The Foundations of Chemistry

Plan

Write the appropriate equations for bothNaCH 3 COO andCH 3 COOH and the ionization

constant expression for CH 3 COOH. Then, represent the equilibriumconcentrations alge-

braically and substitute into the Kaexpression.

Solution

The appropriate equations and ionization constant expression are

rxn 1 NaCH 3 COO88nNa CH 3 COO
 (to completion)

rxn 2 CH 3 COOHH 2 O 34 H 3 OCH 3 COO
 (reversible)

Ka1.8 10 
^5

This Kaexpression is valid for all solutionsthat contain CH 3 COOH. In solutions that contain

both CH 3 COOH and NaCH 3 COO, CH 3 COO
ions come from two sources. The ionization

constant is satisfied by the totalCH 3 COO
concentration.

Because NaCH 3 COO is completely dissociated, the [CH 3 COO
] from NaCH 3 COOwill be

0.20 mol/L. Let x[CH 3 COOH] that ionizes; then xis also equal to [H 3 O] andequal to

[CH 3 COO
] from CH 3 COOH.The totalconcentration of CH 3 COO
is (0.20x) M.The

concentration of nonionized CH 3 COOH is (0.10
x) M.

Substitution into the ionization constant expression for CH 3 COOH gives

Ka1.8 10 
^5

The small value of Kasuggests that xis very small. This leads to two assumptions.

(x)(0.20x)



(0.10
x)

[H 3 O][CH 3 COO
]



[CH 3 COOH]

[H 3 O][CH 3 COO
]



[CH 3 COOH]

19-1 The Common Ion Effect and Buffer Solutions 795

The general equations

NaA88nNaA


and

HA 34 HA


may be used in place of these

equations.

You can verify the validity of the

assumption by substituting the value

for x, 9.0 10 
^6 , into the original

equation.

rxn 1 NaCH 3 COO Na
0.20 M 0.20 M 0.20 M

(0.10 
 x) Mx Mx M

rxn 2 CH 3 COOH H 2 OH 3 O

CH 3 COO

CH 3 COO



Total [CH 3 COO
]  (0.20  x) M

Assumption Implication

x0.20, so Most of the CH 3 COO
comes from NaCH 3 COO

(0.20x)
0.20 (rxn 1) and very little CH 3 COO
comes from

ionization of CH 3 COOH (rxn 2)

x0.10, so Very little of the CH 3 COOH ionizes (rxn 2)

(0.10
x)
0.10

It is reasonable to assume that x(from the ionization of CH 3 COOH) is small, because

CH 3 COOH is a weak acid (rxn 2), and its ionization is further suppressed by the high concen-

tration of CH 3 COO
formed by the soluble salt, NaCH 3 COO (rxn 1).

Introducing these assumptions gives



0

0

.2

.1

0

0

x

1.8^10 
^5 and x9.0^10 
^6

xM [H 3 O]9.0 10 
^6 M so pH5.05

You should now work Exercise 8.