|MadSci Network: Physics|
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... http://mutuslab.cs.uwindsor.ca/schurko/molspec/a nimations/bird_concordia/R otationalSpectrumDiatomic.html 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 by.edu/chemistry/PChem/notes/NormalModes.pdf 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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