Page 256 - Advanced thermodynamics for engineers

11.2 ENERGY OF FORMATION 243

Note that the atomisation and dissociation energies of oxygen are equal (2DH a [O¼O]¼2[O¼O])
and cancel out, i.e. the enthalpy of formation of oxygen is zero. This value of zero is assumed as a base
level for all elements.
Thus

ðDH f Þ ¼ðDH f Þ ¼ 70 MJ=kmol (11.18)
R CH 4
Similarly the enthalpy of formation of the products

X X X X
ðDH f Þ ¼ DH a DHðX YÞ DH res DH latent
P
h i
¼ DH a C graphite þ DH a ½O ¼ OŠþ 2DH a ½H HŠþ DH a ½O ¼ OŠ 2½C ¼ OŠ
(11.19)
2½H OHŠ 2½O HŠ DH res ½CO 2 Š
¼ðDH f Þ þ 2ðDH f Þ
CO 2 H 2 O
¼ 381:5 2 241:7MJ=kmol
The heat of reaction is given by

DH R ¼ðDH f Þ ðDH f Þ R
P
¼ 381:5 2 241:7 ð 70Þ (11.20)
¼ 794:9MJ=kmol

This is close to the value of 802.3 MJ/kmol quoted as the lower enthalpy of reaction of methane.
If the higher heat of reaction of methane is required then Eqn (11.14) becomes

CH 4 ðgÞþ 2O 2 ðgÞ/CO 2 ðgÞþ 2H 2 Oð[Þ (11.21)

Example
Evaluate the lower enthalpy of reaction of benzoic acid (C 6 H 5 COOH). The planar diagram of its
structure is shown in Fig. 11.7.
Solution
The reaction of benzoic acid with oxygen is

C 6 H 5 COOHðgÞþ 7:5O 2 ðgÞ/7CO 2 ðgÞþ 3H 2 OðgÞ (11.22)
The easiest way to evaluate the enthalpy of reaction is from Eqn (11.20)

DH R ¼ðDH f Þ ðDH f Þ R (11.23)
P
The values of H f were calculated above for CO 2 and H 2 O, and hence the only unknown quantity in
Eqn (11.20) is the enthalpy of formation of the benzoic acid, which is
X X X X
ðDH f Þ C 6 H 5 COOH ¼ DH a DHðX YÞ DH res DH latent (11.24)