Page 184 - Modern Analytical Chemistry

1400-CH06 9/9/99 7:41 AM Page 167

Chapter 6 Equilibrium Chemistry 167

–
+
[NH 4 ] = [OH ]
We continue by multiplying together the equations for K sp and b 2 , giving
–
(
[ Ag NH 3 2 + I ] 9 –
) ][
K sp b 2 = 2 = . 10
14 ´
[ NH 3 ]
Substituting in the new mass balance equations for NH 3 and I –
– 2
I
[] –9
= . 14 ´ 10
C ) 2
( NH 3
–
and solving for the [I ] gives
– 2
I
[] –9
= . 14 ´ 10
(. 010 M ) 2
–
[] = . 37 ´ 10 –6 M
I

Before accepting this answer, we first check our assumptions. Using the K sp
+
equation we calculate the [Ag ] to be
. ´10
K sp 83 –17 –11
. ´10
[Ag + ] = – = –6 = 22 M
I
. ´10
[] 37
–
From the simplified mass balance equation for I , we have
–
–6
+
[Ag(NH 3 ) 2 ]=[I ] = 3.7 ´10 M
+
+
Our first assumption that the [Ag ] is significantly smaller than the [Ag(NH 3 ) 2 ],
+
therefore, is reasonable. Furthermore, our third assumption that the [Ag(NH 3 ) 2 ] is
significantly less than the [NH 3 ] also is reasonable. Our second assumption was
+
+
[NH 4 ] << [NH 3 ] + [Ag(NH 3 ) 2 ]
+
To verify this assumption, we solve the K b equation for [NH 4 ]
[NH + ][OH – ] [NH + ] 2
4 = 4 = . 175 ´ 10 –5
] . 010 M
[NH 3
giving
–3
+
[NH 4 ] = 1.3 ´10 M
+
Although the [NH 4 ] is not significantly smaller than the combined concentrations
+
of NH 3 and Ag(NH 3 ) 2 , the error is only about 1%. Since this is not an excessively
large error, we will accept this approximation as reasonable.
–
Since one mole of AgI produces one mole of I , the solubility of AgI is the same
–6
as the concentration of iodide, or 3.7 ´10 mol/L.
6H Buffer Solutions
Adding as little as 0.1 mL of concentrated HCl to a liter of H 2 O shifts the pH from
7.0 to 3.0. The same addition of HCl to a liter solution that is 0.1 M in both a weak
buffer
acid and its conjugate weak base, however, results in only a negligible change in pH.
A solution containing a conjugate weak
Such solutions are called buffers, and their buffering action is a consequence of the acid/weak base pair that is resistant to a
relationship between pH and the relative concentrations of the conjugate weak change in pH when a strong acid or
acid/weak base pair. strong base is added.