How do we know how strong the intermolecular or interatomic forces are? I see on Wiki that the force between two positive charges of one Coulomb that are one meter apart is xyz Newtons. How has that been determined? And is there a good source of general information such as this that explains “How do scientists know this?” ? Thanks, dopers. xo, C.
The fast answer is that you heat the stuff until it falls apart. By keeping track of how much energy is added, you can find just how much is needed to overcome the intrinsic attraction between molecules.
Short and sweet, people, this is what an answer should look like! Thanks Doc.
And now for the more complicated answer. Maybe a physical chemist will come by to do a better job, but this is the best I can do. There are several ways that I know of.
Method 1:
As DrFidelius mentioned, we can measure the decomposition temperature, but this may not help you if you want to know the bond energy of a specific bond in a molecule (although it could be a part of the process if you know the products.) Using known Heat of Formation and energy released in known reactions one can use a Born-Haber cycle to determine Heat of Formation of a compound. For example, if I know the heat of formation of water from oxygen and hydrogen, and I know the heat of formation of carbon dioxide from carbon and oxygen, then by measuring the energy from the reaction of methane with oxygen I can get the heat of formation of methane. Methane is one carbon attached to four hydrogens, so by dividing the Heat of Formation by four I get the Bond Energy of one C-H bond. Since many C-H bonds are similar, this number can be used as an approximation for many other molecules.
But this brings up a problem with your question. There is more than one way to break a bond. In the case of methane I just mentioned, we measured the energy to pull a Hydrogen radical away from a CH[sub]3[/sub] radical. That is called a homolytic Bond Energy because each atom gets 1 electron from the bond. In the gas phase, this type of bond breaking is common, but in solution it’s quite rare (and usually a problem).
You can also imagine splitting the bond heterolytically so that CH[sub]3[/sub]-H goes to CH[sub]3[/sub][sup]-[/sup] and H[sup]+[/sup]. Nevermind how difficult this specific reaction is, the energy of this bond breaking is quite different (and dependent on the environment).
Method 2:
As you eluded to with your mentioning coulombic attraction, computers these days are quite capable of calculating these things. It’s been a long time since I have dealt with the “How” of these calculations and even when I did them in class they were a universe away from what the computers are actually doing. These calculations revolve around the Shroedinger Equation and various published methods of simplification and approximation. I would guess that any of the physicists on this board would be better suited to explain them.
Calculations that are strictly based on the math, using first principles of physics are known as ab-initio calculations. These calculations are very good for small molecules. For larger molecules, the computer time becomes impractical, so these calculations are not often used. (I’m considering DFT to be semi-empirical)
Most calculations are what is known as semi-empirical. In a sense, this is a way of combining the experimental data (acquired in the first method) with the computational methods. For example, from the first method, I have an idea of the bond energy in typical C-H bond. The computer will “find” C-H bonds in your molecular model and use this informations as a starting point.
As molecules become more complex, the computer power required will become too much. In these cases, the Schroedinger Equation is dropped completely and the atoms are dealt with as simple electric field gradients. This is typically what will be used for proteins and the like.
You can get even more precise than that; Bob Millikan’s famous oil drop experiement determined the precise charge of the electron and the resulting force of attraction. (Millikan had the wrong value for the viscosity of air and so his result was a little bit off, but it’s still amazing that he was able to demonstrate the quantum nature of electrodynamic exchange with such a primative experiment.)
The internuclear forces are a little more difficult; you have to calculate the energies of the system and add up the change from the resultant products to figure out what kind of forces are developed by the nuclear binding energies. This is relatively simple to do for something like a hydrogen atom, but painfully convoluted for a more complex element.
Surprisingly, the force we know with the least precision is one we visibly experience every day: gravity. Because it is so weak it’s very hard to measure its effect on a reasonable-sized mass that we can directly measure. Mind you, we know it to enough digits and beyond for any engineering application, including plotting interplanetary orbital ballistics, but it’s still the force we quantify to the least precision.
Other “forces”, like the van der Walls force, air pressure, centrifugal force, et cetera, are really composite or inertial (sometimes called ‘ficticious’) forces; they are a result of the combination of inertia or momentum and one or more of the fundamental forces. For instance, when you catch a ball, the “force” that you feel is from the momentum of the ball and the interaction of electromagnetic forces between the glove and the ball. The force an astronaut feels as he rides a rocket to orbit is a contest between gravity and the thrust of the motor (caused by the necessity of balancing the inertia of the rocket with the propellant being thrown out the back). Any single force acting without opposition–like said astronaut in a free-fall orbit–is unresolved and unfelt.
Stranger
While the title of the thread asked about molecules, the body of the question just asked about Coulomb’s law in general. To which the answer is obvious: You take two charges of known magnitude, put them a known distance apart, and measure the force. Do this with enough different values for the charges and distance, and you can see the pattern, which lets you determine the force even for the cases where you haven’t done the experiment.
In fact, one should more properly view this statement as the definition of a coloumb: it’s the amount of charge that, when imparted to two objects one meter apart, results in a force of one Newton between them. This then allows you to relate charge (and other SI electromagnetic units such as ohms, amperes, tesla, and so forth) to the “mechanical” units of mass, length, and time.
To me, it’s not so obvious how one would take two charges of known magnitude and put them a known distance apart and measure the force. That’s actually my question - how do they do this? Specifically, how do they measure this force?
Wow did I interperet that question wrong. Physicists, this is your game. Anything I have to say is conjecture and probably wrong.
CC: Your title is a bit misleading. Molecular interactions are only a very specific example of coulombic interactions.
I would hope that you’re not defining the coulomb that way… The SI electrical units (coulombs, amps, volts, etc.) are actually defined in terms of the magnetic force between two wires.
Typically, by measuring how much a spring is stretched, the same way (in principle) that the scale at the grocer’s measures the force exerted by the bunch of bananas on it. If you don’t trust the springs, then you can calibrate them by exerting a force on a known mass, and measuring its resulting acceleration.
Yes, upon further reflection, I’m an idiot. In SI, current comes first, then charge & the rest of the electromagnetic units. What’s more, the repulsive force between two one-coulomb charges one meter apart isn’t one newton; I was getting that mixed up with CGS units, in which two one-statcoulomb charges one centimeter apart exert one dyne of force on each other. Mea culpa.
As an aside, in the Feynman Lectures on Physics, it says that if you had two one millimeter on a side cubes, and one was all positive charge, and the other was all negative charge, and they were separated by 30 meters, the force between them would be three million tons.
Now this is, of course impossible to do, but, nonetheless, it shows pretty clearly how chemical bonds can be so strong and why chemical reactions can be so violent.
You can find this in Volume I page 2-4