Determine the [OH-] of a solution that is 0.100 M in F-? Determine the pH of this solution?
Answers
Answer:
p
H
sol
=
8.07
Explanation:
You actually need the base dissociation constant,
K
b
, of the fluoride anion,
F
−
, in order to be able to calculate the concentration of hydroxide ions it produces in aqueous solution.
Since you did not provide that value, I will use the acid dissociaation constant,
K
a
, of hydrofluoric acid,
HF
, to calculate the
K
b
of
F
−
.
The
K
a
of hydrofluoric acid is equal to
7.2
⋅
10
−
4
. You know that water's self-ionization constant,
K
W
, is euqal to
10
−
14
at room temperature.
Moreover, you know that
K
W
=
K
a
×
K
b
This means that
K
b
will be equal to
K
b
=
K
W
K
a
=
10
−
14
7.2
⋅
10
−
4
=
1.39
⋅
10
−
11
So, the fluoride anion will actually react with water to form hydrofluoric acid. Use an ICE table to help you determine the equilibrium concentration of the hydroxide ions
F
−
(aq]
+
H
2
O
(l]
→
HF
(aq]
+
OH
−
(aq]
I
0.100
0
0
C
(
−
x
)
(
+
x
)
(
+
x
)
E
(
0.100
−
x
)
x
x
By definition, the base dissociaation constant will be equal to
K
b
=
[
HF
]
⋅
[
OH
−
]
[
F
−
]
=
x
⋅
x
0.100
−
x
Because
K
b
is so small, you can say that
(
0.100
−
x
)
≈
0.100
, which means that you have
K
b
=
x
2
0.100
=
1.39
⋅
10
−
11
x
=
√
0.100
⋅
1.39
⋅
10
−
11
=
1.18
⋅
10
−
6
The equilibrium concentration of hydroxide ions will thus be
x
=
[
OH
−
]
=
1.18
⋅
10
−
6
M
The
p
O
H
of the solution will be
p
O
H
=
−
log
(
[
OH
−
]
)
=
−
log
(
1.18
⋅
10
−
6
)
=
5.93
Therefore, the pH of the solution will be
p
H
sol
=
14
−
p
O
H
=
14
−
5.93
=
8.07