Page 272 - Advanced Thermodynamics for Engineers, Second Edition

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12.7 EXAMPLES OF SIGNIFICANCE OF K p

is known, the ratio of the partial pressures in the equilibrium state is known. It would be
Thus, if K p r
convenient to manipulate this expression into a more useful form. Consider the general reaction
equation for the carbon monoxide and oxygen reaction (eqn (12.27))
1 a
CO þ O 2 5 ð1 aÞCO 2 þ aCO þ O 2
2 2
then
p 1 a p
n CO 2
p rCO 2 ¼ ¼
n p p 0 1 þ a=2 p 0
n CO p a p
(12.71)
p rCO ¼ ¼
n p p 0 1 þ a=2 p 0
p a=2 p
n O 2
p rO 2 ¼ ¼
n p p 0 1 þ a=2 p 0
can be related to the degree of dissociation, a, through the following
Hence, the value of K p r
equation
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffiffiffiffiffi p ffiffiffiffiffi
p
1 a 1 þ a=2 1 þ a=2 p 0 1 a 1 þ a=2 p 0
ffiffiffi : (12.72a)
K p r ¼ p ffiffiffi ¼ p
1 þ a=2 a a=2 p a a=2 p
and
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 a 1 þ a=2 1 K p r
(12.72b)
ffiffiffiffiffi
K p ¼ p ffiffiffi ¼ p
a a=2 p p 0
and a allows the degree of dissociation, a, to be evaluated if K p is
The relationship between K p r
known. Equation (12.72) shows that, for this reaction, the value of K p is a function of the degree of
dissociation and also the pressure of the mixture. This is because the amount of substance of products
is not equal to the amount of substance of reactants.
12.7.2 EXAMPLE 2
Consider the water–gas reaction:

CO 2 þ H 2 5 CO þ H 2 O (12.73)
By the law of mass action
p rCO p rH 2 O
K p r ¼
p rCO 2 p rH 2
(12.74)

x CO x H 2 O 1þ1 1 1 x CO x H 2 O
p ¼ K p
¼ ¼
x x
x CO 2 H 2 x CO 2 H 2