Page 301 - Advanced Thermodynamics for Engineers, Second Edition

290 CHAPTER 12 CHEMICAL EQUILIBRIUM AND DISSOCIATION

12.13 PROBLEMS
Assume that air consists of 79% N 2 and 21% O 2 by volume.
P12.1. A cylinder contains 1 kg carbon dioxide, and this is compressed adiabatically. Show the
pressure, temperature and specific volume are related by the equation
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 a ð2 þ aÞ p
¼ K p r
a a 1:01325
and
<ð2 þ aÞT
;
pv ¼
88
where a ¼ degree of dissociation.
1
Note that the equilibrium constant for the reaction CO þ O 2 5 CO 2 is given by
2
ðp CO 2 =p 0 Þ
1=2 , where p 0 is the datum pressure of 1 atm.
K p r ¼
ðp CO =p 0 Þðp O 2 =p 0 Þ
P12.2. (a) Calculate the equilibrium constant, K p , at 2000 K at the reference pressure of 1 atm for
the reaction
CO þ H 2 O 5 CO 2 þ H 2
(b) Calculate the equilibrium constant, K p , at 2500 K at the reference pressure of 1 atm for
the reaction

1
CO þ O 2 5 CO 2 :
2
Also calculate the equilibrium constant at 2500 K and a pressure of 1 bar.
[(a) 4.6686; (b) 27.028 atm 1/2 ; 27.206 bar 1/2 ]
P12.3. If it is assumed that the enthalpy of reaction, Q p , is a constant, show that the value of K p is
given by

Q p=<Tþk
K p ¼ e
where k is a constant.
For a particular reaction Q p ¼ 277346 kJ/kmol and K p ¼ 748.7 at T ¼ 2000 K. Evaluate
K p at the temperature of 2500 K.
[26.64]
P12.4. A stoichiometric mixture of propane (C 3 H 8 ) and air is burned in a constant volume bomb.
The conditions just prior to combustion are 10 bar and 600 K. Evaluate the composition of
the products allowing for dissociation if the peak temperature achieved is 2900 K and show
that the combustion process is adiabatic (i.e. the heat transfer is small).