Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Chapter 16 | 803

EXAMPLE 16–4 Effect of Inert Gases on Equilibrium

Composition

A mixture of 3 kmol of CO, 2.5 kmol of O 2 , and 8 kmol of N 2 is heated to

2600 K at a pressure of 5 atm. Determine the equilibrium composition of

the mixture (Fig. 16–13).

Solution A gas mixture is heated to a high temperature. The equilibrium

composition at the specified temperature is to be determined.

Assumptions 1 The equilibrium composition consists of CO 2 , CO, O 2 , and

N 2. 2 The constituents of the mixture are ideal gases.

Analysis This problem is similar to Example 16–3, except that it involves

an inert gas N 2. At 2600 K, some possible reactions are O 2 ∆2O (ln KP

7.521), N 2 ∆2N (ln KP28.304), –^12 O 2 ^1 – 2 N 2 ∆NO (ln KP

2.671), and CO –^12 O 2 ∆CO 2 (ln KP2.801 or KP16.461). Based

on these KPvalues, we conclude that the O 2 and N 2 will not dissociate to

any appreciable degree, but a small amount will combine to form some

oxides of nitrogen. (We disregard the oxides of nitrogen in this example, but

they should be considered in a more refined analysis.) We also conclude that

most of the CO will combine with O 2 to form CO 2. Notice that despite the

changes in pressure, the number of moles of CO and O 2 and the presence of

an inert gas, the KPvalue of the reaction is the same as that used in Exam-

ple 16–3.

The stoichiometric and actual reactions in this case are

Stoichiometric:

Actual:

products reactants inert

(leftover)

C balance:

O balance:

Total number of moles:

Assuming ideal-gas behavior for all components, the equilibrium constant

relation (Eq. 16–15) becomes

Substituting, we get

Solving for xyields

x2.754

16.461

x

13 x 21 2.5x> 221 >^2

a

5

13.5x> 2

b

 1 > 2

KP

NCOnCO 22

NCOnCONOnO 22

a

P

Ntotal

b

nCO 2 nCOnO 2

Ntotalxyz 8 13.5

x

2

8  2 xy 2 z¬or z2.5

x

2

3 xy¬ or y 3 x

3CO2.5O 2 8N 2 ¡xCO 2 yCOzO 2 8N 2

CO^12 O 2 ∆CO 2 1 thus nCO 2 1, nCO1, and nO 2 ^122

3 kmol CO

Initial

composition

x CO 2

Equilibrium

composition at

2600 K, 5 atm

y CO

8 kmol N 2 z O 2

2.5 kmol O 2

8 N 2

FIGURE 16–13

Schematic for Example 16–4.

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