Answer
437.1k+ views
Hint: The base dissociation constant is a measure of the extent to which a base dissociates into its component ions in water. Hydrolysis constant can be defined as the equilibrium constant for a hydrolysis reaction. The base dissociation is inversely proportional to the hydrolysis constant.
Complete step by step answer:
> ${K}_{b}$ is the base dissociation constant of the reaction. It tells us how completely the base dissociates into its component ions in water. The larger the value of ${K}_{b}$ indicates a high level of dissociation of a strong base.
> Pure water also undergoes auto-ionization to form ${H}_{3}{O}^{+}$ and ${OH}^{-}$ ions and this reaction in which auto-ionization takes place always stays in equilibrium. Therefore, the equilibrium constant for auto-ionization of water is known as ${K}_{w}$ and its value is constant at a particular temperature. At room temperature its value is $1.0 \times {10}^{-14}$.
> Hydrolysis constant is the equilibrium constant of a hydrolysis reaction and it is denoted by ${K}_{H}$. The hydrolysis constant is related to the ionic product of water, ${K}_{w}$ and the base dissociation, ${K}_{b}$.
This relation is given as follows.
${ K }_{ H }\quad =\quad \dfrac { { K }_{ w } }{ { K }_{ b } }$
Now, for the given hydrolysis reaction:
${ B }^{ + }\quad +\quad { H }_{ 2 }O\quad \longrightarrow \quad BOH\quad +\quad { H }^{ + }$
Now, the expression for hydrolysis constant is:
${ K }_{ H }\quad =\quad \dfrac { { K }_{ w } }{ { K }_{ b } }$ ------(1)
And is also given that ${K}_{b} = 1.0 \times {1.0}^{-6}$ and we know that the value of ${K}_{w}$ is $1.0 \times {10}^{-14}$. Substituting, these values in equation (1), we get
${ K }_{ H }\quad =\quad \dfrac { 1.0\quad \times \quad { 10 }^{ -14 } }{ 1.0\quad \times \quad { 10 }^{ -6 } }$
${ K }_{ H }\quad =\quad 1.0\quad \times \quad { 10 }^{ -8 }$
Therefore, the value of hydrolysis constant is $1.0 \times {10}^{-8}$.
Hence, the correct answer is option (C).
Note: The auto-ionization reaction always stays in equilibrium because the component ions after the dissociation of water are hydronium ion and hydroxide ion. And the hydronium ion is a very strong acid and the hydroxide ion is a very strong base. Thus they associate again to form water molecules. So, the water molecules and ions always stay in equilibrium.
Complete step by step answer:
> ${K}_{b}$ is the base dissociation constant of the reaction. It tells us how completely the base dissociates into its component ions in water. The larger the value of ${K}_{b}$ indicates a high level of dissociation of a strong base.
> Pure water also undergoes auto-ionization to form ${H}_{3}{O}^{+}$ and ${OH}^{-}$ ions and this reaction in which auto-ionization takes place always stays in equilibrium. Therefore, the equilibrium constant for auto-ionization of water is known as ${K}_{w}$ and its value is constant at a particular temperature. At room temperature its value is $1.0 \times {10}^{-14}$.
> Hydrolysis constant is the equilibrium constant of a hydrolysis reaction and it is denoted by ${K}_{H}$. The hydrolysis constant is related to the ionic product of water, ${K}_{w}$ and the base dissociation, ${K}_{b}$.
This relation is given as follows.
${ K }_{ H }\quad =\quad \dfrac { { K }_{ w } }{ { K }_{ b } }$
Now, for the given hydrolysis reaction:
${ B }^{ + }\quad +\quad { H }_{ 2 }O\quad \longrightarrow \quad BOH\quad +\quad { H }^{ + }$
Now, the expression for hydrolysis constant is:
${ K }_{ H }\quad =\quad \dfrac { { K }_{ w } }{ { K }_{ b } }$ ------(1)
And is also given that ${K}_{b} = 1.0 \times {1.0}^{-6}$ and we know that the value of ${K}_{w}$ is $1.0 \times {10}^{-14}$. Substituting, these values in equation (1), we get
${ K }_{ H }\quad =\quad \dfrac { 1.0\quad \times \quad { 10 }^{ -14 } }{ 1.0\quad \times \quad { 10 }^{ -6 } }$
${ K }_{ H }\quad =\quad 1.0\quad \times \quad { 10 }^{ -8 }$
Therefore, the value of hydrolysis constant is $1.0 \times {10}^{-8}$.
Hence, the correct answer is option (C).
Note: The auto-ionization reaction always stays in equilibrium because the component ions after the dissociation of water are hydronium ion and hydroxide ion. And the hydronium ion is a very strong acid and the hydroxide ion is a very strong base. Thus they associate again to form water molecules. So, the water molecules and ions always stay in equilibrium.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)