Naked Science Forum
Non Life Sciences => Chemistry => Topic started by: Kryptid on 14/06/2008 12:22:17
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The bond dissociation energy for the nitrogen molecule (N≡N) is about about 945 kilojoules per mole. That's how much energy it takes to break the molecule down into its component atoms. However, what I want to know is the amount of force that is holding those two nitrogen atoms together. Is there any way to calculate that? Is there any correlation between bond dissociation energy and the bond force? What about for other molecules like H2 or O2? Is calculating the force different for a heteroatomic molecule like carbon monoxide (CO)?
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There isn't any one value for the force that holds them together. It depends on the distance. If you try to push the two nitrogens together then they will repel eachother- the nearer you get them to eachother the stronger the force.
Similarly as you try to pull them apart the force needed gets bigger as you move them further than their "normal" bond length. Of course, if you pull them far enough apart the bond weaken and the force gets weaker again.
For small diplacemnts from their normal distance they act like a spring. You can work out the strength of that spring from the masses of the atoms and the frequency of the vibration. For many molecules you can get that vibration frequency from infra red spectroscopy. In the case of so called homonuclear diatomics like H2, N2 etc (2 identical atoms stuck together) IR spectra don't work so you would have to use raman spectra.
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You could get a very crude idea of the amount of force in the following way.
Find the energy per molecule (divide by the Avogadro Number).
The separation energy can be looked upon as doing work during separation.
That is force times distance.
The system behaves a bit like a spring over the small distance until bonds actually break.
There is a very good link which puts the problem in these mechanical terms for carbon bonds.
The answer they come up with is about 3.5e-9N for each bond.
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3.5nN for one bond. Bear in mind that 1g weighs 0.01N. That is only 30 million times the binding force of one molecule. There will be something like 10e21 atoms in that 1g of stuff. It certainly brings it home to you how much stronger electrostatic forces are than gravitational forces.
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So does that mean that if you were to apply a force of 3.5 nanonewtons to a single nitrogen molecule, you could dissociate the molecule into its component atoms?
The reason I ask about such forces is because I would like to be able to mathematically predict the tensile strength of a material by knowing the amount of force needed to overcome the chemical bonds in the material. Strictly speaking, I know that a sample of solid nitrogen is held together by van der Waals forces, which is what its tensile strength is dependent on and not its covalent N≡N bonds. More specifically, I'd like to be able to predict the tensile strength of a network solid (like diamond), whose structure is held together by covalent bonds.
My ultimate goal is to be able to estimate some kind of upper limit on the maximum possible tensile strength of normal matter; a limit that technological advances in material science cannot possibly overcome in the future. You might call this "unobtainium".
Here's my (crude) idea. I think of a form of unobtainium whose atoms are arranged in the most compact possible way (either the cubic close-packed or hexagonal close-packed system). In these systems, each atom is surrounded by 12 neighbors. Each atom is covalently bonded to each of its 12 neighbors by bonds of the shortest, strongest possible bond strength (something like N≡N at 945 kJ/mol, C≡N at 754 kJ/mol, or C≡O at 1,077 kJ/mol). In order to estimate the tensile strength/weight ratio of the unobtainium, we model each atom as being as light as possible (the nucleus is a single proton, equal in weight to hydrogen).
I know that a material like this is impossible for more than one reason. For one, no atom can form 12 triple bonds. For another, hydrogen sure can't do it. However, this would still be a revealing calculation, as it could show that no material composed of normal matter could possibly have a tensile strength/weight ratio as high as this unobtainium, regardless of technological advances. The true limit on tensile strength/weight ratio is probably quite a bit less than that of this unobtainium. This doesn't include considerations of exotic matter like neutronium or whatever, though.
If you can think of a more reasonable, conservative way of estimating matter's strength limits, I'd be interested in hearing it.
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Yes, I think so - for the first paragraph.
The rest is a bit speculative and, as you say, is based on an unobtainable model. Why not discuss a vaguely possible option? The logic is that there are a limited number of bonds available so work with that.
Diamond does pretty well! And you can make them.