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Question: At 25°C, the dissociation constant of a base BOH is \(1.0 \times 10^{- 12}\). The concentration of H...

At 25°C, the dissociation constant of a base BOH is 1.0×10−121.0 \times 10^{- 12}. The concentration of Hydroxyl ions in 0.01 M aqueous solution of the base would be.

A

2.0×10−6molL−12.0 \times 10^{- 6}molL^{- 1}

B

1.0×10−5mol 6muL−11.0 \times 10^{- 5}mol\mspace{6mu} L^{- 1}

C

1.0×10−6molL−11.0 \times 10^{- 6}molL^{- 1}

D

1.0×10−7mol 6mu⥂L−11.0 \times 10^{- 7}mol\mspace{6mu} ⥂ L^{- 1}

Answer

1.0×10−7mol 6mu⥂L−11.0 \times 10^{- 7}mol\mspace{6mu} ⥂ L^{- 1}

Explanation

Solution

Initial C 0 0

At eq. C – Cα Cα Cα

Kb=C2α2C(1−α)=Cα2K_{b} = \frac{C^{2}\alpha^{2}}{C(1 - \alpha)} = C\alpha^{2} assuming α<<1\alpha < < 1;1−α–~11 - \alpha\widetilde{–}1

10−12=10−2×α210^{- 12} = 10^{- 2} \times \alpha^{2}; α2=10−10\alpha^{2} = 10^{- 10}; α=10−5\alpha = 10^{- 5}

[OH−]=Cα=.01×10−5=10−7\lbrack OH^{-}\rbrack = C\alpha = .01 \times 10^{- 5} = 10^{- 7}