Question

Match each compound with its appropriate \(p K_{\mathrm{a}}\) value. (a) 4 -Nitrobenzoic acid, benzoic acid, 4 -chlorobenzoic acid \(\mathrm{p} K_{\mathrm{a}}=4.19,3.98\), and \(3.41\) (b) Benzoic acid, cyclohexanol, phenol \(\mathrm{p} K_{\mathrm{a}}=18.0,9.95\), and \(4.19\) (c) 4 -Nitrobenzoic acid, 4-nitrophenol, 4-nitrophenylacetic acid \(\mathrm{p} K_{\mathrm{a}}=7.15,3.85\), and \(3.41\)

Short answer

Question: Match the compounds with their corresponding pKa values. Set (a): 4-Nitrobenzoic acid, benzoic acid, 4-chlorobenzoic acid Set (b): Benzoic acid, cyclohexanol, phenol Set (c): 4-Nitrobenzoic acid, 4-nitrophenol, 4-nitrophenylacetic acid Answer: Set (a): (4-Nitrobenzoic acid, pKa=3.41), (benzoic acid, pKa=4.19), (4-chlorobenzoic acid, pKa=3.98) Set (b): (Benzoic acid, pKa=4.19), (cyclohexanol, pKa=18.0), (phenol, pKa=9.95) Set (c): (4-Nitrobenzoic acid, pKa=3.41), (4-nitrophenol, pKa=7.15), (4-nitrophenylacetic acid, pKa=3.85)

Step-by-step solution

Set (a): 4-Nitrobenzoic acid, benzoic acid, 4-chlorobenzoic acid

First, let's analyze the compounds in this set. The functional groups are nitro (-NO2), hydrogen, and chloro (-Cl) respectively. The nitro group is an electron-withdrawing group (EWG) which increases acidity, and the chloro group is also an EWG, but less so than the nitro group. Therefore, 4-Nitrobenzoic acid should have the lowest pKa value (highest acidity) and benzoic acid should have the highest pKa value (lowest acidity), with 4-chlorobenzoic acid somewhere in between. Based on this information, the correspondence should be: (4-Nitrobenzoic acid, pKa=3.41), (benzoic acid, pKa=4.19), (4-chlorobenzoic acid, pKa=3.98).

Set (b): Benzoic acid, cyclohexanol, phenol

Let's analyze the compounds in this set. Cyclohexanol is a secondary alcohol while phenol has the hydroxyl (-OH) group attached to an aromatic ring. Phenols are generally more acidic due to the resonance stabilization of the negative charge on the oxygen after deprotonation. On the other hand, benzoic acid has a carboxylic acid functional group, which is more acidic than phenols and secondary alcohols. The correspondence should be: (Benzoic acid, pKa=4.19), (cyclohexanol, pKa=18.0), (phenol, pKa=9.95).

Set (c): 4-Nitrobenzoic acid, 4-nitrophenol, 4-nitrophenylacetic acid

Let's analyze the compounds in this set. All three molecules contain a nitro group (-NO2) as an EWG. 4-Nitrophenol has a phenolic hydroxyl group, which makes it a stronger acid than secondary alcohols but weaker than carboxylic acids. 4-Nitrobenzoic acid has a carboxylic acid functional group, making it more acidic than 4-nitrophenol. 4-nitrophenylacetic acid has both a primary alcohol group and a phenolic group, making it somewhere in between the other two in terms of acidity. The correspondence should be: (4-Nitrobenzoic acid, pKa=3.41), (4-nitrophenol, pKa=7.15), (4-nitrophenylacetic acid, pKa=3.85).

Key concepts

Understanding Acid-Base Chemistry

Acid-base chemistry is fundamental in organic chemistry and revolves around the transfer of protons (H+ ions) between molecules—a process famously known as the acid-base reaction. Acids are proton donors, and bases are proton acceptors. The strength of an acid is measured by its acidity constant (Ka), which quantifies its ability to donate a proton. The pKa value is the negative logarithm of the Ka and is inversely related to acid strength—lower pKa values indicate stronger acids.

The pKa values allow chemists to predict the outcome of reactions involving acids and bases, including the direction in which an equilibrium reaction might favor formation of products or reactants. For example, when comparing the pKa values, if compound A has a lower pKa than compound B, compound A is a stronger acid, and will preferentially donate a proton to B.

Understanding this concept allows one to predict organic reaction mechanisms and the acidity of different functional groups presented in various organic compounds.

The Role of Functional Groups

Functional groups are specific groups of atoms within molecules that are responsible for the characteristic chemical reactions of those molecules. They play a crucial role in determining the behavior of organic compounds, including their acid-base properties.

Common functional groups include alcohols (-OH), carboxylic acids (-COOH), and phenols (aromatic ring with -OH). Carboxylic acids are typically stronger acids than alcohols due to the presence of a carbonyl group that can stabilize the negative charge after a proton is lost. This is exemplified in the textbook exercise, where benzoic acid is a stronger acid than cyclohexanol because of the carboxylic acid functional group.

Electron-withdrawing groups, such as nitro (-NO2) and halogens, like the chloro (-Cl) group, attached to aromatic systems can significantly increase acidity by stabilizing the resultant anion via inductive effects, often reflected in lower pKa values as observed in our example with 4-nitrobenzoic acid.

Resonance Stabilization in Acid-Base Chemistry

Resonance stabilization is another critical factor influencing the acidity of organic compounds. It refers to the delocalization of electrons in a molecule that allows for the spreading out of charge over multiple atoms, thereby stabilizing the system.

In the context of acid-base chemistry, the more stable the conjugate base (the species formed after an acid donates a proton), the stronger the original acid. Phenol is a classic example where the negative charge on the oxygen atom after deprotonation is delocalized around the aromatic ring, enhancing its acidity compared to an alkyl alcohol, like cyclohexanol, which cannot benefit from such resonance stabilization.

This principle helps to elucidate why some functional groups have particular pKa values. For instance, phenols have lower pKa values than alcohols because the aromatic ring allows resonance stabilization of the conjugate base. Through a combination of inductive effects and resonance, functional groups and substituents dictate not only the reactivity but also the acid-base properties of organic molecules.