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Introduction and Degree of Hydrolysis

What will be ...

Question

What will be the $K_{b}$ value of a weak base (BOH) of which a 0.1 M solution has a pH of 8, when it is half neutralized with 0.1 M $H N O_{3}$ ?

10^{- 8}

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10^{- 4}

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10^{- 6}

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10^{- 7}

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Solution

The correct option is C $10^{- 6}$
$K_{a} . K_{b} = K_{w}$
under this condition, pH = pKa = 8 since a buffer is formed with equal concentrations of the weak base and the salt of its conjugate acid.
$\Rightarrow K_{a} = 10^{- 8}$
or $10^{- 8} \times K_{b} = 10^{- 14} \Rightarrow K_{b} = 10^{- 6}$

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