Question

The dissociation constant of a weak acid, $HA$ is $4.9\times {10}^{-8}$. The concentration of $O{H}^{-}$ in a decimolar solution of the acid is:

• A. $3.9\times {10}^{-10}M$
• B. $1.43\times {10}^{-10}M$
• C. $2.22\times {10}^{-10}M$
• D. $1.4\times {10}^{-11}M$

Answer 1

The correct option is B $1.43\times {10}^{-10}M$

	$HA$	$H^{+}$	$A^{-}$
Initial concentration	$0.1$	$0$	$0$
Equilibrium concentration	$0.1-x$	$x$	$x$

The equilibrium constant expression is as follows:

$K_a=\frac{\left[H^{+}\right]\left[A^{-}\right]}{\left[HA\right]}$

$4.9\times {10}^{-8}=\frac{x\times x}{0.1-x}$ ......(1)

Since the value of the dissociation constant is very small, $0.1-x\simeq 0.1$

Hence, the equation $\left(1\right)$ becomes

$4.9\times {10}^{-8}=\frac{x^2}{0.1}$

$4.9\times {10}^{-9}=x^2$

$\left[H^{+}\right]=0.00007M$

$\left[O{H}^{-}\right]=\frac{{10}^{-14}}{0.00007}=1.43\times {10}^{-10}$ M