Question

A 0.010M solution of $Pu{{O}_{2}}{{(N{{O}_{3}})}_{2}}$ was found to have a pH of 4.0. What is the hydrolysis constant ${{K}_{h}}$ for $Pu{{O}_{2}}^{2-}$ and what is ${{K}_{b}}$ for $Pu{{O}_{2}}OH$?

Answer 1

Hint:. A hydrolysis constant is an equilibrium constant for the hydrolysis reaction. Hydrolysis of salt obtained from weak acid and strong base.

Complete step by step answer:
The reaction involved in hydrolysis is shown below:
\[{{A}^{-}}+{{H}_{2}}O\to HA+O{{H}^{-}}\]
The value of hydrolysis constant = ${{K}_{h}} = \dfrac{[HA][O{{H}^{-}}]}{[{{A}^{-}}][{{H}_{2}}O]}$
We can find the value of the hydrolysis constant ${{K}_{h}}=\dfrac{{{K}_{w}}}{{{K}_{a}}} or \dfrac{{{K}_{w}}}{{{K}_{b}}}$
The extent to which the hydrolysis of the reaction proceeds is known as the degree of hydrolysis.

Given in the question:
A 0.010M solution of $Pu{{O}_{2}}{{(N{{O}_{3}})}_{2}}$ was found to have a pH of 4.0
The reaction involved is $Pu{{O}_{2}}{{(N{{O}_{3}})}_{2}}+{{H}_{2}}O\to Pu{{O}_{2}}^{2+}+N{{O}_{3}}^{2-}+{{H}_{3}}{{O}^{+}}$

The pH of the solution is calculated by using the formulae
\[\begin{align}
 & pH=pKa+\log \dfrac{[Pu{{O}_{2}}^{2+}][{{H}_{3}}{{O}^{+}}]}{[Pu{{O}_{2}}{{(N{{O}_{3}})}_{2}}]} \\
 & 4=pKa+\log (0.01) \\
\end{align}\]
The value of pKa = 6
The value of ${{K}_{h}}$=${{10}^{-14}}$
And the hydrolysis constant = ${{10}^{-6}}$

Now we have to find the value of ${{K}_{b}}$
$Pu{{O}_{2}}^{2+}+{{H}_{2}}O\to Pu{{O}_{2}}OH+{{H}^{+}}$

Initial	0.01M		0	0
final	0.01-x		x	x

The value of ${{K}_{b}}=\dfrac{x.x}{0.01-x}$
The value of x = ${{10}^{-6}}$
After putting the value of x in the above equation the value of ${{K}_{b}}$ is = ${{10}^{-8}}$

Additional Information: ${{K}_{b}}$ and ${{K}_{b}}$ in chemistry are also known as the molar elevation constant and molar depression constant. The freezing point is the temperature at which the solvent in the liquid state and the solvent in the solid state are present at equilibrium so that their vapour pressure becomes equal.

Note: The equilibrium constant is defined as the product of concentration of product to the product of concentration of reactant each raise to the power of their respective stoichiometric coefficient. Weak acids have the value of degree of dissociation less than 1 whereas the strong bases have the value of degree of dissociation equal to 1.