Chemistry Common Ion Effect, Hydrolysis of Salts and the pH of their Solutions and Buffer solutions

### Topic to be covered

star Common Ion Effect in the Ionization of Acids and Bases.
star Hydrolysis of Salts and the pH of their Solutions.
star Buffer solutions.

### Common Ion Effect in the Ionization of Acids and Bases

=> Consider an example of acetic acid dissociation equilibrium represented as:

color{red}(CH_3COOH(aq) ⇌ H+(aq) + CH_3COO^– (aq))

or color{red}(HAc(aq) ⇌ H^+ (aq) + Ac^– (aq))

color{red}(K_a = [H^+][Ac^– ] // [HAc])

=> Addition of acetate ions to an acetic acid solution results in decreasing the concentration of hydrogen ions, color{red}([H^+]). Also, if color{red}(H^+) ions are added from an external source then the equilibrium moves in the direction of undissociated acetic acid i.e., in a direction of reducing the concentration of hydrogen ions, color{red}([H^+]). This phenomenon is an example of common ion effect.

color{purple}(✓✓)color{purple} " DEFINITION ALERT"

color{green}("COMMON ION EFFECT") : It can be defined as a shift in equilibrium on adding a substance that provides more of an ionic species already present in the dissociation equilibrium. Thus, we can say that common ion effect is a phenomenon based on the Le Chatelier’s principle.

=> In order to evaluate the color{red}(pH) of the solution resulting on addition of 0.05M acetate ion to 0.05M acetic acid solution, we shall consider the acetic acid dissociation equilibrium once again,

color{red}(HAc(aq) ⇌ H^+(aq) + Ac^–(aq))

color{green}("Initial concentration (M)")

color{red}(0.05 \ \ \ \ \ \ \ \ 0 \ \ \ \ \ \ \ 0.05)

Let color{red}(x )be the extent of ionization of acetic acid.

color{green}("Change in concentration (M)")

color{red}(-x \ \ \ \ \ \ \ \ + x \ \ \ \ \ \ \ \ +x)

color{green}("Equilibrium concentration (M)")

color{red}(0.05 -x \ \ \ \ \ \ \ \ x \ \ \ \ \ \ \ 0.05+x)

Therefore,
color{red}(K_a= [H^+][Ac^– ]//[H Ac] = {(0.05+x)(x)}/(0.05-x))

As color{red}(K_a) is small for a very weak acid, color{red}(x < < 0.05).

Hence, color{red}((0.05 + x) ≈ (0.05 – x) ≈ 0.05)

Thus,
color{red}(1.8 × 10^(–5) = (x) (0.05 + x) // (0.05 – x))

color{red}(= x(0.05) // (0.05) = x = [H^+] = 1.8 × 10^(–5)M)

color{red}(pH = – log(1.8 × 10^(–5)) = 4.74)

Q 3150112014

Calculate the pH of a 0.10M ammonia solution. Calculate the pH after 50.0 mL of this solution is treated with 25.0 mL of 0.10M HCl. The dissociation constant of ammonia, K_b = 1.77 × 10^(–5)

Solution:

NH_3 + H_2O → NH_4^+ + OH^–

K_b = [NH_4^+][OH^–] // [NH_3] = 1.77 × 10^(–5)

Before neutralization, [NH_4^+] = [OH^–] = x [NH_3] = 0.10 – x approx 0.10

x^2 // 0.10 = 1.77 × 10^(–5)

Thus, x = 1.33 × 10^(–3) = [OH^–]
Therefore,[H^+] = K_w // [OH^–] = 10^(–14) // (1.33 × 10^(–3)) = 7.51 × 10^(–12)
pH = –log(7.5 × 10^(–12)) = 11.12
On addition of 25 mL of 0.1M HCl
solution (i.e., 2.5 mmol of HCl) to 50 mL of 0.1M ammonia solution (i.e., 5 mmol of NH_3), 2.5 mmol of ammonia molecules
are neutralized. The resulting 75 mL solution contains the remaining unneutralized 2.5 mmol of NH_3 molecules and 2.5 mmol of NH_4^+.

tt (( NH_3 , + , HCl , → , NH_4^+ , + , Cl^(-) ) , ( 2.5 , , 2.5 , , 0 , , 0 ),("At equilibrium " , , , , , , ), (0 , , 0 , , 2.5 , , 2.5))

The resulting 75 mL of solution contains 2.5 mmol of NH_4^+ ions (i.e., 0.033 M) and 2.5 mmol (i.e., 0.033 M ) of uneutralised NH3 molecules. This NH_3 exists in the following equilibrium:

tt (( NH_4OH , ⇌ , NH_4^+ , + , OH^- ) , (0.033M-y , , y , , y))

where, y = [OH^–] = [NH_4^+]

The final 75 mL solution after neutralisation already contains 2.5 m mol NH_4^+ ions (i.e. 0.033M), thus total concentration of NH_4^+ ions is given as:

[NH_4^+ ] = 0.033 + y

As y is small, [NH_4OH] approx 0.033 M and [NH_4^+] approx 0.033M.

We know,

K_b = [ NH_4^+] [ OH^(-) ] // [NH_4OH]

y(0.033)//(0.033) = 1.77 xx 10^(-5) M

Thus, y = 1.77 × 10^(–5) = [OH^–]

[H^+] = 10^(–14) // 1.77 × 10^(–5) = 0.56 × 10^(–9)
Hence, pH = 9.24

### Hydrolysis of Salts and the pH of their Solutions

=> Salts formed by the reactions between acids and bases in definite proportions, undergo ionization in water.

=> The cations/anions formed on ionization of salts either exist as hydrated ions in aqueous solutions or interact with water to reform corresponding acids/bases depending upon the nature of salts. The later process of interaction between water and cations/anions or both of salts is called hydrolysis. The pH of the solution gets affected by this interaction. The cations (e.g., color{red}(Na^+, K^+, Ca^(2+), Ba^(2+)), etc.) of strong bases and anions (e.g., color{red}(Cl^–, Br^–, NO_3^–, ClO_4^–) etc.) of strong acids simply get hydrated but do not hydrolyse, and therefore the solutions of salts formed from strong acids and bases are neutral i.e., their color{red}(pH) is 7. However, the other category of salts do undergo hydrolysis.

color{green}("We now consider the hydrolysis of the salts of the following types :")

(i) salts of weak acid and strong base e.g., color{red}(CH_3COONa).
(ii) salts of strong acid and weak base e.g., color{red}(NH_4Cl), and
(iii) salts of weak acid and weak base, e.g., color{red}(CH_3COONH_4).

=> In the first case, color{red}(CH_3COONa) being a salt of weak acid, color{red}(CH_3COOH) and strong base, color{red}(NaOH) gets completely ionised in aqueous solution. color{red}(CH_3COONa(aq) → CH_3COO^– (aq)+ Na^+(aq))

Acetate ion thus formed undergoes hydrolysis in water to give acetic acid and color{red}(OH^–) ions

color{red}(CH_3COO^–(aq)+H_2O(l) ⇌ CH_3COOH(aq)+OH^–(aq))

Acetic acid being a weak acid color{red}((K_a = 1.8 × 10^(–5))) remains mainly unionised in solution. This results in increase of color{red}(OH^(–)) ion concentration in solution making it alkaline. The color{red}(pH) of such a solution is more than 7.

=> Similarly, color{red}(NH_4Cl) formed from weak base, color{red}(NH_4OH) and strong acid, color{red}(HCl), in water dissociates completely.

color{red}(NH_4Cl(aq) → NH_4^+ (aq) +Cl^– (aq))

Ammonium ions undergo hydrolysis with water to form color{red}(NH_4OH) and color{red}(H^+) ions

color{red}(NH_4^+ (aq) + H_2O (l) ⇌ NH_4 OH (aq) +H^+ (aq))

Ammonium hydroxide is a weak base (color{red}(K_b = 1.77 × 10^(–5))) and therefore remains almost unionised in solution. This results in increased of color{red}(H^+) ion concentration in solution making the solution acidic. Thus, the color{red}(pH) of color{red}(NH_4Cl) solution in water is less than 7.

=> Consider the hydrolysis of color{red}(CH_3COONH_4) salt formed from weak acid and weak base. The ions formed undergo hydrolysis as follow:

color{red}(CH_3COO^– + NH_4^+ + H_2O ⇌ CH_3COOH + NH_4OH)

color{red}(CH_3COOH) and color{red}(NH_4OH), also remain into partially dissociated form :

color{red}(CH_3COOH ⇌ CH_3COO^(–) + H^+)

color{red}(NH_4OH ⇌ NH_4^+ + OH^–)

color{red}(H_2O ⇌ H^(+) + OH^(–))

Without going into detailed calculation, it can be said that degree of hydrolysis is independent of concentration of solution, and
color{red}(pH) of such solutions is determined by their color{red}(pK) values:

color{red}(pH = 7 + ½ (pK_a – pK_b)) ............. (7.38)

The color{red}(pH) of solution can be greater than 7, if the difference is positive and it will be less than 7, if the difference is negative.

Q 3110212110

The pK_a of acetic acid and pK_b of ammonium hydroxide are 4.76 and 4.75 respectively. Calculate the pH of ammonium acetate solution.

Solution:

pH = 7 + ½ [pK_a – pK_b]

= 7 + ½ [4.76 – 4.75]

= 7 + ½ [0.01] = 7 + 0.005 = 7.005

### BUFFER SOLUTIONS

=> Many body fluids e.g., blood or urine have definite color{red}(pH) and any deviation in their color{red}(pH) indicates malfunctioning of the body.

=> The control of color{red}(pH) is also very important in many chemical and biochemical processes.

=> Many medical and cosmetic formulations require that these be kept and administered at a particular color{red}(pH).

color{purple}(✓✓)color{purple} " DEFINITION ALERT"
The solutions which resist change in color{red}(pH) on dilution or with the addition of small amounts of acid or alkali are called Buffer Solutions.

Buffer solutions of known color{red}(pH) can be prepared from the knowledge of color{red}(pK_a) of the acid or color{red}(pK_b) of base and by controlling the ratio of the salt and acid or salt and base. A mixture of acetic acid and sodium acetate acts as buffer solution around color{red}(pH 4.75) and a mixture of ammonium chloride and ammonium hydroxide acts as a buffer around color{red}(pH 9.25).