Thermodynamics of Phase Transitions

When you add heat (energy) to liquid water, the temperature of the water goes up until it reaches a “plateau.” This plateau occurs at the boiling point of water. Instead of increasing the kinetic energy (and speed) of the water molecules, heat added to liquid water at its boiling point is used to separate water molecules held together by intermolecular forces, increasing the distance between water molecules and transitioning them into a gas state. This process takes work, and the energy for that work is called the heat of vaporization. A similar plateau occurs at the melting point of ice… the temperature at which solid ice melts into liquid water. The melting point of ice at standard atmospheric pressure is 0 °C.

However, heat added to ice at its melting point is not being used to separate water molecules. Remember, liquid water is denser than ice, so water molecules in the liquid state are actually closer together than water molecules in the solid state. Intermolecular bonds are being broken between water molecules in the liquid state, unlike the solid state, but an equal number of new intermolecular bonds are being formed at the same time, so this should not have any net effect on the total energy of the system. To help us figure out where the heat added at the melting point is going, we can find a small clue in the temperature versus heat graph in the simulation above.

Notice how the temperature climbs faster when heating up ice compared to heating up liquid water. In our simulation, it only takes 17 kJ of energy to increase the temperature of ice by 50 °C while it takes over 75 kJ of energy to increase the temperature of the same amount of liquid water by 100 °C. Why? We know that the kinetic energy of a molecule is Ek = ½mv2, where m is the mass of the molecule and v is the velocity (or speed) of the molecule. To find the kinetic energy of a substance, all we have to do is add up the kinetic energies of all of its molecules.

At -50 °C, the water molecules in our simulation have a combined kinetic energy of 27.8 kJ. This increases to 34.0 kJ at 0 °C, and 46.5 kJ at 100 °C. This means that, of the 17 kJ of heat that was added to the ice to raise its temperature by 50 °C, only 6.2 kJ (or 36%) of that energy went into increasing the kinetic energy (and speed) of the water molecules themselves. And, of the more than 75 kJ of heat that was added to the liquid water to raise its temperature by 100 °C, only 12.5 kJ (or 17%) of that energy went into increasing the kinetic energy of the water molecules. Where did the rest of our energy go?

Calculating the Kinetic Energy of Water
Internal motions in molecules

Back when I first defined the temperature of a substance, I said that it is “a measure of the average kinetic energy of the molecules in the substance,” and that “kinetic energy is the energy that molecules have from translational motion (moving from point A to point B).” But that is not quite accurate. The temperature of a substance is a measure of the average kinetic energy that the molecules of the substance have from translational motion, but those molecules can also have kinetic energy from other forms of motion.

molecular rotational motion

One kind of motion you have already seen is rotational motion. Molecules rotate, and the faster an object rotates, the more rotational kinetic energy it has. But that’s not all. The atoms in a molecule can also rotate, as well as move back and forth. This back-and-forth motion of the atoms in a molecule is translational motion, but because it is periodic (happens at a regular frequency), it is often described as vibrational motion. A water molecule can vibrate along both of its chemical bond lengths and its chemical bond angle. The larger a molecule, the more complex its geometry, and the more chemical bonds it has (in other words, the more “degrees of freedom” that a molecule has), the more ways the molecule can vibrate.

atomic rotational and vibrational motions

Because these other forms of motion and kinetic energy are internal to the molecule, they do not contribute to a substance’s bulk temperature. But they do contribute to a substance’s heat capacity. Heat capacity is a measure of the amount of energy it takes to raise the temperature of a substance. When you heat liquid water from 0 °C to 100 °C, only 17% of the heat goes into increasing the translational kinetic energy of the water molecules (raising the temperature) while the remaining 83% of the heat goes into speeding up these other internal motions within the water molecules (increasing the internal kinetic energy of the molecules, but not raising the temperature of the substance). Once the liquid water reaches its boiling point at 100 °C, any additional heat goes into pulling the water molecules apart and is stored as electric potential energy.

Melting and the heat of fusion

Water molecules in a solid state do not rotate. The hydrogen (intermolecular) bonds between water molecules causes the molecules to orient themselves so that the oxygen atom in a molecule is always pointing toward the hydrogen atom of another molecule, and the two hydrogen atoms in the molecule are each pointing toward the oxygen atoms of two other molecules. This arrangement creates a repeating, crystalline structure.

If the water molecules in a solid state were to rotate, they would break the existing hydrogen bonds. This is actually what does happen in the liquid state. A water molecule in a liquid state will rotate, breaking the hydrogen bond with one of its neighboring molecules, but then forming a new hydrogen bond with a second neighboring molecule. This constant breaking and re-forming of intermolecular bonds is what gives a liquid its fluidity and distinguishes it from the solidity of a solid.

You can tell that the water molecules in liquid water have much more internal motion than the water molecules in solid ice by comparing their relative heat capacities. It took 17,000 J (17 kJ) of energy to increase the temperature of ice in our simulation by 50 °C. That works out to an average heat capacity of 340 J/°C for 10 mol of solid water. Meanwhile it took over 75,000 J (75 kJ) of energy to increase the temperature of liquid water in our simulation by 100 °C, which works out to an average heat capacity of 750 J/°C for 10 mol of liquid water. The extra energy needed to heat up liquid water goes into the internal motion of the water molecules.

At 0 °C (the melting point of ice), the water molecules in solid ice are not rotating and they have limited internal motion. But the water molecules in liquid water at 0 °C are rotating and they have much more internal motion. In order to transition a water molecule from a solid state to a liquid state, the internal motion of the molecule must be increased. This takes energy. When the temperature of ice plateaus at its melting point despite the continued addition of heat, it is because that heat is now going into increasing the internal motion of the water molecules so that those molecules can enter a liquid state. Once all of the water molecules have entered the liquid state, the temperature will start to climb again.

The energy required to increase the internal motion of water molecules and to transition them from a solid state into a liquid state is called the heat of fusion. The heat of fusion for ice at 0 °C and standard atmospheric pressure is 0.33 kJ/g or 6.01 kJ/mol. The heat of fusion is not stored as potential energy. It is stored as actual kinetic energy; it is just that this internal kinetic energy is not contributing to the substance’s bulk temperature.

Types of phase transitions

A phase transition is the transformation of a substance from one state (or phase) of matter to another. Some phase transitions, such as evaporation, occur at the surface of a substance. These transitions are probability driven and can occur at a range of temperatures. Other phase transitions, such as melting and boiling, occur at specific temperatures and either require or release “latent” heat (e.g., heat of fusion or heat of vaporization).

Phase Transitions
name state change location temperature latent heat
premelting solid → liquid surface range none
melting solid → liquid internal melting point heat of fusion
freezing liquid → solid internal/surface freezing point *heat of fusion*
sublimation solid → gas surface range none
deposition gas → solid surface range none
evaporation liquid → gas surface range none
boiling liquid → gas internal boiling point heat of vaporization
condensation gas → liquid internal/surface range *heat of vaporization*
* depends if the transition is occurring at the surface of a substance or inside a substance

Premelting, sublimation, and evaporation are all similar processes. Molecules at the surface of a substance with higher than average kinetic energy break away from the surface and enter a different state. Premelting (or surface melting) is when molecules at the surface of a solid break away and form a thin layer of liquid on the solid. Sublimation is when molecules at the surface of a solid break away and, instead of entering a liquid state, enter a gas state as vapor in the air. Evaporation is when molecules at the surface of a liquid break away and enter a gas state as vapor in the air. All three processes occur at the surface and are probability driven (the temperature determines the rate of the process, but the process will occur at a wide range of temperatures). The latent heat that an individual molecule requires to change state comes from the energy in the system; external heat is not required and there is no temperature plateau.

Freezing, deposition, and condensation are the reverse of the premelting, sublimation, and evaporation processes. In deposition, molecules in the gas state come into contact with molecules at the surface of a solid state and are “captured” by the intermolecular forces of those molecules, entering the solid state themselves. Deposition is a strictly surface phenomenon. Freezing and condensation are a little more complicated because they can both happen inside a substance and at the surface of a substance. When they occur at the surface of a substance, they are probability driven and the latent heat released by the individual molecules that are freezing or condensing can be absorbed by the system; there is no need to remove heat from the system for surface freezing or condensing to occur, and there is no temperature plateau.

When freezing and condensation occur in a substance, they are the reverse of the melting and boiling processes. A substance will only melt when energy is added to the system. The temperature of the substance will plateau at its melting point, and energy added to the system will go to rotating the molecules and increasing their internal motions until they enter a liquid state. If you stop adding energy to the system, melting will stop (although premelting at any solid/liquid boundaries may continue). It is the same with internal freezing. Place a liquid into the freezer and the temperature will drop until it plateaus at the substance’s freezing point. (In general, the melting point and the freezing point of a substance are at the same temperature.) Energy removed from the system will slow the rotation of the molecules and decrease internal motions until the molecules get locked into a crystalline structure and enter the solid state. Stop removing energy from the system and the internal freezing will also stop. The heat of fusion needed to add to a system to change a solid into a liquid is the same amount of energy that must be removed from the system to change a liquid into a solid.

Nucleation and crystal growth

Nucleation is the extremely localized formation of a different thermodynamic state within a substance. Common examples include the formation of tiny bubbles in boiling, tiny crystals in freezing, and tiny droplets in condensation. (When I say tiny in this case, I mean on the scale of a handful of molecules.) Boiling, freezing, and condensation all have to start somewhere within a substance. A liquid cannot change into a gas everywhere at once. The process has to begin at one or more specific sites, often at a surface or at some impurity within the substance. This is how cloud seeding works… the introduction of foreign substances into clouds to encourage the nucleation of tiny droplets of water from condensation. Without these nucleation sites, it is possible to carefully and slowly superheat or supercool a liquid (bring a liquid slightly above its boiling point or slightly below its freezing point).

The probability that a random group of molecules in a gas state will spontaneously come together to form a liquid cluster is incredibly small. It will happen, but it is much more probable that a molecule in the gas state will join a liquid cluster once one has already formed. So once a tiny bubble, crystal, or droplet has formed in a substance, it becomes the place in the substance where most of the boiling, freezing, or condensing occurs. That tiny bubble, crystal, or droplet will then grow very rapidly. This is called crystal growth in freezing.

Growing a salt (NaCl) crystal is very simple. Bring a cup of water to a boil. Slowly spoon in salt one spoonful at a time until you see salt collecting on the bottom of the cup. (This means that the salt solution is saturated. You will learn much more about solutions and saturation later in this unit.) Hang a thread in the cup so that the thread sits in the water but does not touch the bottom of the cup. Place the cup in a secure location and then wait several days for the water to evaporate. As the water evaporates, the salt that is dissolved in the water will precipitate out of the salt and water solution and form solid salt crystals. These salt crystals will grow along the thread and along the inner surfaces of the cup. Salt crystals would form without the thread, but the thread makes an excellent site for nucleation, so the crystals on the thread will often be larger than the crystals in the cup.

If you would like to try to grow one giant salt crystal instead of many smaller salt crystals, take a single salt crystal from your cup and repeat the crystal growing activity with the single crystal attached to the thread. Other crystals will still grow in the cup and along the thread, but because this seed crystal has a head start, it will grow much faster. Can you guess the geometric shape of the NaCl crystalline structure? If you use other types of salt in this activity, you may also see crystalline structures in other geometric shapes.