular volume of any substance.
Hoping this will be helpful.
Note the temperature dependence, because the density is temperature dependent.
In the solid state, the result will be also different.
Methanol is self-associated by hydrogen bonding, therefore I expect that the experimental value will be less than the volume calculated from van der Walls dimension.
Molar volume and van der Waals volume tends to get confused a lot for some reason. They are different. On this rare instance (maybe not so rare these days with better Wikipedia editors), Wikipedia has a decent explanation:
"The van der Waals volume may be calculated if the van der Waals radii (and, for molecules, the inter-atomic distances and angles) are known. ..... For a molecule, it is the volume enclosed by the van der Waals surface. The van der Waals volume of a molecule is always smaller than the sum of the van der Waals volumes of the constituent atoms: the atoms can be said to "overlap" when they form chemical bonds."
So the van der Waals volume should be essentially constant regardless of the physical state of the molecule (solid, liquid, or gas), so long as the molecule itself is still intact. The van der Waals volume is different from molar volume (which is indeed temperature and phase dependent).
The van der Waals radii are essentially based on crystal data at low temperature, and contact distances between atoms. The estimation of vdW volume is bases on a number of models and it should be noted that the radii depend on the type of functional group in which the atom is engaged.
If the van der Waals radii may be considered as constant, the values are of experimental origin and may be (slightly) revised in the future. The precision of the vdW volume strongly depends on the models and cannot be regarded as very high.
For those who are interested in these evaluations, you may have a look at the Wikipedia article, references 1 and 2 (Bondi seminal paper of 1964 and reevaluation in 1996).
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