Page 261 - Theory and Problems of BEGINNING CHEMISTRY

250 ACID-BASE THEORY [CHAP. 17

the OH concentration; it is neutral if the two concentrations are equal; and it is basic if the OH concentration
−
−
exceeds the H 3 O concentration:
+
−
+
[H 3 O ] > [OH ] acidic
+
−
[H 3 O ] = [OH ] neutral
+
−
[H 3 O ] < [OH ] basic
EXAMPLE 17.8. Calculate the hydronium ion concentration in pure water at 25 C.
◦
Ans. 2H 2 O −→ H 3 O + OH −
+
←−
+
K w = [H 3 O ][OH ] = 1.0 × 10 −14
−
Both ions must be equal in concentration since they were produced in equal molar quantities by the autoionization
reaction. Let the concentration of each be equal to x.
2
x = 1.0 × 10 −14
x = 1.0 × 10 −7 = [H 3 O ] = [OH ]
+
−
EXAMPLE 17.9. Calculate the hydronium ion concentration in 0.0010 M NaOH.
−
+
Ans. K w = [H 3 O ][OH ] = 1.0 × 10 −14
−
[OH ] = 0.0010 M
+
[H 3 O ](0.0010) = 1.0 × 10 −14
+
[H 3 O ] = 1.0 × 10 −11
The OH from the NaOH has caused the autoionization reaction of water to shift to the left, yielding only a tiny
−
+
fraction of the H 3 O that is present in pure water.
17.5. THE pH SCALE
The pH scale was invented to reduce the necessity for using exponential numbers to report acidity. The pH
is defined as
pH =−log[H 3 O ]
+

+
EXAMPLE 17.10. Calculate the pH of (a) 0.010 M H 3 O solution and (b) 0.010 M HCl solution.
+
Ans. (a) [H 3 O ] = 0.010 = 1.0 × 10 −2
−2
+
pH =−log[H 3 O ] =−log(1.0 × 10 ) = 2.00
+
(b) Since HCl is a strong acid, it reacts completely with water to give 0.010 M H 3 O solution. Thus, the pH is the
same as that in part a.
EXAMPLE 17.11. Calculate the pH of (a) 0.0010 M NaOH and (b) 0.0010 M Ba(OH) 2 .
−
Ans. (a) [OH ] = 0.0010 = 1.0 × 10 −3
[H 3 O ] = 1.0 × 10 −11 (See Example 17.9)
+
pH =−log(1.0 × 10 −11 ) =+11.00
(b) [OH ] = 0.0020 M. (There are two OH ions per formula unit.)
−
−
−
[OH ] = 0.0020 = 2.0 × 10 −3
−3
[H 3 O ] = (1.0 × 10 −14 )/(2.0 × 10 ) = 5.0 × 10 −12
+
pH = 11.30
Special note for electronic calculator users: To determine the negative of the logarithm of a quantity, on some
calculators, enter the quantity, press the LOG key, then press the change-sign key, +/− . On other calculators,