Step 1: Understanding the Concept:
We need to identify the correct base dissociation constant, \(K_b\), of pyridine from four given values.
Step 2: Key Formula or Approach:
\[ K_b = \frac{[\text{BH}^{+}][\text{OH}^{-}]}{[\text{B}]} \]
The size of \(K_b\) tells us how strong or weak a base is. A smaller \(K_b\) means a weaker base, and pyridine is known to be a weak base because of how its lone pair is held.
Step 3: Detailed Explanation:
Pyridine's nitrogen sits in an sp2 hybrid orbital that points away from the ring and is not part of the aromatic pi system, so the lone pair is technically available to accept a proton.
At the same time, the sp2 orbital holds electrons closer to the nucleus than an sp3 orbital would, and the aromatic ring withdraws some electron density from the nitrogen, both of which lower its willingness to bind a proton compared to an ordinary aliphatic amine.
This makes pyridine a weak base with a small \(K_b\), well below values typical of amines like methylamine.
Among the given choices, \(1.7 \times 10^{-9}\) is the standard literature value for pyridine, corresponding to a pKb of about 8.8.
Step 4: Final Answer:
The \(K_b\) value of pyridine is \(1.7 \times 10^{-9}\).