Physical Chemistry Third Edition

7.3 Chemical Equilibrium in Solutions 319

∆G◦∆fG◦(H 2 O)+(−1)∆fG◦(OH−)−∆fG◦(H+)

(− 237 .141 kJ mol−^1 )+(−1)(− 157 .244 kJ mol−^1 )+(−1)0

− 79 .892 kJ mol−^1

∆S◦Sm◦(H 2 O)+(−1)Sm◦(OH−)+(−1)S◦m(H+)

(69.95JK−^1 mol−^1 )+(−1)(− 10 .75JK−^1 mol−^1 )− 10

 80 .70JK−^1 mol−^1

There is no need to include the “spectator ions” Na+and Cl−since they occur on both sides

of the equation and their contributions cancel.

The previous example involved a reaction of strong electrolytes, which appear to

ionize or dissociate completely in aqueous solution. There are only six common strong

acids (acids that appear to ionize completely). In addition to HCl, the others are HClO 4 ,

HI, HBr, HNO 3 , and H 2 SO 4. Other acids areweak acids, which means that they ionize

only partially in aqueous solution. NaOH and other metal hydroxides are strong bases.

There are many weak bases, including ammonia (NH 3 ).

EXAMPLE 7.9

Find the equilibrium molality of hydroxide ions in a solution formed from 0.1000 mol of

NH 3 and 1.000 kg of water at 298.15 K.

Solution

The reaction that occurs is

NH 3 (aq)+H 2 O
NH+ 4 +OH−

We omit the label “aq” on the ions since they occur only in the aqueous phase.

∆G◦∆fG◦(NH+ 4 )+∆fG◦(OH−)−∆fG◦(NH 3 )−∆fG◦(H 2 O)

(− 79 .31 kJ mol−^1 )+(− 157 .244 kJ mol−^1 )−(− 26 .50 kJ mol−^1 )

−(237.141 kJ mol−^1 )

− 27 .087 kJ mol−^1

We denote the equilibrium constant of a weak base byKb.

Kb

γ(NH+ 4 )(meq(NH+ 4 )/m◦)γ(OH−)(meq(OH−)/m◦)

γ(NH 3 )(meq(NH 3 )/m◦)γ(H 2 O)xeq(H 2 O)

e−∆G

◦/RT

exp

⎡

⎣− 27087 J mol

− 1

(

8 .3145 J K−^1 mol−^1

)

(298.15 K)

⎤

⎦

 1. 80 × 10 −^5