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(B) For a weak monoacidic base $BOH$,the dissociation equilibrium is represented as: $BOH \rightleftharpoons B^{+} + OH^{-}$.Let the initial concentra

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$\sqrt{K_{b} \cdot c}$

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(B) For a weak monoacidic base $BOH$,the dissociation equilibrium is represented as: $BOH \rightleftharpoons B^{+} + OH^{-}$.Let the initial concentration be $c$ and the degree of dissociation be $\alpha$.The equilibrium concentrations are: $[BOH] = c(1-\alpha)$,$[B^{+}] = c\alpha$,and $[OH^{-}] = c\alpha$.The dissociation constant $K_b$ is given by: $K_b = \frac{[B^{+}][OH^{-}]}{[BOH]} = \frac{(c\alpha)(c\alpha)}{c(1-\alpha)} = \frac{c\alpha^2}{1-\alpha}$.Since the base is weak,$\alpha \ll 1$,so $1-\alpha \approx 1$.Thus,$K_b \approx c\alpha^2$,which gives $\alpha = \sqrt{\frac{K_b}{c}}$.The concentration of $[OH^{-}]$ is $c\alpha = c \cdot \sqrt{\frac{K_b}{c}} = \sqrt{K_b \cdot c}$.

Which of the following formulae is used to find the $[OH^{-}]$ ion concentration of a weak monoacidic base?

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