Question

Oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is a diprotic acid. By using data in Appendix \(\mathrm{D}\) as needed, determine whether each of the following statements is true: (a) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) can serve as both a Bronsted-Lowry acid and a Brønsted-Lowry base. (b) \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) is the conjugate base of \(\mathrm{HC}_{2} \mathrm{O}_{4}^{-}\). (c) An aqueous solution of the strong electrolyte \(\mathrm{KHC}_{2} \mathrm{O}_{4}\) will have \(\mathrm{pH}<7\).

Short answer

All three statements (a), (b), and (c) are true. Oxalic acid (H2C2O4) can serve as both a Brønsted-Lowry acid and base. The doubly deprotonated species (C2O42-) is the conjugate base of the singly deprotonated species (HC2O4-). An aqueous solution of KHC2O4 will have a pH less than 7.

Step-by-step solution

Part a: Determine if H2C2O4 is both an acid and base according to Brønsted-Lowry theory

A Brønsted-Lowry acid is a substance that donates a proton (H+) to another substance (the base). A Brønsted-Lowry base is a substance that accepts a proton from another substance (the acid). Oxalic acid (H2C2O4) is a diprotic acid, meaning it can donate two protons. When it donates one proton, it forms the singly deprotonated species HC2O4-: H2C2O4 (acid) + H2O (base) → HC2O4- (conjugate base) + H3O+ (conjugate acid) Since HC2O4- can accept a proton to revert to H2C2O4, it can act as a Brønsted-Lowry base. Hence, oxalic acid can serve as both a Brønsted-Lowry acid and base. The statement is true.

Part b: Determine if C2O42- is the conjugate base of HC2O4-

The conjugate base is formed when an acid loses a proton. As discussed in part a, when H2C2O4 loses a proton, it forms HC2O4-: H2C2O4 (acid) + H2O (base) → HC2O4- (conjugate base) + H3O+ (conjugate acid) If HC2O4- loses another proton, it forms the doubly deprotonated species C2O42-: HC2O4- (acid) + H2O (base) → C2O42- (conjugate base) + H3O+ (conjugate acid) Thus, C2O42- is the conjugate base of HC2O4-. The statement is true.

Part c: Determine if an aqueous solution of KHC2O4 will have pH < 7

When KHC2O4 is added to water, it dissociates into its constituent ions: KHC2O4 → K+ + HC2O4- Since K+ is a cation from a strong base (KOH), it does not affect the pH of the solution. However, HC2O4- is a weak acid formed by the deprotonation of the oxalic acid and will dissociate as follows: HC2O4- (acid) + H2O (base) ↔ C2O42- (conjugate base) + H3O+ (conjugate acid) This reaction produces H3O+ ions, which increase the hydronium ion concentration in the solution, resulting in a pH value that is less than 7. The statement is true. In summary, all three statements (a), (b), and (c) are true based on the Brønsted-Lowry theory and properties of oxalic acid.

Key concepts

Diprotic Acid

Certain acids have the ability to donate more than one proton (H⁺) when they dissolve in water. These are known as diprotic acids. Oxalic acid, represented as \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \), is a perfect example of a diprotic acid. When oxalic acid is placed in water, it can lose its first proton and transform into \( \mathrm{HC}_{2} \mathrm{O}_{4}^{-} \). This process is called deprotonation. Then, \( \mathrm{HC}_{2} \mathrm{O}_{4}^{-} \) can lose another proton to transform into \( \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \).
Understanding diprotic acids is important because they have distinct steps of ionization, each having its own dissociation constant. This means the strength of the acid in releasing its first versus its second proton can be different, influencing reactions and pH values. In oxalic acid, the ionization of each proton occurs separately, providing a stepwise mechanism that influences how solutions are studied and understood in chemistry.

Conjugate Base

The concept of a conjugate base comes from the Bronsted-Lowry theory. According to this theory, when an acid donates a proton (H⁺), it transforms into its conjugate base. For example, when oxalic acid \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \) loses a proton, it becomes \( \mathrm{HC}_{2} \mathrm{O}_{4}^{-} \), which is its conjugate base.
In a second step, \( \mathrm{HC}_{2} \mathrm{O}_{4}^{-} \) can lose yet another proton to become \( \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \). In this case, \( \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \) is the conjugate base of \( \mathrm{HC}_{2} \mathrm{O}_{4}^{-} \).
In general, a conjugate base is less capable of donating protons compared to its parent acid because it has already donated its proton. Recognizing the conjugate pairs helps to determine the direction and extent of chemical reactions, especially in buffer systems and equilibrium calculations.

pH

The term pH is a measure of how acidic or basic a solution is. It specifically measures the concentration of hydronium ions, \( \mathrm{H}_{3}\mathrm{O}^{+} \), in a solution, and is defined as \( \text{pH} = -\log[\mathrm{H}_{3}\mathrm{O}^{+}] \).
Oxalic acid often contributes to lowering the pH of a solution due to its acidic nature. When a compound like \( \mathrm{KHC}_{2} \mathrm{O}_{4} \) is dissolved in water, dissociation occurs, producing ions. The \( \mathrm{HC}_{2} \mathrm{O}_{4}^{-} \) ion, derived from a weak acid, can further dissociate, contributing to the hydronium ion concentration in the solution. This in turn, reduces the solution's pH, making it more acidic.
It's useful to measure pH since it provides insight into the chemical nature of a solution, predicting how it might behave in different chemical reactions or biological systems. Understanding pH is essential for processes like titration and environmental monitoring.