Untitled - Kelly Walsh High School

Acids and Bases 231
Quick Tip
We need to determine the value of K b to finish the problem. We know K a and
we know that K aK b K w 1.0 10 14 . Therefore, we can find K b from:
K w
Kb 5.7471 1010 1.0 10
(unrounded)
We can add this information to the equilibrium constant expression:
14
1.74 105 Ka Kb 5.7471 1010 [x] [x]
[C2H3O2 ] [0.400 x]
From this equation, we can determine that x 1.51619 10 5 M (unrounded).
This is the hydroxide ion concentration.
There are two ways to determine the pH from the hydroxide ion concentration.
One method uses K w while the other method uses the pOH of the solution. The
K w approach is:
K w
[OH ] [HC 2 H 3 O 2 ]
K w [H ] [OH ] 1.0 10 14
[H ] 6.5955 1010 (unrounded)
pH log [H ] log (6.5955 1010 1.0 10
) 9.18076 9.18
14
1.51619 105 [OH ]
The pOH method begins by determining the pOH of the solution:
pOH log [OH ] log (1.51619 10 5 ) 4.8192 (unrounded)
Next we use the relationship pK w pH pOH 14.00
pH pK w pOH 14.00 4.8192 9.18
Both methods give us a basic solution, which we should expect from a base like
the acetate ion.
The pH of any acid solution must be below 7 and the [H ] must be greater than
10 7 M. The pH of any base solution must be above 7 and the [OH ] must be
greater the 10 7 M ([H ] < 10 7 M). If your results disagree with this, you have
made an error.