Animated Solution for Chemistry - Organic Chemistry: The increasing order of $p{K}_a$ of the following amino acids in aqueous solution is Gly, Asp, Lys, Arg

When you first look at a question asking for the increasing order of $p{K}_a$, it is easy to get intimidated by the math. But here is the beautiful secret: you don't need to calculate a single logarithm. You just need to understand what $p{K}_a$ represents physically.

The $p{K}_a$ value is a measure of acid strength. A strong acid has a low $p{K}_a$, while a weak acid has a high $p{K}_a$. But what does this mean for bases?

According to the Brønsted-Lowry theory, a strong base will have a very weak, highly stable conjugate acid. Because its conjugate acid is weak, it will have a high $p{K}_a$. Therefore, we can establish a golden rule: $p{K}_a$ is directly proportional to basicity. The stronger the base, the higher its $p{K}_a$ value. Our mission is simply to rank these four amino acids by their basic strength.

To determine the basicity of an amino acid, we must look at its side chain, often called the 'R group'. Every standard amino acid has a central carbon attached to an amino group ($-{\text{NH}}_2$) and a carboxyl group ($-\text{COOH}$). It is the R group that gives each amino acid its unique personality.

Let's start with Aspartic Acid (Asp). As the name suggests, it is acidic. Its side chain contains an extra carboxylic acid group ($-\text{COOH}$). Because it has more acidic groups than basic groups, it is the least basic of our four contenders. Consequently, it will have the lowest $p{K}_a$.

Next, we have Glycine (Gly). Glycine is the minimalist of the amino acid world. Its side chain is just a single hydrogen atom ($-\text{H}$). It brings no extra acidic or basic baggage to the table. It is perfectly neutral. Because it is neutral, it is more basic than the acidic Aspartic acid, placing it second in our ranking.

Moving on to Lysine (Lys). If you examine Lysine's long, flexible side chain, you will find an extra amino group ($-{\text{NH}}_2$) at the very end. Nitrogen atoms have a lone pair of electrons that are eager to accept a proton ($-{\text{H}}^{+}$). This extra amino group makes Lysine a basic amino acid. Therefore, its basicity—and its $p{K}_a$—will be higher than both Aspartic acid and Glycine.

Finally, we arrive at the heavyweight champion of basicity: Arginine (Arg). Arginine is not just basic; it is exceptionally basic. But why?

The secret lies in its side chain, which features a complex structure known as the guanidino group. When this group acts as a base and accepts a proton, it forms a conjugate acid with a positive charge.

In most molecules, a localized positive charge creates instability. But the guanidino group has a superpower: Resonance. The positive charge is not stuck on a single nitrogen atom; instead, it is beautifully delocalized and shared equally among three different nitrogen atoms.

Imagine carrying a heavy backpack. If you carry it alone, it is exhausting. But if you and two friends share the weight equally, it becomes incredibly easy to carry. This resonance stabilization makes the conjugate acid of Arginine incredibly stable, which in turn makes Arginine the strongest base among all standard amino acids. Naturally, it claims the highest $p{K}_a$.

By analyzing the side chains, we have successfully ranked the basicity of these amino acids.

Aspartic acid is acidic, Glycine is neutral, Lysine is basic, and Arginine is strongly basic due to resonance.

Basicity Order: $\text{Asp}<\text{Gly}<\text{Lys}<\text{Arg}$

Since $p{K}_a$ perfectly mirrors basicity, the increasing order of $p{K}_a$ is exactly the same:

$p{K}_a$ Order: $\text{Asp}<\text{Gly}<\text{Lys}<\text{Arg}$

This logical deduction leads us straight to the correct answer, proving that understanding the physical chemistry behind the molecules is far more powerful than rote memorization.