Enthalpies of phase changes are fundamentally connected to the electrostatic potential energies between molecules. The first thing you need to know is:
If you make a graph of potential energy vs. distance between two molecules, it will look something like this:  Here the y-axis represents electrostatic potential energy, the x-axis is radial separation (distance between the centers), and the spheres are "molecules." Since this is a potential energy curve, you can imagine the system as if it were the surface of the earth, and gravity was the potential. In other words, the white molecule "wants" to roll down the valley until it sits next to the gray molecule. If it were any closer than just touching, it would have to climb up another very steep hill. If you try to pull them away, again you have to climb a hill (although it isn't as tall or steep). The result is that unless there is enough kinetic energy for the molecules to move apart, they tend to stick together. Now, the potential energy function between any two types of molecules will be different, but it will always have the same basic shape. What will change is the "steepness," width, and depth of the valley (or "potential energy well"), and the slope of the infinitely long "hill" to the right of the well. Since we are talking about relative enthalpies of fusion and vaporization for a given system, we don't have to worry about how this changes for different molecules. We just have to think about what it means to vaporize or melt something, in the context of the spatial separation or relativity of molecules, and how that relates to the shape of this surface. First let's think about what happens when you add heat to a system of molecules (positive enthalpy change). Heat is a transfer of thermal energy between a hot substance and a cold one. It is defined by a change in temperature, which means that when you add heat to something, its temperature increases (this might be common sense, but in thermodynamics it is important to be very specific). The main thing we need to know about this is:
In other words, as the temperature increases, the average kinetic energy (the speed) of the molecules increases. Let's go back to the potential energy diagram between two molecules. You know that energy is conserved, and so ignoring losses due to friction (there won't be any for molecules) the potential energy that can be gained by a particle is equal to the kinetic energy it started with. In other words, if the particle is at the bottom of the well and has no kinetic energy, it is not going anywhere: If it literally has no kinetic energy, we are at absolute zero, and this is an ideal crystal (a solid). Real substances in the real world always have some thermal energy, so the molecules are always sort of "wiggling" around at the bottom of their potential energy wells, even in a solid material. The question is, how much kinetic energy do you need to melt the material?
This means you need enough energy to let the molecules climb up the well at least a little bit, so that they can slide around each other. If we draw a "liquid" line approximating how much energy that would take, it might look something like this: The red line shows the average kinetic energy needed for the particles to pull apart just a little - enough that they can "slide" around each other - but not so much that there is any significant space between them. The height of this line compared to the bottom of the well (times Avogadro's number) is the enthalpy of fusion. What if we want to vaporize the substance?
As the kinetic energy increases, eventually there is enough that the molecules can actually fly apart (their radial separation can approach infinity). That line might look something like this: I have drawn the line a little bit shy of the "zero" point - where the average molecule would get to infinite distance - because kinetic energies follow a statistical distribution, which means that some are higher than average, some are lower, and right around this point is where enough molecules would be able to vaporize that we would call it a phase transition. Depending on the particular substance, the line might be higher or lower. In any case, the height of this line compared to the blue line (times Avogadro's number) is the enthalpy of vaporization. As you can see, it's a lot higher up. The reason is that for melting, the molecules just need enough energy to "slide" around each other, while for vaporization, they need enough energy to completely escape the well. This means that the enthalpy of vaporization is always going to be higher than the enthalpy of fusion.
QUESTION #93 Asked by: Fidel The latent heat of fusion and vaporization both involve the heat required to change the state of a substance without a change in temperature. In the case of the latent heat of fusion it is the heat required to change a substance from a solid (ice) to a liquid (water) or vice versa while the latent heat of vaporization from a liquid (water) to a gas (steam) or vice versa. In solids, the molecules are very close together and the attraction between the molecules are great. This causes a substance to have a structure in which the molecules have little freedom to move, as you would see in the case of ice. In the case of a liquid, the molecules are closely spaced, though not as closely spaced as a solid, they have more freedom to move and the intermolecular forces are weaker that that of a solid. Thus a liquid can flow, unlike a solid. Now in a gas, the molecules are sufficiently far apart that there are little to no attractive forces. Because of this a gas can easily be compressed and take the shape of the container. Now as you heat a solid turning it into a liquid, you increase the kinetic energy of its molecules, moving them further apart until the forces of attraction are reduced to allow it to flow freely. Keep in mind the forces of attraction still exists. Now as you heat a liquid, turning it into a gas, the kinetic energy of the molecules are increased to a point where there are no forces of attraction between the molecules. The energy required to completely separate the molecules, moving from liquid to gas, is much greater that if you were just to reduce their separation, solid to liquid. Hence the reason why the latent heat of vaporization is greater that the latent heat of fusion. Answered by: David Latchman, B.Ss. Physics, University of the West Indies The above answer is essentially correct, however the folowing should be further clarified: The difference in enthalpies comes from the fact that a liquid molecule is stabilized by interactions with other nearby molecules (therefore a small heat of fusion) and a gas has very little intermolecular stabilization (hence a large heat of vaporization). The confusion comes from the idea that temperature is a measure of the average kinetic energy of a system, and since the temperature remains constant, the average kinetic energy must also remain constant. The extra energy required to cause a phase transition is actually potential energy. It is the energy required to overcome the bonds of nearest neighbors to the point that a phase transition can occur. So it really isn't a change in kinetic energy. Answered by: Joe Larsen, Ph.D. Chemistry, Rockwell Science Center, Los Angeles, CA |
Why is the latent heat of vaporization so much greater than the latent heat of melting?
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