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Phase Changes
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 (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 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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