The Foundations of Chemistry

From our calculations we can draw some conclusions. In a solution containing only a
weak monoprotic acid, the concentration of H 3 O
is equal to the concentration of the anion
of the acid. Unless the solution is verydilute, such as less than 0.050 M, the concentration
of nonionized acid is approximately equal to the molarity of the solution. When the value
of Kafor the weak acid is greater than
10 ^3 , then the extent of ionization will be large
enough to make a significant difference between the concentration of nonionized acid and
the molarity of the solution. In such cases we cannotmake the simplifying assumption.

EXAMPLE 18-11 Percent Ionization

Calculate the percent ionization of a 0.10 Msolution of acetic acid.

Plan

Write the ionization equation and the expression for Ka. Next, follow the procedure used in
Example 18-10 to find the concentration of acid that ionized. Then, substitute the concentra-
tion of acid that ionized into the expression for percent ionization. Percentage is defined as
(part/whole)100%, so the percent ionization is

% ionization100%

Solution

The equations for the ionization of CH 3 COOH and its Kaare

CH 3 COOH
H 2 O 34 H 3 O

CH 3 COO Ka1.8 10 ^5

We proceed as we did in Example 18-10. Let x[CH 3 COOH]ionized.

CH 3 COOH
H 2 O 34 H 3 O

CH 3 COO

initial 0.10 M 
 0 M 0 M

change due to rxn x M 
x M 
x M

at equil (0.10x) Mx Mx M

Substituting into the ionization constant expression gives

Ka1.8 10 ^5

If we make the simplifying assumption that (0.10x)
0.10, we have



0

x

.1

2

0

1.8 10 ^5 x^2 1.8 10 ^6 x1.3 10 ^3

(x)(x)



(0.10x)

[H 3 O
][A]



[HA]

[H 3 O
][A]



[HA]

[CH 3 COOH]ionized



[CH 3 COOH]initial

We could write the original [H 3 O
] as

1.0 10 ^7 M. In very dilutesolutions

of weak acids, we might have to take

this into account. In this acid solution,

(1.0 10 ^7 
x)
x.

18-4 Ionization Constants for Weak Monoprotic Acids and Bases 767

square roots of both sides. To check, we see that the result, x5.9 10 ^5 , is only

0.059% of 0.10. This error is much less than 5%, so our assumption is justified. You

may also wish to use the quadratic formula to verify that the answer obtained this way

is correct to within roundoff error.

The preceding argument is purely algebraic. We could use our chemical intuition to

reach the same conclusion. A small Kavalue (10^3 or less) tells us that the extent of

ionization is very small; therefore, nearly all of the weak acid exists as nonionized mole-

cules. The amount that ionizes is insignificant compared with the concentration of

nonionized weak acid.

The pH of a soft drink is measured

with a modern pH meter. Many soft

drinks are quite acidic due to the

dissolved CO 2 and other ingredients.