Coming back to the integral (eqn db3.1), the change in entropy over the entire path must
be zero:(db3.15)Thus the integral of the entropy over the arbitrary path is equal to zero and thus independ-
ent of the path. This establishes that entropy is indeed a state function and that the changes
in the entropy for any given system can be determined by consideration of the initial and
final states of the system. The second law of thermodynamics can then be established for a
system based upon the changes between the final and initial states without consideration
of the path that led to those changes.dS
q
Tq
Thot
hotcold
cold∫ =+ =^0
66 PARTI THERMODYNAMICS AND KINETICS
Research direction: nitrogen fixation
The nitrogen cycle is a complex biogeochemical cycle that involves many
different organisms as well as the soil and atmosphere (Figure 3.11). Part of
the nitrogen cycle involves nitrogen fixation, the conversion of molecular
nitrogen into nitrites and other compounds suitable for assimilation by
algae and plants (Howard & Rees 1996; Ferguson 1998; Barney et al. 2006).
The formation of ammonia, NH 3 , from nitrogen and hydrogen gas is
exothermic:N 2 (gas) +3H 2 (gas) →2NH 3 (gas)
ΔH°=−92.6 kJ(3.37)
Although the reaction is favorable, the rate is extremely slow under
standard conditions. Ammonia is one of the main materials used in the
production of fertilizers as well as explosives. Therefore, optimization of
this reaction for yield on an industrial scale was pursued. Fritz Haber in
1905 devised a process for producing ammonia that was developed for
commercial use by Carl Bosch; who won the Nobel Prizes in Chemistry
in 1918 and 1931, respectively. It was realized that the reaction was
accelerated when the gases were in the presence of a metal surface
(Figure 3.12). The gases bind to the surface and the interactions with
the surface facilitate the weakening of covalent bonds holding the mole-
cules together. These molecules are then very reactive and the formation
of ammonia is favored. The binding of the gas to the surface and the
dissociation process requires both a high temperature (≈500°C) and high
pressure (several hundred atmospheres) for a high yield.
The synthesis of ammonia is thermodynamically favorable but com-
plicated by a slow rate that reflects the kinetic stability of the nitrogen