Derive and expression for the pH of an aqueous solution of a salt of strong base and weak acid
Answers
Pure water is a weak electrolyte. Weak because it does not completely disassociates into hydrogen and hydroxide but exist in equilibrium with these two ions. It is neutral in nature, i.e., H+ ion concentration is exactly equal to OH- ion concentration
[H+] = [OH-]
Self-Ionization of Water
When this condition is disturbed by decreasing the concentration of either of the two ions, the neutral nature changes into acidic or basic. When [H+] > [OH-], the water becomes acidic and when [H+] < [OH-], the water acquires basic nature. This is exactly the change which occurs during the phenomenon known as salt hydrolysis. It is defined as a reaction in which the cation or anion or both of a salt react with water to produce acidity or alkalinity.
Hydrolysis of NaCl
Salts are strong electrolytes. When dissolved in water, they dissociate almost completely into ions. In some salts, cations are more reactive in comparison to anions and these react with water to produce H+ ions. Thus, the solution acquires acidic nature.
M+ + H2O \rightleftharpoons MOH + H+
Weak base
In other salts, anions may be more reactive in comparison to cations and these react with water to produce OH- ions. Thus, the solution becomes basic.
A- + H2O \rightleftharpoons HA + OH-
Weak acid
The process of salt hydrolysis is actually the reverse of neutralization.
Salt + Water \rightleftharpoons Acid + Base
If acid is stronger than base, the solution is acidic and in case base is stronger than acid, the solution is alkaline. When both the acid and the base are either strong or weak, the solution is generally neutral in nature.
As the nature of the cation or the anion of the salt determines whether its solution will be acidic or basic, it is proper to divide the salts into four categories.
Salt of a strong acid and a weak base.
Examples: FeCl3, CuCl2, AlCl3, NH4Cl, CuSO4, etc.
Salt of a strong base and a weak acid.
Examples: CH3COONa, NaCN, NaHCO3, Na2CO3, etc.
Salt of a weak acid and a weak base.
Examples: CH3COONH4, (NH4)2CO3, NH4HCO3, etc.
Salt of a strong acid and a strong base.
Examples: NaCl, K2SO4, NaNO3, NaBr, etc.
NaCl Crystal
Refer to the following video for salt hydrolysis
Salt of a Strong Acid and a Weak Base
The solution of such a salt is acidic in nature. The cation of the salt which has come from weak base is reactive. It reacts with water to form a weak base and H+ ions.
B+ + H2O \rightleftharpoons BOH + H+
Weak base
Consider, for example, NH4Cl. It ionises in water completely into NH4 and CF ions. ions react with water to form a weak base (NH4OH) and H+ ions.
NH+4 + H2O \rightleftharpoons NH4OH + H+
C(1-x) Cx Cx
Thus, hydrogen ion concentration increases and the solution becomes acidic.
Applying law of mass action,
K_h = \frac{[Hx ][NH_4OH]}{[NH_4^+ ]} = \frac{(x^2 C)}{(1-x)} ...... (i)
where C is the concentration of salt and x the degree of hydrolysis.
Other equilibria which exist in solution are
NH4OH \rightleftharpoons NH+4 + OH-,
K_b = \frac{[NH^+_4][OH^-]}{[NH_4OH]} .... (ii)
H2O \rightleftharpoons H+ + OH-,
Kb = [H+][H-] ..... (iii)
From eqs. (II) and (iii)
Kw/Kb =[H+ ][NH4 OH]/[NH4+ ] = Kh .... (iv)
[H+] = [H+ ][NH4+]/[NH4OH] = Kw/Kb ×[NH4+ ]/[NH4 OH]
log [H+] = log Kw - log Kb + log[salt]/[base]
-pH = -pKw + pKb + log[salt]/[base]
pKw - pH = pKb + log[salt]/[base]
pOH = pK_b + log\frac{[salt]}{[base]}
Relation Between Hydrolysis Constant and Degree of Hydrolysis
The extent to which hydrolysis proceeds is expressed as the degree of hydrolysisand is defined as the fraction of one mole of the salt that is hydrolysed when the equilibrium has been attained. It is generally expressed as h or x.
h = (Amount of salt hydrolysed)/(Total salt taken)
Considering again eq. (i),
Kh = x2C/(1-x) or Kh = h2C/(1-h)
When h is very small (1-h) → 1,
H2 = Kh × 1/c
or h = √(Kh/C) = √(Kw/Kb \times C)
[H+] = h × C = √(C \times Kh)/Kb
log [H+] = 1/2 log Kw + 1 1/2log C - 1/2log Kb
pH = \frac{1}{2}pKw - \frac{1}{2} log C - \frac{1}{2} pKb = 7 - \frac{1}{2} pKb - \frac{1}{2}log C
Salt of a Weak Acid and a Strong Base
A Strong BaseThe solution of such a salt is basic in nature. The anion of the salt is reactive. It reacts with water to form a weak acid and OH- ions.
salt of strong base and weak acid is acidic acid .....
PH range is between 0 to 7