Concepts from Chemical Reaction Kinetics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 193

the reverse direction. The driving force for the chemical change is thus Δ G . We also

G 0 H 0 S 0 .If know that Δ G = Δ H − T Δ S and for standard conditions Δ = Δ − T Δ

a reaction has attained equilibrium, Δ G = 0, that is, Δ H = T Δ S .If |Δ H | > | T Δ S | ,

Δ G > 0, whereas if |Δ H | < | T Δ S | , Δ G < 0. However, both the sign and magnitude

of Δ H and Δ S terms together determine the value of Δ G and hence the spontaneity

of a reaction.

E XAMPLE 5.1 D EFINITIONS OF E XTENT OF R EACTION AND F RACTIONAL
C ONVERSION

For a reaction,

−→ +

A B C, (5.18)

we define the extent of reaction ξ such that

d n A
− 1 =

d n B
1 =

d n C
1

ξ =

d . (5.19)

Generalizing, we have

n i − n i
ν i

ξ = , (5.20)

where n i represents the initial conditions in the closed system.
We can also define a fractional conversion χ such that it is 0 (no reaction) and 1
(reaction completed) through the equation

n A = n A ( 1 − χ ) . (5.21)

Note that 0 < χ < 1 only if A is chosen as the limiting reactant, which disappears
completely when χ = 1. For any species in the closed system we can then write the
following equation:

n i − n i
ν i

n A χ =

. (5.22)

5.2 REACTION RATE, ORDER, AND RATE CONSTANT
Since n i = n i + ν i ξ ,wehave

1
ν i ·

d ξ = d n i . (5.23)

As long as the above equation represents a single reaction, it is immaterial as to the
referenced species i . However, if the reaction occurs in a series of steps, then the rate
at which one species is consumed will be different from the rate of production of
another, and hence the rate has to be specified in concert with the species it refers
to. For example, consider the reaction H 2 + ( 1 / 2 ) O 2 → H 2 O, for which the extent of
reaction is

d n H 2 O
( 1 )

d n O 2
−

d n H 2
(

d ξ = =

( 1 / 2 ) = 1 ) .

(5.24)

−