Why is the molar enthalpy the vaporization the a substance larger than that molar enthalpy of blend (at constant pressure); because that example, in the case of ice and water.

You are watching: Why is heat of vaporization greater than fusion  Enthalpies the phase changes are fundamentally associated to the electrostatic potential energies between molecules. The an initial thing you require to recognize is:

There is one attractive force in between all molecule at long(ish) distances, and a repelling force at brief distances.

If you do a graph the potential energy vs. Distance between two molecules, it will look something favor this: Here the y-axis represents electrostatic potential energy, the x-axis is radial separation (distance between the centers), and also the spheres are "molecules."

Since this is a potential energy curve, you deserve to imagine the device as if it were the surface ar of the earth, and gravity was the potential. In other words, the white molecule "wants" to roll under the valley till it sits beside the gray molecule. If the were any closer than simply touching, the would need to climb up another very steep hill. If you try to traction them away, again you have to climb a hill (although that isn"t together tall or steep). The result is that uneven there is sufficient kinetic energy because that the molecule to move apart, they often tend to pole together.

Now, the potential energy role between any type of two varieties of molecules will be different, but it will constantly have the same straightforward shape. What will adjust is the "steepness," width, and depth that the sink (or "potential energy well"), and the slope of the infinitely long "hill" come the right of the well.

Since we space talking about relative enthalpies of blend and vaporization because that a offered system, us don"t need to worry about how this changes for various molecules. Us just have to think about what it method to vaporize or melt something, in the paper definition of the spatial separation or relativity that molecules, and how that relates come the shape of this surface.

First let"s think about what happens once you add heat to a mechanism of molecule (positive enthalpy change). Warm is a transfer of heat energy between a hot substance and a cold one. That is defined by a adjust in temperature, which way that when you add heat to something, the temperature increases (this can be typical sense, but in thermodynamics that is important to be an extremely specific). The main thing we have to know around this is:

Temperature is a measure up of the mean kinetic power of all molecules in a system

In various other words, as the temperature increases, the median kinetic power (the speed) of the molecules increases.

Let"s go back to the potential power diagram between two molecules. You understand that power is conserved, and so skip losses as result of friction (there won"t be any type of for molecules) the potential energy that can be gained by a bit is equal to the kinetic power it began with. In other words, if the fragment is in ~ the bottom that the well and has no kinetic energy, that is not going anywhere: If it literally has actually no kinetic energy, we room at absolute zero, and this is an ideal crystal (a solid). Real substances in the genuine world always have some heat energy, therefore the molecules are always sort the "wiggling" approximately at the bottom of your potential power wells, also in a heavy material.

The concern is, exactly how much kinetic energy do you must melt the material?

In a liquid, molecule are free to move but stay nearby together

This means you need enough power to let the molecules rise up the well at the very least a tiny bit, so that they have the right to slide around each other.

If we attract a "liquid" line approximating just how much power that would take, it could look something choose this: The red line reflects the median kinetic power needed for the corpuscle to pull apart just a small - enough that they have the right to "slide" approximately each various other - however not so lot that over there is any far-ranging space in between them. The elevation of this line compared to the bottom that the fine (times Avogadro"s number) is the enthalpy of fusion.

What if we want to vaporize the substance?

In a gas, the molecules are cost-free to move and are very far apart

As the kinetic power increases, ultimately there is enough that the molecules can actually paris apart (their radial separation can technique infinity). The line can look something prefer this: I have attracted the heat a little bit shy of the "zero" suggest - wherein the typical molecule would acquire to boundless distance - since kinetic energies follow a statistics distribution, which way that part are higher than average, some room lower, and also right approximately this suggest is where sufficient molecules would be able to vaporize that us would contact it a phase transition. Depending upon the certain substance, the line might be higher or lower.

In any type of case, the height of this line contrasted to the bottom that the well (times Avogadro"s number) is the enthalpy that vaporization.

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As you can see, it"s a lot higher up. The reason is that for melting, the molecules simply need enough power to "slide" around each other, while for vaporization, they require enough energy to completely escape the well. This means that the enthalpy the vaporization is always going come be higher than the enthalpy of fusion.