Question
Question: Calculate the degree of hydrolysis and pH of \(0.02{\text{ M}}\) ammonium cyanide \(\left( {{\text{N...
Calculate the degree of hydrolysis and pH of 0.02 M ammonium cyanide (NH4CN) at 298 K. [K1 of HCN=4.99×10−9, Kb for NH4OH=1.77×10−5].
A) 8.2
B) 3.2
C) 9.3
D) 3.9
Solution
The negative logarithm of the H+ ion concentration in the solution is known as the pH of the solution. Calculate the pH using the Henderson-Hasselbalch equation.
Formulae Used: Kh=Ka×KbKw
pKa=pH+log[A−][HA]
Complete step by step answer:
Ammonium cyanide (NH4CN) is a salt of strong base ammonium hydroxide (NH4OH) and weak acid hydrogen cyanide (HCN).
Calculate the hydrolysis constant for ammonium cyanide using the equation as follows:
Kh=Ka×KbKw
Where Kh is the hydrolysis constant,
Kw is the ionization constant of water,
Ka is the acid dissociation constant,
Kb is the base dissociation constant.
Substitute 10−14 for the ionization constant of water, 4.99×10−9 for the acid dissociation constant, 1.77×10−5 for the base dissociation constant. Thus,
Kh=4.99×10−9×1.77×10−510−14
Kh=1.132
Thus, the hydrolysis constant for ammonium cyanide is 1.132.
Calculate the degree of hydrolysis for ammonium cyanide using the equation as follows:
h=1+KhKh
Where h is the degree of hydrolysis.
Thus,
h=1+1.1321.132
h=0.51
Thus, the degree of hydrolysis for ammonium cyanide is 0.51.
Calculate the pH for ammonium cyanide using the Henderson-Hasselbalch equation as follows:
pKa=pH+log[A−][HA]
Thus,
pH=pKa−log[A−][HA]
pH=log(Ka)−log[1−h][h]
Thus,
pH=log(4.99×10−9)−log(1−0.51)(0.51)
pH=9.3
Thus, the pH for ammonium cyanide is 9.3.
Thus, the degree of hydrolysis for ammonium cyanide is 0.51 and the pH for ammonium cyanide is 9.3.
Thus, the correct option is (C) 9.3.
Note: The fraction or percentage of a salt which is hydrolysed at equilibrium is known as the degree of hydrolysis. The Henderson-Hasselbalch equation describes the relationship between the pH and pOH of a solution and the pKa or pKb and the ratio of the concentration of the chemical species that has been dissociated. If the acid dissociation constant is known we can use the Henderson-Hasselbalch equation.