2H 2 O (liquid) →2H 2 (gas) +O 2 (gas) (3.30)
ΔS°=S°(O 2 ) + 2 S°(H 2 ) − 2 S°(H 2 O)
ΔS°=(205.1 J K−^1 ) +2(130.7 J K−^1 ) −2(69.9 J K−^1 ) =326.7 J K−^1
If we calculate the change in the Gibbs energy for the same reaction,
the Gibbs energy change is positive and so the reaction does not occur
spontaneously:
ΔG°=G°(O 2 ) + 2 G°(H 2 ) − 2 G°(H 2 O) (3.31)
ΔG°=(0 kJ mol−^1 ) +2(0 kJ mol−^1 ) −2(−237.2 kJ mol−^1 )
=474.4 kJ mol−^1
Whereas liquid water is stable and does not spontaneously dissociate into
hydrogen and oxygen gases, we should consider the reverse reaction of
hydrogen and oxygen gases forming water:
2H 2 (gas) +O 2 (gas) →2H 2 O (gas) (3.32)
The enthalpy and entropy changes for this reaction can be calculated by
considering each component. For this reaction, the entropy should decrease
due to the ordering of the gases into a liquid:
ΔS°= 2 S°(H 2 O) −S°(O 2 ) − 2 S°(H 2 ) (3.33)
ΔS°=2(188.7 J K−^1 ) −(205.0 J K−^1 ) −2(130.6 J K−^1 ) =−88.7 J K−^1
ΔG°= 2 G°(H 2 O) −G°(O 2 ) − 2 G°(H 2 )
ΔG°=2(−237.2 kJ mol−^1 ) −(0 kJ mol−^1 ) −2(0 kJ mol−^1 )
=−474.4 kJ mol−^1
This reaction has a large negative value and so is spontaneous. When hydro-
gen and oxygen gases are mixed an explosion will occur, as happened in
the disaster of the hydrogen-filled airship, the Hindenburg, in 1937. A
spark is required for the reaction to occur quickly. A spark is needed because
the mechanism has many steps involving different intermediates that take
place at a fast rate only after energy absorption.
Carnot cycle and hybrid cars
Hybrid cars have significantly increased fuel efficiency. Some predictions
suggest that most cars will be hybrids in the not so distant future (see
Chapter 12). Why do hybrids get about 20% better fuel efficiency than
regular cars? To understand this improvement the thermodynamic prin-
ciples that govern the efficiency of any engine need to be discussed. Car
engines operate in a cyclic process of fuel intake, compression, ignition,
60 PARTI THERMODYNAMICS AND KINETICS
