What is the value of Kb for the base?

A 5.00 10-2 M solution of unknown monoprotic weak base has a pH of 9.300. What is the value of Kb for the base?|||a monoprotic base dissociate as follows:


AOH ←→ A⁺ + OH⁻


with


Kb = [A⁺]·[OH⁻] / [AOH]





negliging the self dissociation of water same amounts of OH⁻ and A⁺ are formed in equilibrium, hence:


[A⁺] = [OH⁻]


The concentration of nondissiociated base drops to:


[AOH] = [AOH]₀ - [OH⁻]





The dissociation equilibrium of water is given by:


[H⁺]·[OH⁻] = Kw = 10^-14


hence


log[H⁺] + log[OH⁻] = -14


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log[OH⁻] = -14 - log[H⁺]


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[OH⁻] = 10^(-14+pH)


= 2.0×10-5 M





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[AOH] = [AOH]₀ - [OH⁻]


= 5×10-2 M - 2.0×10-5 M


= 4.998×10-2 M





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Kb = [A⁺]·[OH⁻] / [AOH]


= 2.0×10-5 · 2.0×10-5 / 4.998×10-2


= 8.0×10-9 M