MadSci Network: Physics

Re: How is the bond angle measured between two hydrogens in a water molecule?

Date: Tue Sep 28 12:11:07 2004
Posted By: Kenneth Beck, Senior Research Scientist, Chemistry and Physics of Complex Systems, Pacific Northwest National Laboratory
Area of science: Physics
ID: 1095886516.Ph

Dear David,

The bond angle for water was first determined by rotational analysis of 
its infrared absorption spectra. Experimentally, spectra are recorded 
using water vapor or liguid water.  These spectra are then analyzed using 
a method called "normal mode analysis".  No, there is no direct way to 
measure this angle. Students of Chemistry and Physics generally do not 
appreciate this analysis until they are seniors in college or graduate 
students earning their Ph.D.s.  However, check out this rather long URL 
for a view of how the spectra of a "diatomic" (two-atom molecule) is 
measured and analyzed...

The "classical" method is based on a model of water in which the bonds 
between oxygen and hydrogen are treated much like rigid "springs" (think 
of the suspension on a heavy-duty pickup) and the atoms are treated a 
point masses.  These "springs" can stretch and they can bend.  The water 
molecule interacts with infrared light at specific energies, because 
these specific energies can be absorbed by the stretching and bending 
vibrations the molecule can undergo.  Sometimes, we say a molecule 
is "resonant" with a specific energy of light.  This is because we are 
thinking of the little oscillating "spring" - the molecular bond - as it 
is periodically excited by the light and vibrates.

Hooke's Law for an oscillating force is F = -kX, where the "equilibrium" 
bond length is X and k is the "force constant". The potential energy is V 
= (1/2)kX^2 to which we can equate the specific energies of light 
absorbed by water and then derive the force constant for each stretch and 
bend.  The force constant then allows us to determine the distance of the 
stretch or bend; the bond length and the bond angle.  Here is a more 
detailed description...

=> http://www.col

The "quantum mechanical" method routinely utilizes wave equations in 
place of rigid springs to model the water molecule.  Energies are 
assigned discrete levels and described with a molecular orbital view.

Hope this helps?

---* Dr. Ken Beck


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