Chapter 9 Reaction Energetics

Example 9.11

The following equilibrium pressures were observed at some temperature: [HI] = 0.200 atm; [I

] = 0.500 atm; and [H 2

] = 0.100 atm 2

What is the value of K for the following reaction? 2HI(g)

U

I(g) + H^2

(g) 2

Recall that gases enter the equilibrium expression as their pressures expressed in atmospheres. The coefficient of HI is two, so

its pressure must be squared. We determine

K as follows:

PPIH^2222 HI

(0.500)(0.100)

K =

=

= 1.25

P

(0.200)

THE MEANING OF K The amount of product that forms in a reac

tion can be determined from the amount of

reactant that

reacts

(not just present) and the stoichiometry (mole ratios) of the balanced

chemical equation. However, the amount of reactant that reacts is determined by the equilibrium constant for the reaction. Calcul

ations based solely on the initial amounts of

reactant assume that at least one of the reactants, the

limiting reactant

, is completely

consumed in the reaction. That is, they assume that the reaction is extensive. In reactions that are not extensive, only a fraction of each reactant is consumed. In these cases, the equilibrium constant must be used along with

stoichiometry to determine the amount of

product. For example, consider the following reaction:

Table 9.4

Equilibrium concentrations of A and B resulting

in a solution that is initially

1.0 M in A as a function of the

equilibrium constant for the reaction A

U

2B.

K [A]

[B]

1.0x10

+6 4.0x10

-6 M

2.0 M

10

a 0.23

1.53

1.0

0.61 M

0.78 M

1.0x10

-6 1.0 M

1.0x10

-3 M

a K > 1, but the equilibrium

concentration of A is still

appreciable, so the reaction is

not extensive. This is why

we use K >> 1 for extensive reactions.

(^2)

[B]
A(aq)
2B(aq) K
[A]
U
Stoichiometry predicts that two moles of B are produced for each mole of A that reacts. However, as shown in Table 9.4 that does not mean that two moles of B form simply because 1 mole of A was present initially. The amount of B that is produced depends upon both the amount of A and the value of K. For example, consider the equilibrium concentrations that result when the initial c
oncentration of A is 1.0 M. When K >>1, the
forward reaction (A
→
2B) dominates, so there is very little A remaining at equilibrium,
and the stoichiometric amount of B forms and the final concentration of B is 2.0 M. However, when the reaction is not extensive, the back reaction (2B
→
A) cannot be
ignored. Thus, when K ~ 1, the forward and back reactions are comparable, so the equilibrium concentrations are comparable.
When K <<1, the back reaction dominates, so
very little A reacts and almost no B forms

.^

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