Question

Conjugate base of a weak acid has $K_b={10}^{-9}$. The equilibrium constant for the reaction of acid with strong base is:

• A. ${10}^{-19}$
• B. ${10}^{-3}$
• C. ${10}^9$
• D. ${10}^5$

Answer 1

The correct option is C ${10}^9$

Let consider base $BA$, which dissociates as

$BA\to B^{+}+A^{-}$

$K_b=\frac{\left[B^{+}\right]\left[A^{-}\right]}{\left[BA\right]}$

$\Rightarrow \left[BA\right]=\frac{\left[B^{+}\right]\left[A^{-}\right]}{K_b}=\frac{1}{K_b}$

When $1molar$ weak acid $HA$ reacts with base $BOH$

$HA+BOH\to BA+H_{2}O$

$K=\frac{\left[BA\right]\left[H_{2}O\right]}{\left[HA\right]\left[BOH\right]}=\frac{1}{K_b}=\frac{1}{{10}^{-9}}$

$K={10}^9$