Page 281 - Advanced Thermodynamics for Engineers, Second Edition

270 CHAPTER 12 CHEMICAL EQUILIBRIUM AND DISSOCIATION

12.9 THE EFFECT OF PRESSURE AND TEMPERATURE ON DEGREE
OF DISSOCIATION
12.9.1 THE EFFECT OF PRESSURE

The effect of pressure on the degree of dissociation is defined by Eqn (12.62), viz.
!
x x y d ðy c þy d y a y b Þ
y c
c
d
K p r ¼ y a y b p r
x a x
b
It can be seen that the ratio of the amounts of substance is given by
x x y b p r ðy c þy d y a y b Þ (12.104)
y a
a
b
x c x ¼
y c y d
d K p r
This can be interpreted in the following way. If y c þ y d y a y b ¼ 0 then the mole fractions of the
products will not be a function of pressure. However, if y c þ y d y a y b > 0 then the species on the
left-hand side of the chemical equation (i.e. the reactants) increase, whereas if y c þ y d y a y b < 0
then the species on the right-hand side of the equation (i.e. the products) increase. The basic rule is
that the effect of increasing the pressure is to shift the equilibrium to reduce the total amount of
substance.
Considering the two reactions introduced previously. The equation for the carbon monoxide re-
action (12.27) was
1 a
CO þ O 2 5 ð1 aÞCO 2 þ aCO þ O 2
2 2
and the equilibrium Eqn (12.72) was

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 a 1 þ a=2 1 þ a=2 1 1 a 1 þ a=2 1
K p r ¼ p ffiffiffiffi ¼ p ffiffiffiffi
1 þ a=2 a a=2 p r a a=2 p r
This means that n c þ n d n a n b < 0, and this would result in the constituents on the ‘products’
side of the equation increasing. This is in agreement with the previous statement because the total
amounts of reactants in Eqn (12.27) is 1.5, whilst the total amounts of products is 1 þ a/2, where a is
less than 1.0.
A similar calculation for the combustion and dissociation of a stoichiometric methane (CH 4 ) and
1
air mixture, performed using a computer program entitled EQUIL2 gave the results in Table 12.1. The
chemical equation for this reaction is

CH 4 þ 2ðO 2 þ 3:76N 2 Þ
(12.105)
/ð1 a 1 ÞCO 2 þ a 1 CO þ 2ð1 a 2 ÞH 2 O þ 2a 2 H 2 þða 1 =2 þ a 2 ÞO 2 þ 7:52N 2

1
An executable version of EQUIL2 is available at http://booksite.elsevier.com/9780444633736.