Van der Waals radius

The van der Waals radius, rw, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals equation of state. The van der Waals radius, rw, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals equation of state. The van der Waals volume, Vw, also called the atomic volume or molecular volume, is the atomic property most directly related to the van der Waals radius. It is the volume 'occupied' by an individual atom (or molecule). 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 single atom, it is the volume of a sphere whose radius is the van der Waals radius of the atom: 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. The van der Waals volume of an atom or molecule may also be determined by experimental measurements on gases, notably from the van der Waals constant b, the polarizability α or the molar refractivity A. In all three cases, measurements are made on macroscopic samples and it is normal to express the results as molar quantities. To find the van der Waals volume of a single atom or molecule, it is necessary to divide by the Avogadro constant NA. The molar van der Waals volume should not be confused with the molar volume of the substance. In general, at normal laboratory temperatures and pressures, the atoms or molecules of a gas only occupy about ​1⁄1000 of the volume of the gas, the rest being empty space. Hence the molar van der Waals volume, which only counts the volume occupied by the atoms or molecules, is usually about 1000 times smaller than the molar volume for a gas at standard temperature and pressure. The following table shows the Van der Waals radii for the elements. Unless indicated otherwise, the data is given by Mathematica's ElementData function, which is from Wolfram Research, Inc.. The values are in picometers (pm or 1×10−12 m). The shade of the box ranges from red to yellow as the radius increases; gray indicates lack of data. Van der Waals radii may be determined from the mechanical properties of gases (the original method), from the critical point, from measurements of atomic spacing between pairs of unbonded atoms in crystals or from measurements of electrical or optical properties (the polarizability and the molar refractivity). These various methods give values for the van der Waals radius which are similar (1–2 Å, 100–200 pm) but not identical. Tabulated values of van der Waals radii are obtained by taking a weighted mean of a number of different experimental values, and, for this reason, different tables will often have different values for the van der Waals radius of the same atom. Indeed, there is no reason to assume that the van der Waals radius is a fixed property of the atom in all circumstances: rather, it tends to vary with the particular chemical environment of the atom in any given case. The van der Waals equation of state is the simplest and best-known modification of the ideal gas law to account for the behaviour of real gases: where p is pressure, n is the number of moles of the gas in question and a and b depend on the particular gas, V ~ {displaystyle { ilde {V}}} is the volume, R is the specific gas constant on a unit mole basis and T the absolute temperature; a is a correction for intermolecular forces and b corrects for finite atomic or molecular sizes; the value of b equals the Van der Waals volume per mole of the gas. Their values vary from gas to gas.