In order for a substance to move between the states of matter; for example, to turn from a solid into a liquid, which is called fusion, or from a gas to a liquid , energy must be gained or lost. The heat of fusion (symbolized Hfus) of a substance is the amount of energy that must be put into the substance for it to melt. For example, the heat of fusion of water is 6.01 kJ/mol, or in other terms, 80 cal/g. The heat of vaporization, not surprisingly, is the amount of energy needed to cause the transition from liquid to gas, and it is symbolized Hvap. You will not be required to memorize heat of fusion or vaporization values for the exam.　　Changes in the states of matter are often shown on phase diagrams, and you will probably see at least one of two different types of phase diagrams on the SAT II Chemistry exam. Let’s start with the phase diagram for water. The phase diagram for water is a graph of pressure versus temperature. Each of the lines on the graph represents an equilibrium position, at which the substance is present in two states at once. For example, anywhere along the line that separates ice and water, melting and freezing are occurring simultaneously.

　　The intersection of all three lines is known as the triple point (represented by a dot and a T on the figure). At this point, all three phases of matter are in equilibrium with each other. Point X represents the critical point, and at the critical point and beyond, the substance is forever in the vapor phase. 　　This diagram allows us to explain strange phenomena, such as why water boils at a lower temperature at higher altitudes, for example. At higher altitudes, the air pressure is lower, and this means that water can reach the boiling point at a lower temperature. Interestingly enough, water would boil at room temperature if the pressure was low enough! 　　One final note: If we put a liquid into a closed container, the evaporation of the liquid will cause an initial increase in the total pressure of the system, and then the pressure of the system will become a constant. The value of this final pressure is unique to each liquid and is known as the liquid’s vapor pressure. Water has a relatively low vapor pressure because it takes a lot of energy to break the hydrogen bonds so that molecules enter the gas phase. Water and other liquids that have low vapor pressures are said to be nonvolatile. Substances like rubbing alcohol and gasoline, which have relatively high vapor pressures, are said to be volatile. 　　Example　　What happens to water when the pressure remains constant at 1 atm but the temperature changes from -10oC to 75oC?　　Explanation　　Looking at the phase change diagram for water and following the dashed line at 1 atm, you can see that water would begin as a solid (ice) and melt at 0oC. All of the water would be in liquid form by the time the temperature reached 75oC. 　　The second type of phase change graph you might see on the SAT II Chemistry exam is called a heating curve. This is a graph of the change in temperature of a substance as energy is added in the form of heat. The pressure of the system is assumed to be held constant, at normal pressure (1 atm). As you can see from the graph below, at normal pressure water freezes at 0oC and boils at 100oC.

　　The plateaus on this diagram represent the points where water is being converted from one phase to another; at these stages the temperature remains constant since all the heat energy added is being used to break the attractions between the water molecules. 　　Specific Heat　　On the SAT II Chemistry test, you might see a diagram that looks something like this one, and you might come across a question that asks you to calculate the amount of energy needed to take a particular substance through a phase change. This would be one of the most difficult questions on the exam, but you might see something like it, or at least part of it. If you were asked to do this, you would need to use the following equation:

　　energy (in calories) = mCp DT

　　where m = the mass of the substance (in grams)　　Cp = the specific heat of the substance (in cal/g oC)　　DT = the change in temperature of the substance (in either Kelvins or oC, but make sure all your units are compatible!)　　As you can see, this requires that you know the specific heat of the substance. A substance’s specific heat refers to the heat required to raise the temperature of 1 g of a substance by 1oC. You will not be required to remember any specific heat values for the exam.　　Work through the example below to get a feel for how to use this equation.　　Example　　If you had a 10.0 g piece of ice at -10oC, under constant pressure of 1 atm, how much energy would be needed to melt this ice and raise the temperature to 25.0oC? 　　Explanation　　First, the temperature of the ice would need to be raised from -10oC to 0oC. This would require the following calculation. The specific heat for ice is 0.485 cal/g oC. Substituting in the formula

　　energy = mCp DT; energy = (10.0 g) (0.485 cal/g oC) (10.0oC) = 48.5 cal

　　So 48.5 calories are needed to raise temperature.　　Next, we must calculate the heat of fusion of this ice: we must determine how much energy is needed to completely melt the 10 g of it.

　　energy = mHfus

　　energy = (10.0 g) (80 cal/g) = 800 cal

　　So 800 cal of energy are needed to completely melt this sample of ice.　　Next, we need to see how much energy would be needed to raise the temperature of water from 0oC to 25oC. The specific heat for liquid water is 1.00 cal/g oC. So again use

　　energy = mCp DT to get energy = (10.0 g) (1.00 cal/g oC) (25.0oC) = 250 cal

　　Finally, add together all of the energies to get the total: 48.5 + 800 + 250 = about 1100 calories are needed to convert the ice to water at these given temperatures.

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