In order for a substance to move between the states of matter; forexample, to turn from a solid into a liquid, which is called
fusion, or from a gas to a liquid (
vaporization), 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 thesubstance for it to melt. For example, the heat of fusion of water is6.01 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 oftenshown on phase diagrams, and you will probably see at least one of twodifferent types of phase diagrams on the
SAT II Chemistry exam. Let’sstart with the phase diagram for water. The
phase diagram forwater is a graph of pressure versus temperature. Each of the lines onthe graph represents an equilibrium position, at which the substance ispresent in two states at once. For example, anywhere along the linethat separates ice and water, melting and freezing are occurringsimultaneously.
$yoAj3K(u 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 strangephenomena, such as why water boils at a lower temperature at higheraltitudes, for example. At higher altitudes, the air pressure is lower,and this means that water can reach the boiling point at a lowertemperature. Interestingly enough, water would boil at room temperatureif the pressure was low enough!
One final note: If we put a liquid into aclosed container, the evaporation of the liquid will cause an initialincrease in the total pressure of the system, and then the pressure ofthe system will become a constant. The value of this final pressure isunique to each liquid and is known as the liquid’s
vapor pressure.Water has a relatively low vapor pressure because it takes a lot ofenergy to break the hydrogen bonds so that molecules enter the gasphase. Water and other liquids that have low vapor pressures are saidto 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 forwater and following the dashed line at 1 atm, you can see that waterwould begin as a solid (ice) and melt at 0ºC. All of the water would bein 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 energyis added in the form of heat. The pressure of the system is assumed tobe held constant, at normal pressure (1 atm). As you can see from thegraph below, at normal pressure water freezes at 0ºC and boils at 100ºC.
!A k&@qy8} y(R#c:] The plateaus on this diagram represent thepoints where water is being converted from one phase to another; atthese stages the temperature remains constant since all the heat energyadded is being used to break the attractions between the watermolecules.
Specific Heat
On the SAT II Chemistry test, you might seea diagram that looks something like this one, and you might come acrossa question that asks you to calculate the amount of energy needed totake a particular substance through a phase change. This would be oneof the most difficult questions on the exam, but you might seesomething like it, or at least part of it. If you were asked to dothis, 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)
D
T = 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 heatrefers to the heat required to raise the temperature of 1 g of asubstance by 1ºC. You will not be required to remember any specificheat 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 tomelt this ice and raise the temperature to 25.0ºC?
Explanation
First, the temperature of the ice would needto be raised from -10ºC to 0ºC. This would require the followingcalculation. The specific heat for ice is 0.485 cal/g ºC. Substitutingin 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 fusionof this ice: we must determine how much energy is needed to completelymelt 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 wouldbe needed to raise the temperature of water from 0ºC to 25ºC. Thespecific 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 toget the total: 48.5 + 800 + 250 = about 1100 calories are needed toconvert the ice to water at these given temperatures.
