Animated Solution for Chemistry - Organic Compounds Containing Nitrogen: The increasing order of $p{K}_b$ for the following compounds will be :

Basicity and pKb

When tackling questions about basicity, the first rule to remember is the inverse relationship between basicity and $p{K}_b$.

A stronger base will always have a smaller $p{K}_b$ value.

Therefore, our mission is to determine the order of basicity for these three compounds, and then simply reverse that order to find the increasing order of $p{K}_b$.

To compare the strength of different bases, we must look at the stability of their conjugate acids.

When a base accepts a proton ($H^{+}$), it transforms into its conjugate acid.

The more stable this conjugate acid is, the stronger the original base. This is the fundamental principle that will guide our analysis.

Let's begin with compound C, which is dimethylamine ($C{H}_3-NH-C{H}_3$).

When dimethylamine accepts a proton, it forms a secondary ammonium ion ($C{H}_3-N{H}_2^{+}-C{H}_3$).

If we look closely at this ion, the positive charge is completely localized on the central nitrogen atom. There are no adjacent pi bonds or lone pairs to help share this burden.

Because there is no resonance stabilization, this conjugate acid is relatively unstable, making compound C the weakest base among the three.

Next, we examine compound A, formamidine ($N{H}_2-CH=NH$). This molecule belongs to a class of compounds called amidines.

Upon protonation at the imine nitrogen, it forms a conjugate acid where the positive charge is no longer stuck on a single atom.

The lone pair on the adjacent amino nitrogen can swing in, pushing the pi electrons onto the other nitrogen atom.

This creates two equivalent resonance structures, effectively spreading the positive charge over both nitrogen atoms. This delocalization provides significant thermodynamic stability, making compound A a much stronger base than compound C.

DBN (Compound B)

Finally, let's analyze compound B, known as DBN (1,5-Diazabicyclo[4.3.0]non-5-ene). This is a bicyclic amidine.

Just like formamidine, when DBN is protonated, it forms a resonance-stabilized conjugate acid. The positive charge is perfectly delocalized between the two nitrogen atoms.

However, DBN has two massive advantages over formamidine. First, the alkyl groups in the fused rings provide a strong electron-donating inductive effect (+I effect), which further stabilizes the positive charge.

Second, the rigid bicyclic structure locks the molecule into a perfectly planar geometry. This ensures maximum orbital overlap, making the resonance highly effective.

Because of these combined factors, the conjugate acid of DBN is exceptionally stable, making compound B the strongest base of the group.

Based on our analysis, the order of basicity is: Compound B > Compound A > Compound C

But remember, the question asks for the increasing order of $p{K}_b$. Since $p{K}_b$ is inversely proportional to basicity, we reverse our order.

The strongest base has the lowest $p{K}_b$. Therefore, the increasing order of $p{K}_b$ is: (B) < (A) < (C)