Animated Solution for Chemistry - Organic Chemistry: The increasing order of $p{K}_b$ values of the following compounds is

Welcome, future engineers and doctors! Today, we are going to dissect a beautiful problem from Organic Chemistry that tests your deep understanding of electronic effects—specifically, how substituents influence the basicity of amines. This is a classic JEE concept, and mastering it will give you a massive edge.

Basicity and $p{K}_b$

Before we dive into the molecules, let's set our foundation. What makes an amine basic? It's the lone pair of electrons on the nitrogen atom. The more available this lone pair is to accept a proton, the stronger the base.

Now, the question asks for the order of $p{K}_b$ values. Here is the golden rule: $p{K}_b$ is inversely proportional to basic strength. A stronger base has a smaller $p{K}_b$ value. So, our strategy is simple: find the order of basicity, and then just reverse it!

The Power of Position

Let's look at our four contenders.

In Compound (I), we have a methoxy group ($-OC{H}_3$) sitting at the para position. Oxygen is highly electronegative, but it also has lone pairs. When attached to a benzene ring at the ortho or para position, it donates these electrons through resonance. This is the mighty $+R$ effect. It pumps a massive amount of electron density into the ring and right onto the nitrogen atom. This makes Compound (I) an incredibly strong base.

Compound (II) is our reference point. It's N,N-dimethylaniline with no extra substituents on the ring. It's a decent base, but it doesn't have the extra boost that Compound (I) enjoys.

Why Resonance Fails

Now, things get spicy with Compound (III) and Compound (IV). Look closely at where the cyano ($-CN$) and hydroxyl ($-OH$) groups are attached. They are at the meta position!

This is a classic trap set by examiners. We often associate $-OH$ with a $+R$ effect and $-CN$ with a $-R$ effect. But remember, resonance effects do not operate from the meta position. The electron clouds simply don't align to push or pull electrons all the way to the amino group via resonance.

So, what's left? Only the inductive effect ($-I$). Both $-CN$ and $-OH$ are more electronegative than carbon, so they pull electron density away through the sigma bonds. This decreases the availability of the lone pair on nitrogen, making both of these compounds weaker bases than our reference, Compound (II).

Putting It All Together

We know that both (III) and (IV) are weaker bases than (II). But which one is the weakest?

We need to compare their $-I$ effects. The cyano group ($-CN$) is a much stronger electron-withdrawing group than the hydroxyl group ($-OH$). Therefore, $-CN$ pulls more electron density away from the nitrogen, making Compound (III) the least basic of them all.

So, our basicity order is:

But wait! The question asked for the $p{K}_b$ order. We must reverse our basicity order.

The increasing order of $p{K}_b$ is:

And there we have it! By carefully analyzing the positions and the specific electronic effects, we've cracked the code. Keep your eyes peeled for those meta positions, and never let a silly mistake cost you marks!