Question

A certain buffer contains a weak base $AOH$ and its conjugate acid $\left(A^{+}\right)$ at ${25}^{\circ }C$.
The concentration of $A^{+}$ ions is twice the concentration of $AOH$.
Calculate the $pH$ of the buffer solution.
(Given base dissociation constant for $AOH$ is $K_b={10}^{-5}$)

• A. 8.7
• B. 4.3
• C. 5.3
• D. 9.7

Answer 1

The correct option is A 8.7

This is basic buffer formed by $A^{+}$ and a weak base $AOH$.
Let the concentration of $AOH=xM$
Then, concentration of $A^{+}=(2\times x)M$
$p{K}_b=-log\left(K_b\right)p{K}_b=-log\left({10}^{-5}\right)p{K}_b=5$

$pOH$ of basic buffer formed is given by
$pOH=p{K}_b+log\left(\frac{\left[A^{+}\right]}{\left[AOH\right]}\right)pOH=5+log\left(\frac{2x}{x}\right)pOH=5+log\left(2\right)=5+0.3=5.3pH=14-pOH=14-5.3pH=8.7$