Question

Determine the pH of a 0.2M solution of pyridine ${{C}_{5}}{{H}_{5}}N$. ${{K}_{b}}=1.5\times {{10}^{-9}}$

Answer 1

Hint: pH is generally used to measure the hydrogen ion concentration represented as $[{{H}^{+}}]$ in an aqueous solution. The pH scale ranges from 0 to 14 it generally represents the acidity and basicity of a solution. A low pH value indicates the solution is acidic in nature, pH of 7 is neutral and high value of pH value indicates alkalinity.

Complete Solution :
${{K}_{b}}$ is generally known to be the equilibrium constant of base and it is most helpful in predicting whether a given species will donate or accept protons at a specific pH value. It generally describes the degree of ionization of an acid or base and are true indicators of acid or base strength because adding water to a solution will not change the equilibrium constant.
- Pyridine is generally represented as ${{C}_{5}}{{H}_{5}}N$ and it is a weak base and the reaction of pyridine in an aqueous solution can be represented as:
${{C}_{2}}{{H}_{5}}N+{{H}_{2}}O\to {{C}_{2}}{{H}_{5}}N{{H}^{+}}+O{{H}^{-}}$

At t = 0	0.2	0	0
c	-x	+x	+x
At equilibrium	0.2-x	x	x

Now we know that ${{K}_{b}}$ is represented as:
${{K}_{b}}=\dfrac{[{{C}_{5}}{{H}_{5}}N{{H}^{+}}][O{{H}^{-}}]}{[{{C}_{5}}{{H}_{5}}N]}$
$1.5\times {{10}^{-9}}$ = $\dfrac{{{x}^{2}}}{0.2-x}$
${{x}^{2}} = 3\times {{10}^{-10}}$
$x=1.73\times {{10}^{-5}}$
It represents that $[O{{H}^{-}}] = 1.73\times {{10}^{-5}}$
$pOH = 4.76$
As we know that $pH + pOH = 14$
$\therefore pH=14 - 4.76 = 9.24$
Therefore it determines pH of a 0.2M solution of pyridine is 9.24.

Note: ${{K}_{b}}$ is defined as the base dissociation constant. The base dissociation constant is generally measured by how completely a base dissociates into its component ions in water. A large ${{K}_{b}}$ value indicates the high level of dissociation of a strong base while a lower ${{p}_{kb}}$ value indicates a stronger base.