Physical Chemistry Third Edition

82 2 Work, Heat, and Energy: The First Law of Thermodynamics

Exercise 2.26

Using the values ofa,b, andcfrom Table A.6, calculate the values ofCP, mfor O 2 gas at 298.15 K,

500.0 K, 1000.0 K, and 2000.0 K. Compare with the values in Table A.8.

A transition between two phases of a single substance takes place at a definite

temperature if the pressure is fixed. For example, if the pressure is fixed at 1.000 atm,

the boiling temperature of water is 100.00◦C or 373.15 K and its freezing temperature

is 0.00◦C or 273.15 K. Table A.7 gives specific enthalpy changes (enthalpy changes

per gram) for reversible fusion (melting) and vaporization (boiling) transitions for a

number of substances at a constant pressure of 1.000 atm.

To obtain the molar enthalpy change from the specific enthalpy change, one multi-

plies the specific enthalpy change by the molar mass in grams per mole. To calculate

∆Hfor the fusion ofnmoles of a substance we write

∆Hn∆fusHm (2.6-2)

where∆fusHmis the molar enthalpy change of fusion. For the vaporization ofnmoles

of a substance

∆Hn∆vapHm (2.6-3)

where∆vapHmis the molar enthalpy change of vaporization of the substance.

EXAMPLE2.25

Find∆Handqif 2.000 mol of liquid water at 0.00◦C is reversibly frozen to ice at 0.00◦Cat

a constant pressure of 1.000 atm.

Solution

q∆H( 2 .000 mol)

(

18 .02 g mol−^1

)(

− 333 .5Jg−^1

)

− 1. 202 × 104 J

Since the enthalpy is a state function, we can calculate∆Hfor a given process by

calculating∆Hfor any process having the same initial and final states.

EXAMPLE2.26

Calculate∆Hfor the change of state of 1.000 mol of helium from a volume of 5.000 L and

a temperature of 298.15 K to a volume of 10.000 L and a temperature of 373.15 K. Assume

thatCP, m 5 R/2 and assume that the gas is ideal.

Solution

The value of∆His path-independent. For purposes of calculation, assume that the gas first

expands isothermally and reversibly to a pressure equal to the final pressure (step 1), and is

then heated at constant pressure to its final temperature (step 2). Since the enthalpy depends