Physical Chemistry , 1st ed.

the volume were suddenly decreased to 0.500 L at the same temperature, ef-

fectively doubling the pressure. The equilibrium then shifts to relieve the

stress of the increased pressure. What are the new equilibrium partial pres-

sures? Are the new values consistent with Le Chatelier’s principle?

Solution

If the pressure is suddenly decreased to 0.500 L isothermally, then the partial

pressures of I 2 and I double to 0.470 and 1.030 atm, respectively. In response

to this stress, the equilibrium will shift to re-establish the proper value of the

equilibrium constant, which is 1.13. Our initial and equilibrium amounts are:

Pressure (atm) I 2 2 I

Initial 0.470 1.030

Equilibrium 0.470 x 1.030  2 x

Notice in this example that we are working directly with partial pressures.

We can substitute the equilibrium partial pressures into the equilibrium con-

stant expression:

K(p

p

I

I

/

2 /

p

p

°

°

)^2 (1

0

.0

.4

3

7

0

0





2

x

x)^2 1.13

Using the known value for the equilibrium constant, we can simplify the

fraction and multiply through. Simplifying, we get the quadratic equation

4 x^2 5.25x0.5298  0

which has two roots:x1.203 and x0.110. The first root is not physically

possible because then we would have a negative pressure for I. Thus,x0.110

is the only acceptable algebraic solution, and our final pressures are

pI1.030 2(0.110) 0.810 atm

pI 2 0.470 0.110 0.580 atm

You can verify that these values still give the correct equilibrium constant

value. Note that the partial pressure of I has gone down from its original, in-

stantaneously doubled pressure, and that the partial pressure of I 2 has gone

up—in accordance with Le Chatelier’s principle.

Finally, let us note that if an inert gas is added to a gas-phase equilibrium,
one of two things happens depending on the conditions. If the addition of in-
ert gas does notchange the partial pressures of the gas-phase species (say, the
total volume increases instead), the position of the equilibrium does not
change. However, if the inert gas pressure does change the partial pressures of
the gas-phase species, then the equilibrium position does change as illustrated
in Example 5.11.

5.6 Amino Acid Equilibria

As section 2.12 and Example 5.10 show, the principles of thermodynamics are
applicable even to the complex reactions that occur in living cells. The topic of
equilibrium is also applicable, even though living cells are not isolated or even
closed systems.
First, we should point out the seldom-recognized idea that most chemical
reactions in cells are not at chemical equilibrium. If an organism or cell were

QP

5.6 Amino Acid Equilibria 135