Physical Chemistry , 1st ed.

The heat involved in the reverse process,condensation,can also be calculated

with equations 2.52 and 2.53 with the understanding that once again we will

have to keep track of which direction heat is going. When determining work

for a vaporization or sublimation, it is common to neglect the volume of the

condensed phase, which is usually negligible. The following example illustrates.

Example 2.15

Calculate q,w,H, and Ufor the vaporization of 1 g of H 2 O at 100°C and

1.00 atm pressure. The vapHof H 2 O is 2260 J/g. Assume ideal gas behavior.

The density of H 2 O at 100°C is 0.9588 g/cm^3.

Solution

Using equation 2.52, the heat and Hfor the process are straightforward:

q(1 g)(2260 J/g) 2260 J into the system

qH+2260 J

In order to calculate the work, we need the volume change for the vaporiza-

tion. For the process H 2 O ()→H 2 O (g), the change in volume is

VVgasVliq

Using the ideal gas law, we can calculate the volume of the water vapor at

100°C 373 K:

Vgas

1.00 atm

Vgas1.70 L

The volume of liquid H 2 O at 100°C is 1.043 cm^3 , or 0.001043 L. Therefore,

VVgasVliq1.70 L 0.001043 L 1.70 L Vgas

In this step, we show that the volume of the liquid is negligible with respect

to the volume of the gas, so to a very good approximation VVgas. To cal-

culate the work of the vaporization:

wpextV

w(1.00 atm)(1.70 L)^1

1

0

L

1



.

a

3

t

2

m

J



w172 J

Since Uq+ w,

U2260 J 172 J

U2088 J

This is an example where the change in enthalpy does not equal the change

in internal energy.

Table 2.3 lists some values for fusHand vapHfor various substances.

The values for fusHand vapHare indicative of how much energy is neces-

sary to change the phase, and as such are related to the strength of the in-

teratomic or intermolecular interactions in the materials. Water, for example,

52 CHAPTER 2 The First Law of Thermodynamics

Table 2.3 fusHand vapHfor various

substances (J/g)

Material fusH vapH

Al 393.3 10,886

Al 2 O 3 1,070

CO 2 180.7 573.4 (sublimes)

F 2 26.8 83.2

Au 64.0 1,710

H 2 O 333.5 2,260

Fe 264.4 6,291

NaCl 516.7 2,892

C 2 H 5 OH, ethanol 188.99 838.3

C 6 H 6 , benzene 127.40 393.8

C 6 H 14 , hexane 151.75 335.5

(0.0555 mol)(0.08205 mLoaltmK)(373 K)