First slide

Ionization constants of weak bases, PH of weak bases

Question

At $25^{0} C,$ the dissociation constant of a base BOH is $1.0 \times 10^{- 12}$ . The concentration of hydroxyl ions in 0.01 x M aqueous solution of the base would be

Moderate

A

$2.0 \times 10^{- 6} mol L^{- 1}$
B

$1.0 \times 10^{- 5} mol L^{- 1}$
C

$1.0 \times 10^{- 6} mol L^{- 1}$
D

$1.0 \times 10^{- 7} mol L^{- 1}$

Solution

$B O H ⇌ B^{+} + O H^{-}$
So, the dissociation constant of BOH base
$K_{b} = \frac{[B^{+}] [{OH}^{-}]}{[BOH]} At equilibrium [B^{+}] = [{OH}^{-}] ∴ K_{b} = \frac{{[{OH}^{-}]}^{2}}{[BOH]} Given that K_{b} = 1.0 \times 10^{- 12} and [BOH] = 0.01 M Thus, 1.0 \times 10^{- 12} = \frac{{[{OH}^{-}]}^{2}}{0.01} {[{OH}^{-}]}^{2} = 1 \times 10^{- 14} [{OH}^{-}] = 1.0 \times 10^{- 7} {molL}^{- 1}$

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