The Common Ion Effect: pH

The Common Ion Effect is the shift in equilibrium that occurs because of the addition of an ion already involved in the equilibrium reaction.

AgCl(s) <=> Ag+(aq) + Cl-(aq)

<-----------------Addition of NaCl Shifts this equilibrium to the left.

Addition of common ion to a weak acid/base system:

HA <=> H+ + A-
Now add A- ( as a salt ) and the reaction will be driven to left
and [ H+ ] will decrease

Example:

CH3COOH <=> H+ + CH3COO-

Now add NaCH3COO, where acetate is the common ion.

This increases concentration of acetate ion and the reaction is driven to left and the [H+] decreases. The addition of the common ion CH3COO- to a CH3COOH solution is similar to titrating the acid with NaOH since both operations reduce the [H+]. However instead of converting protons to water the common ion combines with protons to form more weak acid.

Practice Problem:

What is the [H+] in a solution containing both 0.50 M HF and 0.10 M NaI?

Remember that salts generally dissociate strongly in water so that the concentration of the anion is roughly the same as the initial concentration of the salt:

Now let's consider the mixture of a weak acid (HA) and its salt formed by strong base (XA) in aqueous solution in more general terms. We know that the weak acid partially dissociates to form H+ and A- and the salt completely dissociates to form X+ and A-.

From the acid equilibrium we can write the following relationship:

The amount of pure weak acid that dissociates is small. It will only be ~ 1.6% for a 0.1 M CH3COOH solution (pKa = 4.74). Thus the concentration of acid HA is still about the same as the amount of acid initially added to water. Likewise, the amount of A- formed by dissociation of the acid will be much smaller than the amount of A- formed by dissociation of the salt -- hence [A-] is approximately the same as the concentration of salt added.We can use these facts to create an equation to simplify the calculation like the one we just completed above:

LIMITATIONS:

It is assumed that the amount of acid that dissociates is small – thus this relationship applies best to weaker acids. It cannot be used with any confidence for acids with pKa < 2.0.

The assumption is also made that very little anion (A-) is contributed by dissociation of weak acid. This is not the case during the initial part of a titration of a weak acid by strong base (or weak base with strong acid) - calculation of titration curves using the Henderson-Hasselbalch equation is subject to error in initial phase.

Using the Henderson-Hasselbalch Equation:

1) Calculate the concentration of H+ and the pH of a solution that is 0.15 M in acetic acid and 0.25 M in sodium acetate. (Ka=1.8e-5)

We can do this easily enough using an ICE table

HC2H3O2      +
H2O
<=>      H+
C2H3O2-
0.15M
0.25M
-x
+x
+x
0.15-x
x
0.15+x

Ka = [(x)(0.25+x)]/0.15-x = 1.8e-5

Assuming x is very small compared to the concentration, the equation reduces to: 0.025x/0.015 = 1.8e-5; and x = 1.08e-5 so the pH is 4.96.

OR

We can use the Henderson-Hasselbalch Equation:

pH = -log(1.8e-5) + log(0.25/0.15) = 4.74 + .2218 = 4.96