van der Waals radius
Element | radius (Å) |
---|---|
Hydrogen | 1.2 (1.09)[1] |
Carbon | 1.7 |
Nitrogen | 1.55 |
Oxygen | 1.52 |
Fluorine | 1.47 |
Phosphorus | 1.8 |
Sulfur | 1.8 |
Chlorine | 1.75 |
Copper | 1.4 |
van der Waals radii taken from Bondi's compilation (1964).[2] Values from other sources may differ significantly (see text) |
Types of radii |
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|
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.
van der Waals volume
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
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 gas only occupy about 1⁄1000 of the volume of the gas, the rest is 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.
Table of van der Waals radii
Van der Waals radius of the elements in the periodic table | |||||||||||||||||||||
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Group →
|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |||
↓ Period
|
|||||||||||||||||||||
1 | H 110[1] or 120 |
He140 | |||||||||||||||||||
2 | Li182 | Be153[3] | B 192[3] | C 170 | N 155 | O 152 | F 147 | Ne154 | |||||||||||||
3 | Na227 | Mg173 | Al184[3] | Si210 | P 180 | S 180 | Cl175 | Ar188 | |||||||||||||
4 | K 275 | Ca231[3] | Sc211[3] | Ti | V | Cr | Mn | Fe | Co | Ni163 | Cu140 | Zn139 | Ga187 | Ge211[3] | As185 | Se190 | Br185 | Kr202 | |||
5 | Rb303[3] | Sr249[3] | Y | Zr | Nb | Mo | Tc | Ru | Rh | Pd163 | Ag172 | Cd158 | In193 | Sn217 | Sb206[3] | Te206 | I 198 | Xe216 | |||
6 | Cs343[3] | Ba268[3] | Lu | Hf | Ta | W | Re | Os | Ir | Pt175 | Au166 | Hg155 | Tl196 | Pb202 | Bi207[3] | Po197[3] | At202[3] | Rn220[3] | |||
7 | Fr348[3] | Ra283[3] | Lr | Rf | Db | Sg | Bh | Hs | Mt | Ds | Rg | Cn | Nh | Fl | Mc | Lv | Ts | Og | |||
La | Ce | Pr | Nd | Pm | Sm | Eu | Gd | Tb | Dy | Ho | Er | Tm | Yb | ||||||||
Ac | Th | Pa | U 186 | Np | Pu | Am | Cm | Bk | Cf | Es | Fm | Md | No | ||||||||
Legend | |||||||||||||||||||||
Values for the van der Waals radii are in picometers (pm or 1×10−12 m)
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The shade of the box ranges from red to yellow as the radius increases; Gray indicate a lack of data. | |||||||||||||||||||||
Unless indicated otherwise, the data is from | |||||||||||||||||||||
Primordial From decay Synthetic Border shows natural occurrence of the element |
Methods of determination
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
Van der Waals equation of state
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:
The van der Waals equation also has a microscopic interpretation: molecules interact with one another. The interaction is strongly repulsive at a very short distance, becomes mildly attractive at the intermediate range, and vanishes at a long distance. The ideal gas law must be corrected when attractive and repulsive forces are considered. For example, the mutual repulsion between molecules has the effect of excluding neighbors from a certain amount of space around each molecule. Thus, a fraction of the total space becomes unavailable to each molecule as it executes random motion. In the equation of state, this volume of exclusion (nb) should be subtracted from the volume of the container (V), thus: (V - nb). The other term that is introduced in the van der Waals equation, , describes a weak attractive force among molecules (known as the van der Waals force), which increases when n increases or V decreases and molecules become more crowded together.
Gas | d ( Å )
|
b (cm3mol–1) | Vw (Å3) | rw (Å) |
---|---|---|---|---|
Hydrogen | 0.74611 | 26.61 | 44.19 | 2.02 |
Nitrogen | 1.0975 | 39.13 | 64.98 | 2.25 |
Oxygen | 1.208 | 31.83 | 52.86 | 2.06 |
Chlorine | 1.988 | 56.22 | 93.36 | 2.39 |
van der Waals radii rw in Å (or in 100 picometers) calculated from the van der Waals constants of some diatomic gases. Values of d and b from Weast (1981). |
The
For helium,[5] b = 23.7 cm3/mol. Helium is a monatomic gas, and each mole of helium contains 6.022×1023 atoms (the Avogadro constant, NA):
Crystallographic measurements
The molecules in a
A simple example of the use of crystallographic data (here
Molar refractivity
The
Polarizability
The polarizability α of a gas is related to its electric susceptibility χe by the relation
When the atomic polarizability is quoted in units of volume such as Å3, as is often the case, it is equal to the van der Waals volume. However, the term "atomic polarizability" is preferred as polarizability is a precisely defined (and measurable) physical quantity, whereas "van der Waals volume" can have any number of definitions depending on the method of measurement.
See also
- Atomic radii of the elements (data page)
- van der Waals force
- van der Waals molecule
- van der Waals strain
- van der Waals surface
References
- ^ .
- ^ .
- ^ PMID 19382751.
- ^ "van der Waals Radius of the elements". Wolfram.
- ISBN 0-8493-0462-8., p. D-166.
- ISBN 978-0-8014-0333-0.
- PMID 23632803.
- .
- ^ Kaye & Laby Tables, Refractive index of gases.
- ^ Kaye & Laby Tables, Dielectric Properties of Materials.
Further reading
- Huheey, James E.; Keiter, Ellen A.; Keiter, Richard L. (1997). Inorganic Chemistry: Principles of Structure and Reactivity (4th ed.). New York: Prentice Hall. ISBN 978-0-06-042995-9.
External links
- van der Waals Radius of the elements at PeriodicTable.com
- van der Waals Radius – Periodicity at WebElements.com