Physical Chemistry Third Edition

340 7 Chemical Equilibrium

which gives

4. 0540 α^2 + 2. 1750 α+ 0. 1054  0

Use of the quadratic formula gives

α− 0. 0539

where a root to the quadratic equation has been disregarded that gives a physically impossible

value ofα. Note thatαcan be negative since additional NO 2 has been added. The final amount

of N 2 O 4 is equal to 1.0539 mol. The mole fraction of NO 2 has shifted to a value of 0.271

instead of 0.506, in agreement with the principle of Le Châtelier.

Exercise 7.20

Verify the result of the previous example by substituting the value ofα. Find the physically

unacceptable root and explain why it cannot be correct.

The action of a buffer solution can also be interpreted according to the principle of

Le Châtelier.

EXAMPLE7.21

Assume that 0.00200 mol of solid NaOH is added to the buffer solution of Example 7.16.

Calculate the change in the pH of the solution.

Solution

The resulting solution is the same as a solution made with 0.3980 mol of acetic acid and

0.6020 mol of sodium acetate. Neglect the ionization and hydrolysis and use the value ofγ

from the example. Letxm(H+)/m◦.

Ka 1. 75 × 10 −^5 

γ^2 x(ms/m◦)

ma/m◦



(0.740)^2 (0.6020)x

0. 3980

 0. 8283 x

x

1. 75 × 10 −^5

0. 8283

 2. 11 × 10 −^5

pH−log 10 ((0.740)(2. 11 × 10 −^5 )) 4. 81

The pH has changed by only 0.01.

Exercise 7.21

Calculate the change in the pH if 0.00200 mol of solid NaOH is added to a solution of HCl with

the same pH as the buffer solution of Example 7.21.