I read in Voet & Voet that the hydrogen bonds are at least 0.5 angstrom shorter than the calculated van der waals distance. As I understand, van der waals distance is the distance of closest approach between two atoms/molecules. How are two water molecules able to break this to get closer to each other and form hydrogen bonds?
We also know that ice is less dense than liquid water. In ice, water molecules are hydrogen bonded to each other and the distance between them is shorter than van der waals distance. but it liquid water not all of them is hydrogen bonded and it should be ideally at a minimum distance of van der waals and the density should be less. What is making the water molecules to interact closer to make liquid water more dense than ice?
Regular ice is hexagonal ice, meaning that the crystal structure in the hexagonal unit cell is the reason for ice to have a low density. The liquid state due to larger thermal energy does not allow it to form strong and thermally stable long lasting hydrogen bonds, like in hexagonal ice.
http://www1.lsbu.ac.uk/water/hexagonal_ice.html
It starts with your premise. Van der Waals distances are not the closest approaches between two atoms/molecules. VdW distances (and vdW radii) are averaged quantities stemming from typical and essentially unpolar organic molecular crystals (if we restrict the discussion to the upper part of the periodic system).
A well known feature of all weak and medium strong hydrogen bonds is that as e.g. in the H2O dimer, (H2O)2, with an O-H---O hydrogen bond, the H---O distance is significantly shorter (about 2.0 Angstrom) than the sum of the vdW radii (about 2.9 angstrom).
Due to non-additivity effects the hydrogen bonds are additionally further reduced in hydrogen-bonded clusters, liquids and solids as e.g. in liquid water or ice, thus even farther away (by an additional 0.2 angstroms) from vdW distances. Similar findings are also encountered in other intermolecular mechanisms, like halogen bonding, etc.
The main reason for the occurence of significantly shorter intermolecular distances in hydrogen-bonded systems X-H---Y is the strong contribution of electrostatics when X-H is polar (proton donor) and Y is an electronegative atom with a lone pair.
Concerning the differences between water and ice, I suggest to google "hydrogen bond water ice".
As Alfred points out, there is considerable averaging associated with the Van der Waals forces, which typically become important for nonpolar molecules. Water is highly polar, so there is considerable dipole-dipole attraction. Not only that, consider the geometry of approach. Suppose a hydrogen of one water molecule is pointed at the lone pair of another water molecule - the approach would be purely attractive, with nothing to overcome.
As a side note: In (some) molecular-mechanics force fields, hydrogen atoms in OH groups are conveniently defined as point charges with zero van der Waals radii.
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