Question

Account for the fact that nitroacetic acid, \(\mathrm{O}_{2} \mathrm{NCH}_{2} \mathrm{COOH}\left(\mathrm{p} K_{\mathrm{a}} 1.68\right)\), is a considerably stronger acid than acetic acid, \(\mathrm{CH}_{3} \mathrm{COOH}\left(\mathrm{pK} \mathrm{a}_{\mathrm{a}} 4.76\right)\).

Short answer

Question: Explain why nitroacetic acid is a stronger acid than acetic acid. Answer: Nitroacetic acid is a stronger acid than acetic acid because its conjugate base is more stable due to the electron-withdrawing effect of the nitro group and more resonance structures. This increased stability allows the conjugate base of nitroacetic acid to better stabilize the negative charge resulting from the loss of a proton. This is reflected in their pKa values: 1.68 for nitroacetic acid and 4.76 for acetic acid, where a lower pKa value indicates a stronger acid.

Step-by-step solution

Write the dissociation reactions of both acids

For nitroacetic acid (O2NCH2COOH) and acetic acid (CH3COOH), write the dissociation reactions in which they lose a proton (H+) to form the conjugate base: Nitroacetic acid: O2NCH2COOH \(\rightarrow\) O2NCH2COO\(^{-}\) + H\(^{+}\) Acetic acid: CH3COOH \(\rightarrow\) CH3COO\(^{-}\) + H\(^{+}\)

Compare the conjugate bases

Now, we need to compare the conjugate bases of both acids to understand their ability to stabilize the negative charge resulting from the loss of a proton. The conjugate base of nitroacetic acid is O2NCH2COO\(^{-}\), and the conjugate base of acetic acid is CH3COO\(^{-}\).

Analyze the effect of electron-withdrawing groups on stability

The difference between the two conjugate bases is the presence of a nitro group (O2N) in nitroacetic acid's conjugate base, which is an electron-withdrawing group (EWG). The EWG increases the stability of the conjugate base by spreading the negative charge across the nitro group through resonance.

Draw resonance structures of the conjugate bases

To demonstrate the stabilizing effect of the nitro group, we can draw resonance structures for both conjugate bases: O2NCH2COO\(^{-}\) has 3 resonance structures where the negative charge is delocalized across the nitro group and the oxygen of the carboxylate group. CH3COO\(^{-}\) has only 2 resonance structures where the negative charge is delocalized between the two oxygen atoms of the carboxylate group.

Relate the stability of the conjugate base to the acidity

An acid is stronger if its conjugate base is more stable. Because the conjugate base of nitroacetic acid is more stable due to the electron-withdrawing effect of the nitro group and more resonance structures, nitroacetic acid is a considerably stronger acid than acetic acid. This is reflected in their pKa values: 1.68 for nitroacetic acid and 4.76 for acetic acid (a lower pKa value indicates a stronger acid).

Key concepts

pKa values

The pKa value is a numerical representation of an acid's strength. It's derived from the acid dissociation constant, Ka, and is defined as the negative logarithm of Ka: \( \text{pKa} = -\log(\text{Ka}) \). A lower pKa value indicates a stronger acid because it implies a higher Ka, meaning the acid dissociates more readily in solution.

Considering nitroacetic acid with a pKa of 1.68 and acetic acid with a pKa of 4.76, the former is a stronger acid, as evidenced by its lower pKa value. When confronted with such pKa differences, it's clear that the molecular structure of the acids influences their acidity, leading us to explore the factors that can stabilize the conjugate bases formed upon acid dissociation.

Acid dissociation

Acid dissociation is a chemical reaction in which an acid donates a proton (\(\text{H}^+\)) to a base, often water, resulting in a conjugate base and a hydronium ion (\(\text{H}_3\text{O}^+\)) in aqueous solution. Looking at the acid dissociation reactions:

Nitroacetic acid: \(\text{O}_2\text{NCH}_2\text{COOH} \rightarrow \text{O}_2\text{NCH}_2\text{COO}^- + \text{H}^+\)
Acetic acid: \(\text{CH}_3\text{COOH} \rightarrow \text{CH}_3\text{COO}^- + \text{H}^+\)

The strength of an acid can be assessed by how freely it dissociates in this manner. Notably, the acid that forms a more stable conjugate base will dissociate more readily, favoring the formation of products and signifying a stronger acid.

Electron-withdrawing groups

An electron-withdrawing group (EWG) is an atom or group of atoms attached to a molecule that pulls electron density away from other parts of the molecule. EWGs, such as the nitro group (\(\text{O}_2\text{N}-\)), increase the electronegativity of the overall molecule, making it more prone to releasing protons. This is because EWGs can stabilize the negative charge on the conjugate base by distributing the charge throughout the molecule.

In nitroacetic acid, the nitro group acts as an effective EWG, stabilizing the negative charge on the conjugate base after acid dissociation. Such stabilization by the EWG is the key to understanding why nitroacetic acid is a stronger acid compared to acetic acid, which lacks such an electron-withdrawing substituent.

Resonance stabilization

Resonance stabilization occurs when a molecule has multiple valid structures, known as resonance structures, that contribute to the overall hybrid structure. This delocalization of electrons across the different structures can stabilize an ions or molecules, such as a conjugate base formed from acid dissociation.

For the conjugate bases of nitroacetic and acetic acids:

\(\text{O}_2\text{NCH}_2\text{COO}^- \) has three resonance structures, with the negative charge distributed between the oxygen in the nitro group and carboxylate group, while \( \text{CH}_3\text{COO}^- \) has only two resonance structures, sharing the charge between the oxygens of the carboxylate group. More resonance forms indicate enhanced charge delocalization and hence more stability, which in turn contributes to the stronger acidity of nitroacetic acid.