Page 296 - Advanced Thermodynamics for Engineers, Second Edition

12.11 DISSOCIATION PROBLEMS 285

nitric oxide is positive, i.e. the reaction which forms it is endothermic, and hence combination of
nitrogen and oxygen tends to reduce the Gibbs energy of the mixture. Note that other compounds tend
to dissociate at high temperature because their energies of formation are negative, i.e. the reactions
which form them are exothermic.

Example
Methane is burned with a stoichiometric quantity of air and achieves a pressure of 99.82 bar and a
temperature of 2957 K after combustion, if dissociation of the carbon dioxide and water vapour are
taken into account. The mole fractions of the constituents are 7.495% CO 2 , 1.890% CO, 18.183%
H 2 O, 0.6425% H 2 , 1.267% O 2 and 70.58% N 2 . Calculate the amount of nitric oxide formed at this
temperature, neglecting the effect of the NO formation on the dissociation of carbon monoxide and
water. Estimate the effect of the NO formation on the temperature of the products. The energy of the
reactants, U R (T R ) ¼ 179377 kJ.
Solution:
Chemical equation without dissociation

CH 4 þ 2ðO 2 þ 3:76N 2 Þ/CO 2 þ 2H 2 O þ 7:52N 2 (12.152)
Chemical equation with dissociation

CH 4 þ 2ðO 2 þ 3:76N 2 Þ

/n P ð0:07495CO 2 þ 0:0189CO þ 0:18183H 2 O þ 0:006425H 2 þ 0:01267O 2 þ 0:7058N 2 Þ
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a 1 a 2
þ
n P ¼10:52þ
2 2
(12.153)
It is possible to evaluate the total amount of substance in the products as follows.
1 a 1 a 1
; giving n P ¼ 10:655:
0:07495 ¼ ; and 0:0189 ¼
n P n P
and hence

CH 4 þ 2ðO 2 þ 3:76N 2 Þ
(12.154)
/ 0:7986CO 2 þ 0:2014CO þ 1:9315H 2 O þ 0:06845H 2 þ 0:13495O 2 þ 7:52N 2
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
n P ¼10:655
Assume that combination of the nitrogen and oxygen occurs to form nitric oxide.

a 3 a 3
a 3 NO 5 N 2 (12.155)
2 O 2 þ 2
The temperature of the products is T P ¼ 2956 K, giving
p rNO
: (12.156)
K p r3 z 0:11279 ¼ 1=2 1=2
p p
rO 2 rN 2