Amines are reactive in nature, mainly due to difference in electronegativity between Nitrogen and Hydrogen and, due to lone pair of electrons on Nitrogen. Amines behaves like nucleophiles and as good Lewis bases and there are various reactions to support this. Different degree of amines differ in their reactivity due to steric hinderance and electronic effects. Aromatic amines are less basic due to +R effect, hence have higher \(pK_b\) value than the aliphatic amines. Basic strength of amines also depend on stability of corresponding conjugate acid in aqueous medium.

Which of the following will be having the lowest \(pK_b\) in gaseous medium?

N,N-Diethyethanamine

The correct answer is option 1. N,N-Diethyethanamine.

To understand which amine has the lowest \(pK_b\) (and thus the highest basicity) in a gaseous medium, we need to look at how the structure of the amine affects its basicity. Basicity in gaseous phase is influenced mainly by the electron-donating effects of substituents on the nitrogen atom, which impact the availability of the lone pair of electrons on nitrogen for protonation.

Factors Affecting Basicity and \(pK_b\):

Electron donating Effects:

Alkyl groups are electron-donating through their inductive effects. More electron-donating groups around the nitrogen increase the electron density on nitrogen, making it more basic.

Steric Effects:

While steric hindrance can affect the accessibility of the nitrogen atom for protonation, in the gaseous phase, the electron-donating effects of substituents have a more pronounced effect on basicity.

Analysis of Each Amine:

1. N,N-Diethylethanamine:

This amine has two ethyl groups and an additional ethyl group attached to the nitrogen. The three alkyl groups provide significant electron donation to the nitrogen, increasing its electron density and basicity. The additional alkyl group (ethyl chain) provides more stabilization, making nitrogen more basic and thus lowering \(pK_b\).

2. sec-Butylamine:

It has a secondary butyl group that provides moderate electron donation to nitrogen. The butyl group is a strong electron-donating group, but its effect is less pronounced than that of multiple ethyl groups.

3. Diethylamine:

This amine has two ethyl groups, which provide a significant electron-donating effect, making the nitrogen more basic. Although it is a strong base, it has slightly less electron-donating effect compared to N,N-Diethylethanamine.

4. Ethylamine:

Ethylamine has only one ethyl group attached to the nitrogen. This provides some electron donation, but less than the other options. It is the least basic among the listed amines due to the fewer number of electron-donating groups.

Basicity and \(pK_b\) Relationship:

Low \(pK_b\) corresponds to a strong base. A lower \(pK_b\) value indicates that the base is more effective at accepting a proton.

Conclusion:

Among the options, N,N-Diethylethanamine has the most electron-donating groups (two ethyl groups plus an additional alkyl chain), resulting in the highest electron density on the nitrogen. This makes it the most basic amine and hence has the lowest \(pK_b\).

The compound with the lowest \(pK_b\) (the strongest base) is option 1: N,N-Diethylethanamine