Approximate pH Calculation of Acids

​
C
a
pK
a
This Demonstration compares approximate and exact values of the
pH
for strong and weak acids.

Details

Acids dissociate by the reaction
HA
+
H
+
-
A
. The initial concentration of acid
HA
is
C
a
and the acid dissociation constant is
K
a
. This is often expressed as
p
K
a
=-log
K
a
, where logarithms to base 10 are understood. Stronger acids have higher
K
a
(smaller
p
K
a
) than weaker acids. The acid constant is defined by
K
a
=
[
+
H
][
-
A
]
[HA]
=
2
(
C
a
α)
C
a
(1-α)
,with
[
+
H
]=[
-
A
]=
C
a
α
, where
α
is the fraction of protonation. This implies that
α=
-
K
a
+
K
a
4
C
a
+
K
a
2
C
a
. Thus given
K
a
, one can calculate the exact value of
pH=-log
+
H
=-log(
C
a
α
). In this Demonstration, these exact
pH
values are shown as blue curves.
With the strong acid,
K
a
is very high and
α≈1
, so
pH≈-log
C
a
. This approximation for a strong acid is shown by the red curves, which intersect the
pH
axis at
-log
C
a
.
With the weak acid,
K
a
is very small compared with
C
a
, so
α≈
C
a
K
a
C
a
, thus
pH=
1
2
(p
K
a
-log
C
a
)
. This approximation is shown as the green line with slope
1
2
and intercept at
-
1
2
log
C
a
.
We can see that the approximation for a weak acid is not valid at higher concentrations
C
a
. Thus the approximation for strong acids is only applicable if either
p
K
a
or the concentration is small.
This Demonstration is intended for first year chemistry students (in course LC102, University Pierre Marie Curie, Paris, France).

Permanent Citation

Quang-Dao Trinh
​
​"Approximate pH Calculation of Acids"​
​http://demonstrations.wolfram.com/ApproximatePHCalculationOfAcids/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011