Problem 92 - General Chemistry: Principles and Modern Applications

Question

Oxalic acid, HOOCCOOH, a weak diprotic acid, has \(\mathrm{p} K_{\mathrm{a}_{1}}=1.25\) and \(\mathrm{p} K_{\mathrm{a}_{2}}=3.81 .\) A related diprotic acid, suberic acid, \(\mathrm{HOOC}\left(\mathrm{CH}_{2}\right)_{8} \mathrm{COOH}\) has \(\mathrm{p} K_{\mathrm{a}_{1}}=4.21\) and \(\mathrm{p} K_{\mathrm{a}_{2}}=5.40 .\) Offer a plausible reason as to why the difference between \(\mathrm{pK}_{\mathrm{a}_{1}}\) and \(\mathrm{pK}_{\mathrm{a}_{2}}\) is so much greater for oxalic acid than for suberic acid.

Step-by-Step Solution

Answer

The difference between pKa1 and pKa2 in Oxalic acid is larger than in Suberic acid because in Oxalic acid, the negative charge developed after losing the first proton is more locally concentrated due to the direct connection of the carboxyl groups. This leads to stronger repulsion when trying to remove the second proton. In Suberic Acid, the long carbon chain allows better separation of the resultant negative charges, resulting in less repulsion when removing the second proton.

Step 1: Understanding pKa values

The pKa value of an acid is a measure of its acidity. The lower the pKa value, the stronger the acid. In the case of diprotic acids, we have two pKa values. The first, pKa1, indicates the ease of removal of the first proton, and the second, pKa2, indicates the ease of removal of the second proton.

Step 2: Comparing the pKa values of Oxalic and Suberic Acids

The difference between pKa1 and pKa2 for Oxalic acid is 2.56, while for Suberic acid it's 1.19. It's noticeable that the difference for Oxalic acid is larger, meaning that the removal of the second proton is a lot more difficult (i.e. the acid becomes considerably weaker) than the removal of the first proton.

Step 3: Analyzing the Structure of the Acids

The structural difference between Oxalic acid and Suberic acid need to be considered. Oxalic acid has two carboxyl groups directly linked together, whereas Suberic acid has a long carbon chain separating the two carboxyl groups.

Step 4: Making Inferences based on Structure

After losing a proton, the remaining structure of the acid molecule becomes negatively charged. This negative charge is more localized in Oxalic acid because the carboxyl groups are directly connected, thus resulting in a stronger negative-negative repulsion when the second proton is being removed. In Suberic acid, the large carbon chain between the carboxyl groups allows effective separation of the negative charges, resulting in less repulsion and thus easier removal of the second proton.

Key Concepts

pKa values

pKa values are essential in understanding acid strength and proton removal efficiency. They denote how well an acid ionizes in solution. For acids, the lower the pKa value, the easier it is for the acid to donate a proton, making it a stronger acid.
Diprotic acids, like oxalic and suberic acids, have two pKa values because they can donate two protons. The first pKa (\( ext{pKa}_1 \)) represents the ease of removing the first proton, while the second pKa (\( ext{pKa}_2 \)) indicates how readily the second proton is removed.
Key Points:

• Lower pKa values reflect stronger acid strength.
• In diprotic acids, \( ext{pKa}_1 \) is typically lower than \( ext{pKa}_2 \) due to proton-proton repulsions.

Chemical structure

The chemical structure of an acid profoundly affects its pKa values. It determines how easily protons can be lost and how stable the resultant ion is. Oxalic acid has its two acidic groups, carboxyl (-COOH), directly linked.
Suberic acid, however, has a long carbon chain separating these groups.
Structural Influences:

• Direct linkage in oxalic acid leads to more significant electrical interactions between acidic groups.
• The longer carbon chain in suberic acid reduces interactions between acidic sites.

Understanding these structural differences helps explain why oxalic acid shows a larger difference in its \( ext{pKa}_1 \) and \( ext{pKa}_2 \) values.

Proton removal

Proton removal in diprotic acids occurs in two steps, each associated with its pKa value. The process starts when the first proton is relatively easily removed, often due to favorable charge distribution within the molecule.
After removing the first proton, a negative charge develops.
This charge significantly impacts the removal of the second proton. For oxalic acid, after the first proton is lost, the remaining negative charges on the closely spaced carboxyl groups repel each other. This repulsion makes it much harder to remove the second proton.
In contrast, the long carbon chain in suberic acid reduces this repulsion effect, allowing for comparatively easier removal of the second proton.

Acid strength

Acid strength indicates how easily an acid can donate its protons. As we have seen, smaller pKa values reflect stronger acids.
In oxalic acid, the differences in \( ext{pKa}_1 \) and \( ext{pKa}_2 \) values result in a significant drop in acid strength following the removal of the first proton.
This means that oxalic acid becomes significantly weaker after losing one proton, due to increased negative charge repulsion.For suberic acid, the initial removal of the first proton similarly results in weaker acid strength; however, the change is less drastic than in oxalic acid.
The long carbon chain buffer between the carboxyl groups aids in stabilizing the negative charge and maintains a more consistent acid strength for both proton removal stages.