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, \(\mathrm{CH}_{3} \mathrm{COOH}\left(\mathrm{p} K_{\mathrm{a}} 4.76\right)\).

Understanding the correlation between pKa and acid strength is fundamental in chemistry. The pKa value is an inverse measure of the acid strength of a compound, which means lower pKa values indicate stronger acids. This is because pKa is logarithmically related to the acid dissociation constant (Ka), a direct measure of an acid's ability to donate a proton (H+). The pKa of nitroacetic acid is 1.68, significantly lower than the pKa of acetic acid, which is 4.76. Thus, nitroacetic acid is the stronger acid as it more readily donates a proton to form its conjugate base compared to acetic acid.

When comparing acids, a lower pKa value also points to a higher degree of ionization in water, enhancing the acid's reactivity. A smaller pKa means a greater proportion of the acid molecules have given up their protons, producing more hydronium ions (H3O+) in solution, thus more acidic the environment.

Electron-withdrawing groups, such as nitro (-NO2), chloro (-Cl), and cyano (-CN), play a pivotal role in determining the acidity of a molecule. These groups pull electron density away from the rest of the molecule through a mechanism known as the vector resonance effect or through induction. With nitroacetic acid, the nitro group is a powerful electron-withdrawing substituent. The presence of this group on the alpha carbon, adjacent to the carboxylic acid group, significantly increases the acid's strength.

The nitro group's ability to draw electrons toward itself results in a weakened bond between the carboxylic hydrogen and oxygen, making it easier for the hydrogen proton to dissociate and leave as a hydronium ion. By reducing the electron density on the carboxylic acid's oxygen, the nitro group actively facilitates the release of the acidic proton, contributing to the acidity of nitroacetic acid.

The stability of a conjugate base is directly related to the parent acid's strength. Conjugate bases are the species left behind after an acid has donated a proton. A stable conjugate base will not readily recombine with a proton, indicating that the forward reaction (proton loss) is favored, and thus the acid is strong.

In the context of nitroacetic acid, once it has donated a proton, the resulting nitroacetate ion benefits from the electron-withdrawing effect of the nitro group, dispersing the negative charge over the molecule. This dispersal, or delocalization, leads to greater stability of the conjugate base. In contrast, acetic acid's conjugate base, the acetate ion, receives comparatively less stabilization from its methyl group. This difference in stabilization between the nitroacetate and acetate ions is a key reason behind the significantly greater acidity of nitroacetic acid.

The inductive effect involves the transmission of charge through a chain of atoms in a molecule, which can influence the molecule's reactivity and properties. The presence of electron-withdrawing groups can enhance an acid's strength via the inductive effect as they pull electron density away from the functional group responsible for acidity, often a carboxyl (-COOH) group.

Nitroacetic acid exhibits a pronounced inductive effect due to the nitro group, which pulls electron density through the sigma bonds of the molecule, away from the acidic proton. This redistribution of electron density leads to an increased positive character of the hydrogen in the carboxyl group, facilitating proton detachment. Meanwhile, acetic acid's methyl group slightly pushes electron density toward the carboxylic group, reducing its acidity. The contrasting inductive effects of the nitro and methyl groups are central to understanding why nitroacetic acid is a considerably stronger acid than acetic acid.