Problem 17 - Chemistry and Chemical Reactivity

Question

Several acids are listed here with their respective equilibrium constants: $$\begin{array}{l} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}^{-}(\mathrm{aq}) \\ \mathrm{K}_{\mathrm{a}}=1.3 \times 10^{-10} \\ \mathrm{HCO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{HCO}_{2}^{-}(\mathrm{aq}) \\ K_{\mathrm{a}}=1.8 \times 10^{-4} \\ \mathrm{HC}_{2} \mathrm{O}_{4}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(\mathrm{aq}) \\\ K_{\mathrm{a}}=6.4 \times 10^{-5} \end{array}$$ (a) Which is the strongest acid? Which is the weakest acid? (b) Which acid has the weakest conjugate base? (c) Which acid has the strongest conjugate base?

Step-by-Step Solution

Answer

(a) Strongest: Formic acid; Weakest: Phenol. (b) Weakest base: Formic acid's base. (c) Strongest base: Phenol's base.

Step 1: Identify Strongest and Weakest Acid

The strength of an acid is determined by the size of its equilibrium constant \( K_a \). The higher the \( K_a \), the stronger the acid. Compare \( K_a \) values: \( 1.8 \times 10^{-4} \) (formic acid) \( > \) \( 6.4 \times 10^{-5} \) (hydrogen oxalate ion) \( > \) \( 1.3 \times 10^{-10} \) (phenol). Thus, formic acid is the strongest, and phenol is the weakest.

Step 2: Determine Conjugate Base Strength

A strong acid has a weak conjugate base, and a weak acid has a strong conjugate base. Since formic acid is the strongest, it has the weakest conjugate base, \( ext{HCO}_2^- \). Conversely, phenol, being the weakest acid, has the strongest conjugate base, \( ext{C}_6 ext{H}_5 ext{O}^- \).

Step 3: Summarize Findings

(a) Formic acid is the strongest acid; phenol is the weakest acid. (b) Formic acid has the weakest conjugate base. (c) Phenol has the strongest conjugate base.

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K_a \), is a significant factor when it comes to assessing the strength of an acid. It describes how well an acid can donate a proton to water to form a hydronium ion \( (H_3O^+) \) and its conjugate base. A larger \( K_a \) value means the acid can successfully donate its proton more readily, making it stronger. Conversely, a smaller \( K_a \) signals weaker proton donation ability and thus a weaker acid.
Understanding this concept helps in directly comparing acids like formic acid, phenol, and hydrogen oxalate ion, where each has its unique \( K_a \) value.

• Formic acid has the highest \( K_a \), making it the strongest acid among the three.
• Phenol has the smallest \( K_a \), indicating it is the weakest acid.

Conjugate Base

Conjugate bases play a crucial role in acid-base chemistry. When an acid donates a proton, it forms its conjugate base. Acid strength is closely related to its conjugate base. A strong acid has a weak conjugate base because the strong acid readily gives up its proton and remains stable afterwards.
In this case:

• Formic acid, being the strongest acid, produces the weakest conjugate base, \( ext{HCO}_2^- \).
• Phenol, which is the weakest acid, generates the strongest conjugate base, \( ext{C}_6 ext{H}_5 ext{O}^- \).

Formic Acid

Formic acid (\( ext{HCO}_2 ext{H} \)) has a noticeable place in discussing acid strength due to its higher \( K_a \) value among the selected acids.
Formic acid is naturally found in some ant and bee stings, which gives it its name (from "formica," Latin for ant).
In the exercise, its \( K_a = 1.8 \times 10^{-4} \), illustrating its capability to dissociate in water efficiently, making it stronger than hydrogen oxalate ion and phenol.

Phenol

Phenol (\( ext{C}_6 ext{H}_5 ext{OH} \)) is an interesting compound often used in discussions about acidity. Despite being a weaker acid, phenol is commonly recognized due to its aromatic ring which affects its acidity.
In the provided exercise, phenol has a \( K_a = 1.3 \times 10^{-10} \), indicating that it dissociates very little in water compared to formic acid.
This lower tendency to donate protons makes phenol a much weaker acid, thus explaining its position as the weakest acid in the list.

Hydrogen Oxalate Ion

The hydrogen oxalate ion (\( ext{HC}_2 ext{O}_4^- \)) is an intriguing anion which functions as an acid with a middle-range \( K_a \) value. This ion results from the oxalic acid losing its first proton and can further dissociate slightly, given its \( K_a = 6.4 \times 10^{-5} \).
This \( K_a \) is less than formic acid but slightly more than phenol, placing it between the two in terms of acid strength.
Its intermediate strength makes it a fascinating subject for examining changes in the conjugate base upon losing a proton, leading to the formation of \( ext{C}_2 ext{O}_4^{2-} \).