H 2 O can exist at 0°C as either a solid or a liquid. Because there is no T,equa-
tion 2.9 does not apply. Instead, the amount of heat involved is proportional
to the amount of material. The proportionality constant is called the heat of
fusion,fusH, so that we have a simpler equation:
qmfusH (2.50)The word fusionis a synonym for “melting.” If amount mis given in units of
grams,fusHhas units of J/g. If the amount is given in units of moles, equa-
tion 2.50 is more properly written as
qnfusH (2.51)and fusHis a molar quantity with units of J/mol. Since freezing and melting
are simply opposite processes, equations 2.50 and 2.51 are valid for both
processes. The process itself dictates whether the label exothermic or en-
dothermic is appropriate. For melting, heat must be put into the system, so the
process is endothermic and the value ofHfor the process is positive. For
freezing, heat must be removed from the system, so freezing is exothermic and
the value for His negative.
Example 2.14
The heat of fusion fusHfor water is 334 J/g.
a.How much heat is required to melt 59.5 g of ice (about one large ice cube)?
b.What is the value ofHfor this process?Solution
a.According to equation 2.50,
q(59.5 g)(334 J/g)
q1.99 104 J
b.Because heat must be put into the system in order to go from solid to
liquid, the Hfor this process should reflect the fact that the process is
endothermic. Therefore,H1.99 104 J.Changes in volume when going from solid to liquid, or from liquid to solid,
are usually negligible, so that H U. (Water is an obvious exception. It
expands approximately 10% when freezing.) On the other hand, the change in
volume in going from a liquid to a gas (or a solid to a gas) is considerable:
H 2 O (, 100°C)→H 2 O (g, 100°C)In going from a liquid to a gas, a process called vaporization,again the tem-
perature stays constant while the phase change occurs, and the amount of heat
necessary is again proportional to the amount. This time, the proportionality
constant is called the heat of vaporization,vapH, but the form of the equation
for calculating the heat involved is similar to equation 2.50:
qmvapH for amounts in grams (2.52)or equation 2.51:
qnvapH for amounts in moles (2.53)2.9 Phase Changes 51