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Beyond simply observing and assigning names to the various phase changes that a substance can undergo, SCIENTISTS are interested in obtaining quantitative data to help us better understand these changes. There are several ways of representing quantitative information about a substance and its phase changes. One such graphical representation is called a heating (or cooling) curve. Heating (cooling) curves show how the temperature of the substance increases (decreases) as heat is added to (removed from) the sample. Figure 11.18 in your text show the heating curve for water. The figure below show the corresponding cooling curve:

The regions at the top of the graph illustrate the behavior of the molecules during each stage. Notice that Stage 2 and Stage 4 are equilibrium states where the removal of heat does not result in a temperature change. For example, once a sample of steam is cooled to 100oC, removing heat results in the condensation of the gas with no further change in temperature until all of the gas has condensed.

Try this: Calculate the amount of heat released when 100g of water (g) at 110oC is cooled to water (l) at 50oC. These points have been labeled on the graph. On a test you would be provided with the following useful constants:

 specific heat water (g) = 1.84 J/g K

 specific heat water (l) = 4.18 J/g K

 heat of vaporization of water = 40.67 kJ/mol

Before we look at another way of representing phase information for a substance (the phase diagram), let's take a closer look at one particular phase change: (l)(g). This process happens on two levels, as a surface phenomenon (in the case of evaporation) and as a bulk property of the liquid (in the case of boiling or vaporization).

Look at the drawing of the two closed bottles below. Evaporation of liquids can occur well below their boiling point because, even thought the average molecule in the sample does not have sufficient energy to break free from the liquid (and become a gas) statistically, there are a few molecules that can "escape" the evil clutches of the liquid's IMF. At low temperature, only a few of the molecules have sufficient KE to overcome the IMF and only a small fraction of those are at the surface so the pressure of the gas above the liquid is low, P(1). This build up of pressure prevents all the liquid from evaporating as would happen if the bottle were open. At high temperature, the number of surface molecules with escape velocity is greater, resulting in a greater pressure of gas, P(2). When these pressures are measured at equilibrium, they are called Vapor Pressure.

The vapor pressure of a liquid is seen to increase with temperature as shown in Figure 11.22 in your text.

Try this: Explain the relative vapor pressures for the different liquids in figure 11.22. For example, at a given temperature, why does ethylene glycol have a lower vapror ressure than water which is lower than...

Figure 11.22 is also significant in that it illustrates the relationship between vapor pressure (VP) and boiling point (BP).

Try this: What is the relationship between VP and BP?

This allows us to play some tricks with the boiling point of a liquid.

Try this: Using Figure 11.22 what pressure would you have to be at to lower the boiling point of water to 80oC?

Now let's make sure you are familiar with everything you'll need to know about phase diagrams which provide information about the phase of a substance as a function of pressure and temperature.

Try this: Using the figure below, answer the following questions about phase diagrams

1. What phase(s) is (are) present at points A, E, F, G and B?

2. What point corresponds to the critical point? The triple point?

3. What curve corrsponds to conditions at which the solid and gas are at equilibrium?

4. Describe what happens when you start at point A and increase the temperature at constant pressure.

5. Describe what happens when you start at point G and decrease the pressure at constant temperature.

6. Is the liquid in the phase diagram more or less dense than the solid? Based on this, can you guess what the substance might be?

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