0
$\begingroup$

I know that during melting, latent heat is used in increasing potential energy (as intermolecular distance increases) of the complete structure of given solid to liquid. But it can also happen gradually. For example, when we gradually increase the temperature of ice from -10 degrees to -5 degrees to 0 degrees, we should just see an increase in potential as well as kinetic energy. Because while giving energy, it can also increase the distance of molecules as well as change its kinetic energy. But in contrast, it is observed that water has a sharp melting point. Why is that? Also, I am aware that amorphous solids have a range of temperature for melting phase, but don't know how this actually works.

$\endgroup$
5
  • $\begingroup$ Review the guide How to ask and Asking FAQs to prevent clarification requests, objections, downvoting or closure. $\endgroup$
    – Poutnik
    Commented Apr 8 at 12:37
  • $\begingroup$ Actually it is the contrary for melting. In the context of introductory chemistry, energy is given to decrease the potential energy and increase the kinetic energy so that the average intermolecular distance increases. Potential energy is so high in solids that they do not flow, and its kinetic energy only serves for the mode of vibration regarding motion. On the contrary, liquids also have a high potential energy, but its kinetic energy is sufficient that they can flow or 'slide' between layers of fluids at the macroscopic scale. This is very loosely speaking. $\endgroup$ Commented Apr 8 at 12:42
  • $\begingroup$ @MetalStorm Is it true for all cases? For example, if a solid just below its melting point has significantly higher density than liquid just above the melting point, can it be, that potential energy also increases with melting? $\endgroup$
    – Paul Kolk
    Commented Apr 8 at 16:03
  • $\begingroup$ @PaulKolk As a general rule, yes. The fact that the solid has a higher density, means that the potential energy of the solid is greater than the liquid. The potential energy decreases, and as a consequence the density decreases, as it happens in liquids. There are anomalies, water is one for example. Of course, I am avoiding the question of what we refer to as potential energy when the state of aggregation is a solid, or liquid, or gas. I am speaking in the context of introductory chemistry. $\endgroup$ Commented Apr 8 at 21:24
  • $\begingroup$ @MetalStorm So, You are saying, in "introductory chemistry" sign convention for potential energy is opposite to sign convention for kinetic energy. In physics, for example, I think potential energy of a bound state is said to increase, as it is becoming less bound (that happens, if density decreases with thermal expansion). $\endgroup$
    – Paul Kolk
    Commented Apr 9 at 10:43

3 Answers 3

1
$\begingroup$

You ask why a single melting point exists. In a pure crystal each identifiable unit repeats itself throughout the crystal so that if all of it is at the same temperature then each part behaves in the same way, on average, and melting happens over a very small temperature range. You can imagine amorphous material as a mixture so you would expect a range of melting points.

We will suppose that the crystal consists of atoms for simplicity. There are weak intermolecular bonds holding the crystal together, weak compared to chemical bonds that is. Each of these has a potential energy (much like a vibrational harmonic potential in a diatomic) and the energy levels are quantised. The average energy of the vibration is $k_BT$ ($k_B$ is the Boltzmann constant) which is $k_BT/2$ of kinetic energy and $k_BT/2$ potential energy. The vibrations occur between two atoms and in a crystal the inherent symmetry allows these vibrations to form wavelike motion called phonons much like the way photons form waves. This means that the vibrations from each quantum level are in phase with one another. As the temperature rises many more levels become populated and more phonons produced, and these 'crash' about the crystal. As the energy increases the distance between the atoms increases and the vibrational energy levels become closer to one another because the potential must level off with distance, much like a Lennard-Jones or Morse potential does, simply because the crystal will melt. At high average energy (temperature) the phonons can no longer remain in phase with one another and each vibration moves randomly wrt all others and melting occurs.

Many years ago Lindemann suggested from some simple calculations that melting is related to the amplitude of vibrations between atoms, crudely put the solid shakes itself apart. The calculation suggest that at about an extension of $1/20$ of bond length melting occurs. This seems to be a v small change in length for such a big effect as melting, but a similar fraction is observed for the melting of many elements. It also explains why the melting temperature mirrors the Debye temperature (obtained from heat capacity vs temperature) as here the vibrations become independent of one another. It also explains why high melting temperatures are associated with high enthalpy of fusion, the ratio enthalpy(fus)/T(melt) across the elements being more or less constant (but there are exceptions). If bonds between atoms are strong it needs more energy to stretch/bend and break them.

$\endgroup$
0
$\begingroup$

The sharp melting point of water (or any pure substance) is due to the specific nature of phase transitions. When you heat a solid, the added energy indeed increases the kinetic energy of the molecules, causing them to vibrate more. However, the solid does not start to melt until a specific temperature, the melting point. At this temperature, the kinetic energy is sufficient to overcome the intermolecular forces holding the solid together, and the solid begins to turn into a liquid.

During the phase transition (melting), the temperature does not increase even though you're still adding heat. This is because the added energy goes into breaking the intermolecular bonds rather than increasing kinetic energy. Only after all the solid has melted will the temperature of the liquid start to rise again.

As for amorphous solids, they do not have a sharp melting point like crystalline solids do. This is because amorphous solids do not have a long-range ordered structure like crystals. Instead, their molecules are arranged more randomly. When heated, different parts of the amorphous solid will start to flow at different temperatures, resulting in a range of melting temperatures rather than a single melting point.

$\endgroup$
0
$\begingroup$

A pure substance has a chemical potential that is essentially a function of its temperature. This potential generally can be represented as a line as a function of temperature in a 3-dimensional space of temperature, pressure, and energy and is usually reduced to a line in a phase diagram. The energy factor is omitted. Each phase has its own line, the point of intersection is the melting point. If the substance becomes more complicated, externally with impurities, or internally with conformations, the phase lines become a tight bundle possibly making the intersection point larger. Additional components add dimensions to the system. The Gibbs phase Rule explains it well. The Physics complexity starts here: https://en.wikipedia.org/wiki/Brane.

If the solid-liquid lines are divergent an attempted change in temperature [associated with an addition or subtraction of energy] will induce a phase change depending on the change in energy content or the entropy increase.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.