Physical Chemistry Third Edition

96 2 Work, Heat, and Energy: The First Law of Thermodynamics

b. V 2 (2.000 mol)(18 cm^3 mol−^1 )36 cm^3 ^3.^6 ×^10 −^5 m^3

V 1 

(3.000 mol)(8.3145 J K−^1 mol−^1 )(298.15 K)

100000 Pa

 0 .0743690 m^3

∆V 3. 6 × 10 −^5 m^3 − 0 .0743690 m^3 − 0 .07433 m^3

Since the pressure is constant atP◦100000 Pa,

∆(PV)P∆V(100000 Pa)(− 0 .07340 m^3 )−7433 J mol−^1

This value compares with the value of−7437 J mol−^1 in part a.

Exercise 2.30

Find∆U◦for the reaction of Eq. (2.7-6) at 298.15 K.

Calorimetry

The most common procedure for the determination of enthalpy changes of formation

of combustible substances is to carry out combustion reactions in abomb calorimeter.

Figure 2.12 depicts such a calorimeter. The reaction is carried out in a rigid container

that is called the “bomb.” A pellet of a solid reactant is placed in the bomb along with

an excess of oxygen at a pressure of about 25 atm.

The bomb is placed in a bucket containing a measured amount of water, and the

water is stirred until a steady or steadily changing temperature is attained, as measured

by a thermometer in the water. The sample is ignited electrically, the reaction occurs,

and the bomb, water, and bucket are allowed to stabilize. The amount of heat transferred

to the calorimeter (bomb, water, and bucket) is calculated from knowledge of the heat

capacity of the calorimeter. This heat capacity is very nearly independent of temperature

so that

q−qcal−Ccal∆T (2.8-6)

Because the water continues to be stirred and because the water does not attain its

final temperature instantaneously, extrapolation techniques are used to determine∆T.^6

Since the system is at constant volume,w0 and

q∆U (2.8-7)

From the amount of solid reactant present,∆Ufor 1 mol of reaction is calculated,

and then∆Hfor 1 mol of reaction is calculated from Eq. (2.8-4). This value of∆H

is not quite equal to∆H◦for the isothermal reaction. Neither the final pressure nor

the initial pressure is equal to the standard-state pressure and the gases present are

(^6) C. W. Garland, J. W. Nibler, and D. P. Shoemaker,Experiments in Physical Chemistry, 7th ed.,
McGraw-Hill, Boston, 2003, pp. 145ff.