Question

The \(\mathrm{p} K_{\mathrm{a}}\) values for phenol, o-nitrophenol, \(m\)-nitrophenol, and \(p\)-nitrophenol are \(9.89,7.17,8.28\), and \(7.15\), respectively. Explain the origin of these differences in \(\mathrm{p} K_{a}\).

Short answer

The pKa differences among phenol and its nitro derivatives arise from the electron-withdrawing effects of nitro groups and their positions relative to the hydroxyl group, with ortho and para positions offering greater resonance stabilization and acidity than the meta position.

Step-by-step solution

Understanding pKa

The pKa value is a measure of the acidity of a substance. It is the negative logarithm of the acid dissociation constant (Ka) of the substance. A lower pKa value indicates a stronger acid, meaning it donates protons (H+) more easily.

Analyzing the Effect of Substituents

Substituents on a benzene ring can affect the acidity of phenol by influencing the stability of the phenoxide ion formed when phenol donates a proton. Electron-withdrawing groups, such as nitro groups, stabilize the negative charge on the phenoxide ion through resonance and inductive effects, thus enhancing the acidity.

Positional Effects of Substituents

The position of the substituent on the benzene ring relative to the hydroxyl group also plays a role. Ortho and para positions allow for resonance stabilization of the phenoxide ion, while meta positions do not. This means that o-nitrophenol and p-nitrophenol are more acidic than m-nitrophenol.

Comparing pKa Values

The given pKa values show that o-nitrophenol and p-nitrophenol are more acidic (lower pKa) than m-nitrophenol, which is more acidic than phenol. This is due to the resonance stabilization in the ortho and para positions and the electron-withdrawing nature of the nitro group.

Key concepts

Acid Dissociation Constant

Understanding the acid dissociation constant (Ka) is foundational to grasping why different substances have varying acidic strengths. The Ka value quantifies how readily an acid donates its proton (H+) to a base. It's key to remember that the lower the pKa, the stronger the acid, as it indicates a higher propensity to lose a proton. Importantly, the pKa is simply the negative logarithm to base 10 of the Ka. Therefore, a smaller pKa value signals a larger Ka, meaning stronger acid.

To translate this to phenols, consider the pKa values as a direct measure of how easily each phenol sheds a proton. Phenol with a higher pKa is less willing to part with its proton compared to its nitro-substituted counterparts. This difference in 'willingness' or strength of acidity is determined by the underlying stability of the negatively charged phenoxide ion that forms upon loss of a proton.

Substituent Effects on Acidity

The acidity of phenols is intimately linked to what is attached to the benzene ring—the substituents. Each type of substituent imparts its own electronic effect on the ring, altering the molecule's overall acidic behavior. Two primary effects to highlight are resonance and inductive effects. Notably, electron-withdrawing groups like nitro (-NO2) are potent in this arena, pulling electron density away from the ring, accommodating the negative charge more effectively on the phenoxide ion.

So, when considering the varying pKa values of substituted phenols, you are observing the outcome of substituents manipulating the electron cloud. In essence, if a substituent can help delocalize the negative charge following proton donation, it strengthens the acid. This is a central theme when comparing non-substituted phenol with its nitro-substituted variants.

Resonance Stabilization

Dive deeper into the concept of resonance stabilization to fully understand its role in acidity—specifically in organic molecules like phenol. Resonance indicates the delocalization of electrons, spreading out the negative charge over multiple atoms, which generally enhances stability. A stabilized anion form, such as the phenoxide ion, inherently suggests a stronger parent acid.

For phenols, the hydroxyl group's unique ability to participate in resonance adds a layer of complexity to acidity. The ortho and para positions on the ring relative to the hydroxyl group enable this delocalization via overlapping p-orbitals. This is why o-nitrophenol and p-nitrophenol boast lower pKa values—they benefit from added resonance stabilization which m-nitrophenol cannot match due to its meta position, which restricts this stabilizing resonance.

Electron-Withdrawing Groups

Isolating electron-withdrawing groups and their effects shines a light on their profound impact on molecular acidity. These groups are characterized by their ability to pull electron density towards themselves, away from other parts of the molecule. In terms of acidity, this phenomenon helps stabilize the negative charge after an acid (like phenol) donates its proton.

For instance, the nitro group is a strong electron-withdrawing group due to its highly electronegative oxygen atoms and the positive charge on the nitrogen. When situated on the benzene ring of phenol, it enhances the acidic character by stabilizing the resulting phenoxide ion. The pKa values reflect this: both o-nitrophenol and p-nitrophenol, which can engage in resonance stabilization benefiting from the nitro group's electron-withdrawing power, display lowered pKa values indicating stronger acidity when compared to unsubstituted phenol.