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Question: What is the percentage of pyridine \({{C}_{5}}{{H}_{5}}N\) that forms pyridinium ion \({{C}_{5}}{{H}...

What is the percentage of pyridine C5H5N{{C}_{5}}{{H}_{5}}N that forms pyridinium ion C5H5N+H{{C}_{5}}{{H}_{5}}{{N}^{+}}H in a 0.10 M aqueous pyridine solution (Kb{{K}_{b}} for C5H5N{{C}_{5}}{{H}_{5}}N= 1.7×10−91.7\times {{10}^{-9}})?
A. 0.77%
B. 1.6%
C. 0.0060%
D. 0.013%

Explanation

Solution

Pyridine is a basic heterocyclic compound having the chemical formula C5H5N{{C}_{5}}{{H}_{5}}N and its structure is related with benzene where one methine group (=CH)(=CH) is replaced with nitrogen atom. It is highly flammable in nature.

Step by step solution: Ka{{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. Ka{{K}_{a}} value shows the strength of the acid whereas Kb{{K}_{b}} is base dissociation constant and in water both weak and strong bases attains an equilibrium value that value is known as Kb{{K}_{b}} value. There is another term Kw{{K}_{w}} defined by water dissociation constant having fixed value of 10−14{{10}^{-14}} and the relation between these terms is given by
Ka=KwKb{{K}_{a}}=\dfrac{{{K}_{w}}}{{{K}_{b}}}; Kb{{K}_{b}} for C5H5N{{C}_{5}}{{H}_{5}}N= 1.7×10−91.7\times {{10}^{-9}}(Given)
Ka=10−141.7×10−9=5.88×10−6{{K}_{a}}=\dfrac{{{10}^{-14}}}{1.7\times {{10}^{-9}}}=5.88\times {{10}^{-6}}
The reaction of pyridine can be as follows:
C5H5N+H2O⇄C5H5NH+C5H5NH++OH−{{C}_{5}}{{H}_{5}}N+{{H}_{2}}O\rightleftarrows {{C}_{5}}{{H}_{5}}NH+{{C}_{5}}{{H}_{5}}N{{H}^{+}}+O{{H}^{-}}

Initial concentration0.1000
Final concentration0.1-xxx

Ka=x20.1−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 Ka{{K}_{a}} is 5.88×10−65.88\times {{10}^{-6}} as we find earlier.
x2=5.88×0.1×10−6{{x}^{2}}=5.88\times 0.1\times {{10}^{-6}}
x=7.6×10−4x=7.6\times {{10}^{-4}}
Therefore percentage of pyridine can be calculated by:
7.6×10−40.1×100=0.77\dfrac{7.6\times {{10}^{-4}}}{0.1}\times 100=0.77%
This formula can be explained on the basis of
dissociated ionsconcentration of solution×100\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.