Question

What is the percentage of pyridine ${{C}_{5}}{{H}_{5}}N$ that forms pyridinium ion ${{C}_{5}}{{H}_{5}}{{N}^{+}}H$ in a 0.10 M aqueous pyridine solution (${{K}_{b}}$ for ${{C}_{5}}{{H}_{5}}N$= $1.7\times {{10}^{-9}}$)?
A. 0.77%
B. 1.6%
C. 0.0060%
D. 0.013%

Answer 1

Hint: Pyridine is a basic heterocyclic compound having the chemical formula ${{C}_{5}}{{H}_{5}}N$ and its structure is related with benzene where one methine group $(=CH)$ is replaced with nitrogen atom. It is highly flammable in nature.

Step by step solution: ${{K}_{a}}$ value defines the acid dissociation constant or we can say that an equilibrium constant for the dissociation of acids. Strong acids completely dissociate in water while weak acids do not. ${{K}_{a}}$ value shows the strength of the acid whereas ${{K}_{b}}$ is base dissociation constant and in water both weak and strong bases attains an equilibrium value that value is known as ${{K}_{b}}$ value. There is another term ${{K}_{w}}$ defined by water dissociation constant having fixed value of ${{10}^{-14}}$ and the relation between these terms is given by
${{K}_{a}}=\dfrac{{{K}_{w}}}{{{K}_{b}}}$; ${{K}_{b}}$ for ${{C}_{5}}{{H}_{5}}N$= $1.7\times {{10}^{-9}}$(Given)
${{K}_{a}}=\dfrac{{{10}^{-14}}}{1.7\times {{10}^{-9}}}=5.88\times {{10}^{-6}}$
The reaction of pyridine can be as follows:
${{C}_{5}}{{H}_{5}}N+{{H}_{2}}O\rightleftarrows {{C}_{5}}{{H}_{5}}NH+{{C}_{5}}{{H}_{5}}N{{H}^{+}}+O{{H}^{-}}$

Initial concentration	0.1	0	0	0
Final concentration	0.1-x		x	x

${{K}_{a}}=\dfrac{{{x}^{2}}}{0.1-x}$; x is very less value i.e. less than 0.1 so it can be neglected and the value of ${{K}_{a}}$ is $5.88\times {{10}^{-6}}$ as we find earlier.
${{x}^{2}}=5.88\times 0.1\times {{10}^{-6}}$
$x=7.6\times {{10}^{-4}}$
Therefore percentage of pyridine can be calculated by:
$\dfrac{7.6\times {{10}^{-4}}}{0.1}\times 100=0.77%$
This formula can be explained on the basis of
$\dfrac{dissociated\text{ ions}}{concentration\ \text{of solution}}\times 100$

From this we can conclude that option A is correct.

Note:
Pyridine is a weakly alkaline and water miscible compound having unpleasant fish-like smell and colorless in nature but when it gets old its impure sample becomes yellow in color. The main application of pyridine is used as pesticides.