The Foundations of Chemistry

Because the product (0.050
x)(x) is a very small number, we know that xmust be very small.

Thus, it will not matter whether we add xto 0.050; we can assume that (0.050
x)
0.050.

We substitute this approximation into the equation and solve.

1.0 10 ^14 (0.050)(x)orx2.0 10 ^13 M[OH]

We see that the assumption that xis much smaller than 0.050 was a good one.

You should now work Exercise 14.

In solving Example 18-2 we assumed that allof the H 3 O
(0.050 M) came from the

ionization of HNO 3 and neglected the H 3 O
formed by the ionization of H 2 O. The

ionization of H 2 O produces only 2.0 10 ^13 MH 3 O
and 2.0 10 ^13 MOHin this

solution. Thus, we were justified in assuming that the [H 3 O
] is derived solely from the

strong acid. A more concise way to carry out the calculation to find the [OH] concen-

tration is to write directly

Kw[H 3 O
][OH]1.0 10 ^14 or [OH]

Then we substitute to obtain

[OH]2.0 10 ^13 M

From now on, we shall use this more direct approach for such calculations.

When nitric acid is added to water, large numbers of H 3 O
ions are produced. The

large increase in [H 3 O
] shifts the water equilibrium far to the left (LeChatelier’s Prin-

ciple), and the [OH] decreases.

H 2 O(
)
H 2 O(
) 34 H 3 O
(aq)
OH(aq)

In acidic solutions the H 3 O
concentration is always greater than the OHconcen-

tration. We should not conclude that acidic solutions contain no OHions. Rather, the

[OH] is always less than 1.0 10 ^7 Min such solutions. The reverse is true for basic

solutions, in which the [OH] is always greater than 1.0 10 ^7 M. By definition, “neutral”

aqueous solutions at 25°C are solutions in which [H 3 O
][OH]1.0 10 ^7 M.

1.0 10 ^14



0.050

1.0 10 ^14



[H 3 O
]

1.0 10 ^14



0.050

Recall that

[OH]from H 2 O[H 3 O
]from H 2 O

in allaqueous solutions. So we know
that [H 3 O
]from H 2 Omust also be
2.0 10 ^13 M.

756 CHAPTER 18: Ionic Equilibria I: Acids and Bases

Solution General Condition At 25°C

acidic [H 3 O
][OH][H 3 O
]1.0 10 ^7 [OH]1.0 10 ^7

neutral [H 3 O
][OH][H 3 O
]1.0 10 ^7 [OH]1.0 10 ^7

basic [H 3 O
][OH][H 3 O
]1.0 10 ^7 [OH]1.0 10 ^7

THE pH AND pOH SCALES

The pH and pOH scales provide a convenient way to express the acidity and basicity of

dilute aqueous solutions. The pHand pOHof a solution are defined as

pHlog [H 3 O
]or[H 3 O
] 10 pH

pOHlog [OH] or [OH] 10 pOH

18-3