The Potential Energy Diagram for a Diatomic Molecule
The states of a molecule are quantized and can be represented by a potential energy diagram. This potential energy diagram represents a diatomic molecule. On the x axis, we examine the internuclear distances between the two atoms. As the atoms approach an internuclear distance of zero, their potential energy is infinite. This is because the two atoms cannot occupy exactly the same point at the same time. Repulsion forces dominate, and there is no chemical bond. The point with the lowest potential energy of the graph is the ideal bond length of the diatomic molecule. Then, for increasing values of internuclear distance between the nuclei of the two atoms the potential energy increases and no bonding occurs as the attractive forces are too weak. Essentially, the two atoms are too far apart to have a bond. Note that when two atoms approach one another from infinite distance (righthand side of graph), the energy of the system is lowered.
This can be compared to you and a not so close friend sitting on a chesterfield (sofa, couch, whatever) together. Let's call your friend Matthew. If Matthew and you both sit on the far ends of the chesterfield, chances are you are less likely to have a conversation and be friendly together. Other elements in your environment aka other friends could come and sit between you both, and so you might be closer these other friends, and hence more engaged with them. This is analogous to no bonding at great distances. Now if you decide to sit on top of Matthew, he will not be very happy with you because he doesn't know you very well. Chances are he'll go all cactus mode and repel the physical contact. Sounds like what happens to two atoms with a internuclear distance approaching zero! However, to achieve the optimal comfort level, you would sit beside Matthew close enough to be friendly, but far enough away to respect both of your personal bubbles. Hence, you experiencing bonding at this distance.
Now the funky stripes on the potential energy diagram represent the vibrational energy of the molecule. The lowest vibrational state is above the minimum potential energy on the curve. Why? Well, according to the Heisenburg Uncertainty Principle, the both the bond length at equilibrium and the vibrational motion can not simultaneously be known. This point is called the zero point.
Taking a Closer Look
Let's zoom in on some of these vibrational states on the potential energy diagram.
We find in between them superimposable rotational states that also describe the state of the molecule. Even further in between these rotational states we find the translational states of the molecule. This is because
Now, I can't really use the Matthew analogy here, because a vibrating Matthew is just a very, very bad idea (yikes, did I actually just write that?), but I will attempt to explain in greater detail where on earth these states come from!
Molecular Quantum States
The states of a molecule are quantized. Here is how these various quantizations are defined (I realize the definitions here may be crude, however this is the level we are expected to understand for this course, so it isn't too elaborate.):
a) electronic states: recall the s, p, d, f orbitals for atoms. There is a similar method out there for molecular states.
b) rotational states: these the same as other angular momentum, like the angular momentum in orbitals. These are usually denoted by quantum numbers Jmj where J goes from 0 to infinity and -J < mj < +J . Spin also has angular momentum given by either +1/2 or -1/2.
c) vibrational states: go in integer values from v=0 to infinity.
d) translational states: can be eliminated by sitting on the frame reference of the molecule and hence are usually not of interest. This can be done by taking a frame of reference. For insistence if you bus from your apartment to St. Viateur bagel, the motion of the bus is counted as stationary if you consider the frame of reference of the bus. So if you "sit" on top of a molecule, its translational states can be ignored.
The states we examine in thermodynamics are all from the world of the macroscopic.
These states (electronic, rotational, vibrational, translational) discussed above are from the quantum world - the microscopic. However, since the lectures took a substantial aside in this direction to explain heat capacity as it is related to the thermal energy of the substance, the information above is probably relevant.
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