Question

A 40.0 mL solution of a weak base, BOH is titrated with 0.1 N HCl solution. The pH of the solution is found to be 10.04 and 9.14 after adding 5.0 mL and 20.0 mL of the acid respectively. The dissociation constant of the base is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Writing the concerned chemical reaction

$BOH$ + $HCl$ $\to$ $BCl$ + $H_{2}O$

Moles before reaction $x$ $0.1\times 5$ = $0.5$ 0 0

Moles after reaction (x - 0.5) 0 0.5 0.5

Molar concentration $\frac{x-0.5}{V}$ $\frac{0.5}{V}$ $\frac{0.5}{V}$

Since the solution represents a basic buffer, lets us use the corresponding version of Henderson equation.

$pOH$ = $p{K}_b$ + $log\frac{\left[salt\right]}{\left[Base\right]}$

$14$ - $10.04$ = - $log{K}_b$ + $logpOH$ -(1)

For the second part, 20 mL of N/10 HCl

Unlike the previous case, this is an acidic buffer:

$pH$ = $p{K}_a+log\frac{\left[salt\right]}{\left[Base\right]}$

$14$ - $9.14$ = $-log{K}_b+logpOH$ -(2)

So we have two equations in two unknowns. Solving, we get

$x$ = $0.088mol{L}^{-1}$and $K_b$= $1.828\times {10}^{-5}$