Problem 15 - Chemistry and Chemical Reactivity

Question

Several acids are listed here with their respective equilibrium constants: $$\begin{aligned}&\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}^{-}(\mathrm{aq})\\\&K_{\mathrm{a}}=1.3 \times 10^{-10}\end{aligned}$$ $$\begin{aligned}&\mathrm{HCO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{HCO}_{2}^{-}(\mathrm{aq})\\\&K_{\mathrm{a}}=1.8 \times 10^{-4} \end{aligned}$$ $$\begin{aligned}&\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(\mathrm{aq})\\\&K_{\mathrm{a}}=6.4 \times 10^{-5}\end{aligned}$$ (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 Conjugate Base: Formic Acid's. (c) Strongest Conjugate Base: Phenol's.

Step 1: Identify Equilibrium Constants for Acids

Write down the given equilibrium constants (\(K_a\)) for each acid:- Phenol (\(\mathrm{C}_6\mathrm{H}_5\mathrm{OH}\)): \(K_a = 1.3 \times 10^{-10}\)- Formic Acid (\(\mathrm{HCO}_2\mathrm{H}\)): \(K_a = 1.8 \times 10^{-4}\)- Hydrogen Oxalate Ion (\(\mathrm{HC}_2\mathrm{O}_4^-\)): \(K_a = 6.4 \times 10^{-5}\).

Step 2: Compare Strengths of Acids

The strength of an acid is directly proportional to its \(K_a\) value; a larger \(K_a\) indicates a stronger acid. - Formic Acid has the highest \(K_a\), making it the strongest acid.- Phenol has the lowest \(K_a\), making it the weakest acid.

Step 3: Determine Weakest Conjugate Base

The stronger the acid, the weaker its conjugate base. Since Formic Acid is the strongest due to its highest \(K_a\), its conjugate base \(\mathrm{HCO}_2^-\) is the weakest.

Step 4: Determine Strongest Conjugate Base

The weakest acid will have the strongest conjugate base. Since Phenol is the weakest acid, its conjugate base \(\mathrm{C}_6\mathrm{H}_5\mathrm{O}^-\) is the strongest.

Key Concepts

Equilibrium Constants

Equilibrium constants, specifically the acid dissociation constant denoted as \(K_a\), are crucial in understanding the strength of acids. These constants measure the extent to which an acid dissociates in water to form its ions.
In the reaction:$$\text{HA} + \text{H}_2\text{O} \rightleftarrows \text{H}_3\text{O}^+ + \text{A}^-$$- \(\text{HA}\) is the acid, and \(\text{A}^-\) is its conjugate base.

The equilibrium constant for this reaction is given by:- \(K_a = \frac{[\text{H}_3\text{O}^+][\text{A}^-]}{[\text{HA}]}\)
- A larger \(K_a\) signifies a stronger acid, meaning more dissociation into \(\text{H}_3\text{O}^+\), indicating higher acidity.
- Conversely, a smaller \(K_a\) value means weaker acid strength.

By comparing the \(K_a\) values of the acids: Phenol \((K_a = 1.3 \times 10^{-10})\), Formic Acid \((K_a = 1.8 \times 10^{-4})\), and Hydrogen Oxalate Ion \((K_a = 6.4 \times 10^{-5})\), we can determine which acid is strongest or weakest based on these values.

Conjugate Bases

Conjugate bases form when an acid loses its hydrogen ion \((\text{H}^+)\) during the dissociation process. Understanding the strength of conjugate bases is important in predicting acid behavior and reactivity.

Here are some key points:- A strong conjugate base usually results from a weak acid.
- Conversely, a weak conjugate base typically comes from a strong acid.For instance, with our acids:

• Formic Acid \((\text{HCO}_2\text{H})\) loses \(\text{H}^+\), forming \(\text{HCO}_2^-\) as its conjugate base.
• Phenol \((\text{C}_6\text{H}_5\text{OH})\) forms \(\text{C}_6\text{H}_5\text{O}^-\) when it loses \(\text{H}^+\).
• Hydrogen Oxalate Ion \((\text{HC}_2\text{O}_4^-)\) forms \(\text{C}_2\text{O}_4^{2-}\) as its conjugate base.

From the equilibrium constants previously discussed, Formic Acid is the strongest, indicating \(\text{HCO}_2^-\) is its weakest conjugate base. Meanwhile, Phenol, being the weakest acid, results in \(\text{C}_6\text{H}_5\text{O}^-\) as the strongest conjugate base.

Acid-Base Reactions

Acid-base reactions occur when an acid donates a proton (\(\text{H}^+\)) to a base. This transfer alters the chemical structure and nature of the molecules involved, leading to new compounds and equilibrium states.
The key components of these reactions include:

• Acids, which are proton donors.
• Bases, which are proton acceptors.
• Conjugate acid-base pairs that result from the exchange of protons.

For example, in the dissociation of Formic Acid in water:- Formic Acid \((\text{HCO}_2\text{H})\) donates \(\text{H}^+\) to water, forming \(\text{H}_3\text{O}^+\) and \(\text{HCO}_2^-\).
- \(\text{H}_3\text{O}^+\) is the conjugate acid of water, a modified base.
Similarly, Phenol in water forms \(\text{H}_3\text{O}^+\) and \(\text{C}_6\text{H}_5\text{O}^-\).

Each of these reactions reflects the principle that the stronger the acid, the more profound its effect in transferring a proton, modifying the equilibrium constant and influencing the strength of the conjugate base. This interconnectedness highlights the dynamic nature of acid-base chemistry in aqueous solutions.