Chemistry - A Molecular Science

Reactions that are expected to have appr

eciable amounts of the reactants present at

equilibrium are often distinguished from those th

at are extensive with the use of double or

single arrows, respectively. Thus, the reaction is often written A

→

2B when K >> 1 (the

reaction is extensive). However, it should be written A

U

2B when K is not very large

(the reaction is not extensive). The amount of

product formed can be

determined strictly

from stoichiometry without the use of K for ex

tensive reactions, but K must be used to

determine the amount of product formed in a reaction that is not extensive.* Note that reactions written with single arrows also

achieve equilibrium; the single arrow simply

implies that the back reaction occurs to such

a small extent that it can be ignored when

determining the amount of product that is formed. THERMODYNAMIC DEFINITION OF K In Section 9.8, we showed that

ΔG = 0 is the thermodynamic definition of equilibrium,

and that

ΔG

o < 0 for an extensive reaction. As shown in Equation 9.8, the standard free

energy of a reaction is related to its temp

erature and the natural logarithm of its

equilibrium constant.

ΔG

o = - RT

ln

K or K = exp{-

ΔG

o/RT}* Eq.

9.8

* Such calculations are beyond the

scope of this text but are covered

extensively in

Chemistry – A Quantitative Science

.

Table 9.5

ΔG

o and K at 298K

GΔ

o^

(kJ/mol)

(^) K
Comments
-75 1.4x10
13
extensive reaction that goes to completion
-10 57
extensive reaction but measurable amounts of reactants remain
0 1
equilibrium amounts of reactants and products are comparable
+10 0.018
not an extensive reaction but measurable amounts of product form
+75 7.1x10
-13
essentially no reaction
Consider Table 9.5, which shows some values of
ΔG
o and K as determined with Equation
9.8. When
ΔG
o is very large and negative, K is very
large, which can occur only when the
denominator (amounts of reactants remaining) is exceedingly small. Thus, such reactions go nearly to completion and are said to be
extensive. At low negative values of
ΔG
o, K >1
and the reaction is still said to be extensive because the equilibrium amounts of products are higher than those of the reactants. However, substantial amounts of reactant can be present at equilibrium. When
ΔG
o = 0, K = 1, so the product and reactant amounts are
comparable. As
ΔG
o becomes positive, the reactants begin to dominate the equilibrium
mixture.
As mentioned earlier,
ΔG
o can be determined from tables, and the equilibrium
constant can be determined from the value of
ΔG
o. In our treatment, we will
assume
that
ΔG
o is dominated by the value of
ΔH
o in reactions that do not involve a change in the
number of moles of gas because the T
ΔS
o term for these reactions is normally negligible
compared to the much larger
ΔH
o term. Consequently,
we assume that K is large for
exothermic reactions and small for endothermic reactions
that do not involve a change in
the number of moles of gas

.^

Chapter 9 Reaction Energetics

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