What is difference between a pH of 8 and a pH of 12 in terms of H+ concentration?
Answers
The pH of a solution is simply a measure of the concentration of hydrogen ions,
H
+
, which you'll often see referred to as hydronium cations,
H
3
O
+
.
More specifically, the pH of the solution is calculated using the negative log base
10
of the concentration of the hydronium cations.
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
pH
=
−
log
(
[
H
3
O
+
]
)
a
a
∣
∣
−−−−−−−−−−−−−−−−−−−−−−−−
Now, we use the negative log base
10
because the concentration of hydronium cations is usually significantly smaller than
1
.
As you know, every increase in the value of a log function corresponds to one order of magnitude. For example, you have
log
(
10
)
=
1
log
(
10
⋅
10
)
=
log
(
10
)
+
log
(
10
)
=
1
+
1
=
2
log
(
10
⋅
10
2
)
=
log
(
10
)
+
log
(
10
2
)
=
1
+
2
=
3
and so on. In your case, the difference between a pH of
8
and a pH of
12
corresponds to a difference of four units of magnitude between the concentration of hydronium cations in the two solutions.
Keep in mind, however, that because you're dealing with numbers that are smaller than
1
, and thus with negative logs, that the solution with a higher pH will actually have a lower concentration of hydronium cations.
More specifically, you have
pH
1
=
−
log
(
[
H
3
O
+
]
1
)
=
8
This is equivalent to
[
H
3
O
+
]
1
=
10
−
pH
1
=
10
−
8
M
Similarly, you have
pH
2
=
−
log
(
[
H
3
O
+
]
2
)
=
12
This is equivalent to
[
H
3
O
+
]
2
=
10
−
pH
2
=
10
−
12
M
As you can see, the first solution has a concentration of hydronium cations that is
10
−
8
M
10
−
12
M
=
10
4
times higher than the concentration of hydronium cations of the second solution. This corresponds to the fact that you have
pH
2
−
pH
1
=
12
−
8
=
4
Simply put, a solution that has a pH that is
4
units lower than the pH of a second solution will have a concentration of hydronium cations that
10
4
times higher than that of the second solution.
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