pH calculation - Hydrolysis of salts

A salt is a compound formed by ions, electrically neutral, the product of an acid-base reaction. The salts are strong electrolytes, and placed in water (if soluble) will completely dissociate into their constituent ions, ensuring the solution a certain electrical conductivity. This is regardless of whether they are made from weak or strong acids and weak or strong bases.

In general, the salts may be formed from:

1 - strong acid and strong base

2 - strong acid and weak base

3 - strong base and weak acid

4 - weak acid and weak base

The pH imparted by a salt to a solution is due to the interaction of the ions constituting the salt with H₂O.

Let's see how to calculate the pH for aqueous solutions of these four different kind of salts.

1 - salt of strong acid and strong base

Let's take the simplest example absolute; sodium chloride, NaCl. The constituent ions are Na⁺ and Cl^-. The acid-base theory of Bronsted-Lowry has taught us that the more strong the base the weaker it will be its conjugate acid and vice versa, the more strong the acid the weaker will be its conjugate base.

In this case, we have Na⁺, which is the conjugate acid of NaOH, and Cl^-, which is the conjugate base of HCl. NaOH is a strong base, and in the same way HCl is a strong acid. It follows that the Na⁺ acid behavior and Cl^- basic behavior are totally irrelevant.

If none of the two ions interacts with H₂O then we will have no pH changes.

It follows that the pH of an aqueous solution of NaCl is neutral, 7.

The salts derived from strong acid and strong base leave unchanged the pH of a solution.

2 - salt of weak acid and strong base

Take for example the sodium acetate, CH₃COONa. And 'it is including respectively CH₃COO^- and Na⁺. Na⁺ is the conjugate acid of NaOH, and as we saw in the previous example, its contribution to the pH is null. CH₃COO^- instead it is the conjugate base of CH₃COOH, a weak acid. As the conjugate base of a weak acid, it shows a certain affinity towards the proton, and it behaves then as a base:

$CH_3COO ^ - + H_2O \ rightleftharpoons CH_3COOH + OH ^ -$

The acid-base reaction of CH₃COO^- with water is called "hydrolysis." In this case we are speaking of basic hydrolysis, because the reaction generates an excess of OH^-.Since the reaction generates this excess, the salt of a weak acid and a strong base in water give a pH> 7, therefore alkaline. For the calculation of pH, we can consider the solution of this salt exactly as the solution of just a weak base (in our case CH₃COO^-). We have seen that the formula for calculating $[OH^-]$ generated resulting from a weak base is:

$[OH ^ -] = \ sqrt {k_B \ cdot C_b}$

The K_b of the weak base CH₃COO^- can be obtained from K_a of acetic acid as it follows:

$K_w k_B = \ cdot K_a$ $K_B = \ frac {} {K_w K_a}$

The base concentration $C_b$ in this case is the concentration $C_s$ of our salt.

From this considerations the formula for calculating the $[OH^-]$ a salt-strong base weak acid solution:

$\ Bg_white \ bg_white [OH ^ -] = \ sqrt {\ frac {} {K_w K_a} \ cdot C_s}$

from which you can derive the pH every time you have this specific circumstances.

3 - salt of weak base and strong acid

Take for example the ammonium chloride, NH₄Cl. Its constituent ions are NH₄⁺ and Cl^-.NH₄⁺ is the conjugate acid of NH₃_, ammonia, a weak base. It will therefore have a tendency, altough small, to cede that acid hydrogen. Cl^- instead is the conjugate base of HCl, and as we have seen in the examples above its contribution to the pH is practically zero, and then we can overlook it. We can simply consider a solution of this salt as an aqueous solution of the weak acid NH₄⁺ (which will then give an acid pH)

$NH_4 ^ + + H_2O \ rightleftharpoons NH_3 H_3O + ^ +$

The approximate formula to calculate the pH of a weak acid is the following:

$[H_3O ^ +] = \ sqrt {K_a \ cdot C_A}$

The K_a of the ammonium ion can be easily obtained from the K_b of ammonia. The concentration of acid in the formula, Ca , is therefore in this case the concentration C_s of our salt.

$\ Bg_white \ bg_white \ bg_white [H_3O ^ +] = \ sqrt {\ frac {} {K_w k_B} \ cdot C_s}$

4 - salt of weak acid and weak base

Let's take for example ammonium acetate, CH₃COONH_4. The constituent ions are CH₃COO^- and NH₄^+. Both of these ions are able to give hydrolysis (as we have seen in the previous examples); CH₃COO^- gives basic hydrolysis, while acid hydrolysis is given by NH₄⁺.The pH of a salt composed of weak acid and weak base will depend on the strength relationship of the acidic and basic components of the salt. If the base strength and the acid strength are equal the result is a neutral solution. And that's right the case for example of CH₃COONH₄ .

K_aNH₄⁺= K_b CH₃COO^-

If base strength is prevailing on acid strength the salt will give the solution an alkaline pH. And that's the case for example of NH₄CN.

K_bCN^-> K_a NH₄⁺

If the prevailing acid strength on the base strength of course the result will be an acid pH.

In any case if we want to exactly calculate the pH of a salt formed by weak acid and weak base (also what we called a neutral solution if we wanted to be accurate, has to be calculated like this because K_a and K_b are always at least slightly different), there is a very simple formula:

$[H_3O ^ +] = \ sqrt {K_w \ cdot \ frac {} {K_a k_B}}$

In which:

- K_a is the constant of the conjugate acid of the weak base which forms the salt. For example, in the case of CH₃COONH₄ would be the K_a of CH₃COOH.

- K_b is the constant of the conjugate base of the weak acid that constitutes the salt. For example, in the case of CH₃COONH₄ would be the K_b of NH_3.

In summary, when:

K_a> K_b the resulting solution is acidic.
K_b> K_a the resulting solution is alkaline.
K_a = K_b the resulting solution is neutral.