Question

Low-molecular-weight dicarboxylic acids normally exhibit two different \(\mathrm{p} K_{\mathrm{a}}\) values. Ionization of the first carboxyl group is easier than the second. This effect diminishes with molecular size, and for adipic acid and longer chain dicarboxylic acids, the two acid ionization constants differ by about one \(\mathrm{p} K\) unit. $$ \begin{array}{|llll|} \hline \text { Dicarboxylic Acid } & \text { Structural Formula } & \mathrm{p} \kappa_{\mathrm{a} 1} & \mathrm{p} K_{\mathrm{a} 2} \\ \hline \text { Oxalic } & \mathrm{HOOCCOOH} & 1.23 & 4.19 \\ \text { Malonic } & \mathrm{HOOCCH}{ }_{2} \mathrm{COOH} & 2.83 & 5.69 \\ \text { Succinic } & \mathrm{HOOC}\left(\mathrm{CH}_{2}\right)_{2} \mathrm{COOH} & 4.16 & 5.61 \\ \text { Glutaric } & \mathrm{HOOC}\left(\mathrm{CH}_{2}\right)_{3} \mathrm{COOH} & 4.31 & 5.41 \\ \text { Adipic } & \mathrm{HOOC}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{COOH} & 4.43 & 5.41 \\ \hline \end{array} $$ Why do the two \(\mathrm{p} K_{\mathrm{a}}\) values differ more for the shorter chain dicarboxylic acids than for the longer chain dicarboxylic acids?

Short answer

Answer: The two pKa values of low-weight molecular dicarboxylic acids differ more for the shorter chain acids due to the stronger repulsion effect between the carboxylate groups in the shorter chains. As the chain length increases, the repulsion effect between carboxylate groups decreases because they are further apart, resulting in a smaller difference between the pKa values of the two carboxyl groups.

Step-by-step solution

Understand pKa values and molecular structure

pKa is the measure of the strength of an acid. A lower pKa value indicates a stronger acid, and a higher pKa value indicates a weaker acid. In dicarboxylic acids, there are two carboxyl groups (--COOH), each having a different pKa value. This means one carboxyl group is more acidic than the other. In general, the easier the ionization of a carboxyl group, the lower its pKa. Dicarboxylic acids have a chain of carbon atoms with carboxyl groups at both ends. As the number of carbon atoms in the chain increases, the molecular size of the dicarboxylic acid increases, resulting in a different effect on the acidity of the two carboxyl groups.

First ionization of carboxyl group

The first ionization of the carboxyl group (-COOH) occurs when it loses a proton (H+), forming a carboxylate anion (-COO-). Due to the resonance stabilization of the carboxylate anion through the electronegative oxygen atoms, this ionization is relatively easy, making the first carboxyl group more acidic (lower pKa value).

Second ionization and the effect of molecular size

The second ionization of the dicarboxylic acid occurs when the other carboxyl group (-COOH) also loses a proton (H+), forming a dianionic species (-COO- -COO-). Ionizing the second carboxyl group is more difficult, because the first carboxylate anion (already ionized) will exhibit a repulsion effect on the second carboxyl group due to the negatively charged oxygen atoms. However, as the size of the dicarboxylic acid increases (more CH2 units in the chain), the repulsion effect between the carboxylate groups becomes weaker, as they are now further apart from each other. This results in a smaller difference between the pKa values of the two carboxyl groups.

Conclusion

The two pKa values for low-weight molecular dicarboxylic acids differ more for shorter chain acids because of the stronger repulsion effect between the carboxylate groups in shorter chains. As the chain length increases, the repulsion effect decreases, due to the carboxylate groups being further apart. This results in the diminishing difference between the two acid ionization constants in longer chain dicarboxylic acids such as adipic acid.