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The correct formula to calculate the hydroxyl ion concentration of an aqueous solution of NH4NO3 is,
A) C×KwKb
B) Kw×KbC
C) C×KwKa
D) Ka×KwC$$


Answer
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Hint: NH4NO3 is the salt of a weak base and a strong acid. It is the salt of NH4OH and HNO3[H+][OH]=KW, KW is the ionization constant of water

Complete step by step solution:
The requirement of the question is to find an equation that is used for the calculation of the concentration of aqueous NH4NO3 solution from the above options given.
So we know that theNH4NO3 is the salt of NH4OH and HNO3
NH4NO3NH4OH+HNO3
(Weak base) (Strong acid)
As NH4OHis a weak base, it undergoes hydrolysis in aqueous solution,
NH4++H2ONH4OH+H+
When time changes the concentration of the reactants and products are also changing.

NH4++H2ONH4OH+H+
When time, t =o C 0 0
When time, t=t C(1-h) Ch Ch


C is the concentration
So we write the hydrolysis constant,Kh as,
Kh=Ch×ChC(1h)
Here(1h)1, applying this condition on the above equation.
Hence the equation becomes,Kh=(Ch)2C=Ch2
h=KhC
Here as the NH4+ ion is acting as the acid hence Kh can be written as,
Kh=Ka=KwKb ,
Ka=Dissociation or ionization constant of acid
Kb= Ionization constant of base
Kw= ionization of water

Concentration of [H+] can be written as,
[H+]=Ch=Kw×CKb
We know the relation, [H+][OH]=Kw
So writing the equation for [OH]
Hence, [OH]=Kw[H+]
[OH]=Kw×KbC$$

So the correct option for the answer is option (B)

Note: Derivation should be done with utmost care while substituting one equation with the other. And from the standard equation we could find the concentration term, dissociation constant of acid or dissociation constant of base. And so the extent to which ions have dissociated.
Kh=Ka=KwKb
Kais related to Kb,by the equation ,
We should always write the ionization equations of the ions for the better results. As the chemical equation the dissociation of compounds to respective ions and it is easy for us to interpret.
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