Consider a weak base ' B ' of $\mathrm{pK}_{\mathrm{b}}=5.699$. ' $x$ ' mL of 0.02 M HCl and ' y ' mL of 0.02 M weak base ' B ' are mixed to make 100 mL of a buffer of pH 9 at $25^{\circ} \mathrm{C}$. The values of ' $x$ ' and ' $y$ ' respectively are: [Given: $\log 2=0.3010, \log 3=0.4771, \log 5=0.699$]

• A

  \(\begin{array}{|c|c|}\hline x & y \\\hline85.7 & 14.3 \\\hline\end{array}\)
• Correct answer
  B

  \(\begin{array}{|c|c|}\hline x & y \\\hline14.3 & 85.7 \\\hline\end{array}\)
• C

  \(\begin{array}{|c|c|}\hline x & y \\\hline11.1 & 88.9 \\\hline\end{array}\)
• D

  \(\begin{array}{|c|c|}\hline x & y \\\hline42.7 & 57.3 \\\hline\end{array}\)

Solution

$pOH = pK_b + \log \left[ \dfrac{Salt}{Base} \right]$
$5 = 5.699 + \log \left[ \dfrac{Salt}{Base} \right]$
$\dfrac{x}{y - x} = \dfrac{1}{5}$
$6x = y$
$7x = 100$
$x = \dfrac{100}{7} \text{ ml}$
$y = \dfrac{600}{7} \text{ ml}$

Hence, the correct answer is option: 'B'.