Exact and Approximate Calculations of Acid-Base Equilibria

​
acid dissociation equilibrium
water dissociation equilibrium with small concentrations of strong acid/base
acid concentration (M)
0.01
acid dissociation constant (M)
-5
concentration precision
3
acid dissociation precision
6
7
8
9
10
base concentration (M)
1.01×
-8
10
zoom
-8
acid/base
initial concentration of acid
C
a
(M)
0.01
1
​
acid dissociation constant (M)
0.00001
1
[​
+
H
​]
exact
0.00031127
[​
+
H
​]
approximate
0.00031623
% deviation
1.59364
exact
approximate
In this Demonstration, we show exact and approximate calculations for acid-base equilibria.
The equation for acid dissociation (and similarly for base)
HA
k
⇌
-
A
+
+
H
is given by
x=
k(C-x)
, where
C
is the acid (base) concentration and
K
is the acid (base) dissociation constant. This equation can be approximated in the case
x≪C
by
x=
kC
. The first graphic shows the results for concentration and the dissociation calculated both exactly and approximately. The appropriate number of significant digits is used.
In the case of a strong acid/base concentration, the water dissociation is determined by
2
x
=-xC+
K
w
, where
C
is the acid (base) concentration and
K
w
is the autoionization constant of water (at
T=25°C
,
K
w
=
-14
10
2
M
). When
C≫x
, this can be approximated by
x=
K
w
C
. Use the checkbox to switch from acid to base.

Details

Snapshot 1: Exact and approximate equations give the same result since the initial concentration is high and the extent of dissociation is very low (weak acid).
Snapshot 2: Exact and approximate equations are very different since we have a very high acid dissociation constant. In this case, the acid is completely dissociated (strong acid).
Snapshot 3: Incorrect use of the approximate equation gives the pH of a base although the solution is a slightly acidic.

References

[1] D. C. Harris, Quantitative Chemical Analysis, 8th ed., New York: W. H. Freeman and Company, 2010.

External Links

Successive Dissociations of Polyprotic Acid

Permanent Citation

A. Ratti, D. Meliga, L. Lavagnino, S. Z. Lavagnino
​
​"Exact and Approximate Calculations of Acid-Base Equilibria"​
​http://demonstrations.wolfram.com/ExactAndApproximateCalculationsOfAcidBaseEquilibria/​
​Wolfram Demonstrations Project​
​Published: June 18, 2021