Now that we have the laws of thermodynamics and the primary state functions defined, let's see what we can do with them to predict some chemistry. To keep it simple, let's restrict ourselves to single-component systems for this initial foray into chemical phenomena and investigate phase transitions. Depending upon the temperature and pressure, one, two or even three phases of the same compound might possibly be stable at the same time. Changing either temperature or pressure could upset the equilibrium and result in a loss of a phase through a phase transition. Temperatures at 1 bar for elemental phase transitions can be found at this web site.

At 298 K both water vapor and liquid water are stable phases, with an equilibrium vapor pressure of about 24 torr (0.032 bar). First, let's keep the temperature constant and vary the pressure of the system (our water) by playing with the volume of the container. If we decrease the container volume, causing the vapor pressure temporarily to exceed 24 torr, water will condense from the gas phase until the vapor is again at 24 torr. If we increase the volume of the container, causing the pressure to drop temporarily, liquid water will evaporate until either all the liquid is gone or the vapor pressure is again 24 torr. If we keep the temperature constant, there is one and only one equilibrium vapor pressure in our two-phase water system.

Now let's increase the temperature, letting the volume vary to maintain equilibrium, and study what happens to the gas-liquid system. Once we know the equilibrium vapor pressure (P₁) at one temperature (T₁), we can find it at any other temperature by using theClausius-Clapeyron equation

where Δ_vapH is the enthalpy of vaporization of the liquid. This equation was derived by setting the Gibbs free energy of the vapor and the liquid equal so that Δ_vapG = 0, our equilibrium condition. There are a number of assumptions made in deriving the Clausius-Clapeyron equation, including that the vapor pressure behaves as an ideal gas and the enthalpy of vaporization is independent of temperature (which allows us to use tabulated values at the liquid's normal boiling point). Nevertheless, it works pretty well most of the time. The equation can also be used for solid-vapor equilibria where the enthalpy of sublimation is substituted for Δ_vapH in the equation above. If you want to practice some problems using the Clausius-Clapeyron equation, this web site will check your answers for you.

The equilibrium vapor pressure will increase with temperature as predicted by the Clausius-Clapeyron equation, but will not do so indefinitely if the ambient pressure is held constant, for example if the liquid-vapor system is exposed to the atmosphere. Eventually, the equilibrium vapor pressure will reach that of the ambient and the liquid will boil. Above this temperature, only the vapor will be thermodynamically stable and there will no longer be a liquid-vapor equilibrium. For water at 1 bar, the highest temperature at which liquid water is thermodynamically stable is 373.15 K, its normal boiling point. You can, of course, have liquid water at higher temperatures than the normal boiling point if you allow the pressure to increase, for example if you heat the liquid in a closed container. A pressure cooker contains vapors to about 1 bar over atmospheric pressure before letting stem escape. As the water evaporates, its vapor pressure adds to the ambient pressure raising the boiling point of the liquid accelerating the cooking of food. Use this calculator showing change in boiling point of water with pressure change to calculate the temperature in a pressure cooker. Atmospheric pressure at high altitudes causes water to boil at a lower temperature. Try Denver at 5000 ft above sealevel in the calulator. Underwater vents in the ocean may display very temperatures without boiling.

If we were to supply heat at a constant rate, dq, to a liquid below its normal boiling point, we would notice that the temperature would increase in inverse proportion to the heat capacity of the liquid

until the normal boiling point of the liquid was reached. At that point, boiling would begin and the temperature would remain constant at the normal boiling point and the heat supplied to system would be used to boil the liquid. The temperature would not begin to increase again until all the liquid had been converted to gas, at which point the temperature of the system would again increase, this time in inverse proportion to the heat capacity of the gas. If we plot this experiment over a wide enough range of temperature to go from solid to liquid to vapor, the plot would look something like this

In this plot, time (the x-axis) corresponds to energy supplied in the form of heat, since we assume we are adding heat at a constant rate. Note that this graph is somewhat idealistic; the slopes (temperature increase) for the solid, liquid and gas will not be equal (each slope will be the inverse of the heat capacity for that particular phase) nor will they be linear since we know that heat capacity increases with temperature. Still, over a short enough range - say a few tens of degrees below the phase transition to a few degrees above it - we can approximate the heat capacities of each phase as being constant.

The heat that must be supplied to convert one phase to another (solid to liquid, liquid to vapor) is just the enthalpy of the phase transition, (Δ_fusH, Δ_vapH), adjusted appropriately for the number of moles of substance. Because this amount of energy (in the form of heat) has to be supplied to the lower-temperature phase to convert it into the higher-temperature phase, it is called the latent heat of the phase transition. Not all phase transitions have latent heats, although most of the ones with which your students will be familiar (boiling, freezing, subliming) will have a latent heat. For phase transitions with latent heat, the entropy of the phase change will be

The latent heat of fusion and vaporization play a major role in meteorology, so if you are interested in content integration this might be an interesting tack to take with your students. Here is a lab that aims to measure the latent heat of fusion (enthalpy of fusion, Δ_fusH for ice. The lab calls for a calorimeter; you could easily use the coffee cup calorimeter discussed in the calorimetry section of this tutorial. Specific heat and latent heat learning objectives and a series of suggested projects to study these concepts are given on this web page.

Phase transitions with latent heats are called first-order transitions. The phase jump from one state to the other is discontinuous (sudden) with temperature. In second-order transition, such as the demagnetization of iron, the change is continuous over a range of temperatures, exhibiting a gradual change in behavior rather than a sharp break. Magnetic phase transitions are discussed at this web site While second order types of phase transitions might be less familiar to most of us, we are familiar with many materials and phenomena that experience such transitions. Glass in going from a liquid to a solid experiences a second order transition. Upon cooling liquid glass does not solidify at a single, sharp temperature. Rather, it solidifies slowly over a range of temperatures. Here are some thermodynamic properties for first and second order transitions as a function of temperature:

For a more realistic picture of these quantities, follow this link to a Journal of Chemical Education paper that discusses second order phase transitions in greater detail.This site will only give you the abstract. Talk to your librarian if you want to obtain a copy of the actual paper.