Problem 191 - A Complete Resource Book in Chemistry for JEE Main

Question

Among the following acids which has the lowest pKa value? (a) \(\mathrm{CH}_{3} \mathrm{COOH}\) (b) \(\mathrm{HCOOH}\) (c) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{COOH}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COH}\)

Step-by-Step Solution

Answer

Formic acid (b) \\(\mathrm{HCOOH}\\) has the lowest pKa value.

Step 1: Understand the Concept

The pKa value of an acid is a measure of its acidity. Lower pKa values correspond to stronger acids, meaning they dissociate more completely in water to release hydrogen ions.

Step 2: Review the Acids Presented

The acids in the question are: (a) Acetic acid \(\mathrm{CH}_{3} \mathrm{COOH}\), (b) Formic acid \(\mathrm{HCOOH}\), (c) Isobutyric acid \((\mathrm{CH}_{3})_{2} \mathrm{CH}-\mathrm{COOH}\), and (d) Propanoic acid \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\). We need to determine which of these has the lowest pKa value.

Step 3: Recognize Structural Influences

The acid dissociation strength can be influenced by factors such as the presence of electronegative atoms and the stability of the conjugate base. Electron-withdrawing groups increase acidity, decreasing pKa. Formic acid has no additional alkyl groups, unlike other candidates which can donate electron density, slightly increasing their pKa.

Step 4: Compare the Common pKa Values

Typical pKa values for these acids are: acetic acid \(4.75\), formic acid \(3.75\), isobutyric acid \(4.84\), and propanoic acid \(4.87\). From these, we can see that formic acid has the lowest pKa value.

Key Concepts

Acid Dissociation

Acid dissociation is a fundamental concept in understanding the behavior of acids in solution. When an acid dissociates in water, it releases hydrogen ions ( \( ext{H}^+\) ), which are responsible for the acidic nature of the solution. The extent to which an acid dissociates can be quantified using its dissociation constant, \(K_a\) . This constant provides insight into the ratio of dissociated ions to the overall concentration of the acid.A key point to remember is that a lower \(pK_a\) value indicates a stronger acid. This is because the \(pK_a\) value is the negative logarithm of the \(K_a\) value, meaning that the larger the \(K_a\) , the smaller the \(pK_a\) . This inverse relationship emphasizes the acid's ability to release \( ext{H}^+\) ions more readily. For students trying to determine which acid is stronger, focusing on the \(pK_a\) values makes comparison straightforward.

Conjugate Base

Understanding conjugate bases is crucial because they provide insights into the stability and behavior of the acids from which they are derived. When an acid donates a hydrogen ion, the remaining species is called its conjugate base. The strength and stability of this base can significantly influence the acid's dissociation process.A stable conjugate base arises when it can hold onto the extra electron density efficiently. This stability is often due to the presence of electronegative atoms, which can stabilize negative charges through resonance or inductive effects. The more stable the conjugate base, the more likely the acid will dissociate completely, thus having a lower \(pK_a\) value. Therefore, analyzing the conjugate base gives insight into acid strength and its dissociation potential.

Electronegativity

Electronegativity refers to an atom's ability to attract and hold electrons within a bond. It plays a pivotal role in the acidity of molecules. Highly electronegative elements can stabilize the negative charge of a conjugate base, making the parent acid more acidic.For acids, the presence of electronegative elements like oxygen can enhance acid strength. Electronegativity helps explain why formic acid ( \( ext{HCOOH}\) ) has a lower \(pK_a\) compared to acetic acid ( \( ext{CH}_3 ext{COOH}\) ). In formic acid, the absence of additional electron-donating alkyl groups allows the electronegative oxygen to stabilize the conjugate base better. This factor results in a stronger acid due to more efficient electron distribution and minimizes destabilic influences present in other competing acids.