Physical Chemistry Third Edition

2.6 Calculation of Enthalpy Changes of Processes without Chemical Reactions 81

2.41A sample of 3.00 mol of argon is heated from 25.00◦Cto
100.00◦C, beginning at a pressure of 1.000 atm
(101,325 Pa).

a. Findq,w,∆U, and∆Hif the heating is done at

constant volume.

b. Findq,w,∆U, and∆Hif the heating is done at

constant pressure.

2.6 Calculation of Enthalpy Changes of Processes

without Chemical Reactions

The most useful calculations of∆Hare for constant-pressure processes in closed

systems. If no phase change or chemical reaction occurs,

∆Hq

∫

c

dH

∫T 2

T 1

(

∂H

∂T

)

P,n

dT

∫T 2

T 1

CPdT (2.6-1)

The integration in this formula is carried out on a constant-pressure path.

EXAMPLE2.24

a.Find a formula for∆Hfor the heating of a sample of a gas from temperatureT 1 to

temperatureT 2 at constant pressure ifCP, mis represented by

CP, ma+bT+cT−^2

b.Find∆Handqfor the heating of 2.000 mol of oxygen gas from 25.00◦C to 100.00◦Cat

a constant pressure of 1.000 atm.

Solution

a. ∆Hqn

∫T 2

T 1

(

a+bT+cT−^2

)

dT

n

[

a(T 2 −T 1 )+

b

2

(

T 22 −T 12

)

−c

(

1

T 2

−

1

T 1

)]

b.Using the values of the parameters for oxygen from Table A.6,

∆Hq(2.000 mol)

{(

30 .0JK−^1 mol−^1

)

( 75 .00 K)

+

1

2

(

4. 18 × 10 −^3 JK−^2 mol−^1

)

(373.15 K)^2 −(298.15 K)^2

−(− 1. 67 × 105 J K mol−^1 )

(

1

373 .15 K

−

1

298 .15 K

)}

( 2 .000 mol)

(

2250 J mol−^1 +105 J mol−^1 −113 J mol−^1

)

4484 J