Problem 94 - Chemistry The Molecular Science

Question

Several acids and their respective equilibrium constants are: $$ \begin{array}{ll} \mathrm{HF} & K_{\mathrm{a}}=6.8 \times 10^{-4} \\ \mathrm{HS}^{-} & K_{\mathrm{a}}=1 \times 10^{-19} \\ \mathrm{CH}_{3} \mathrm{COOH} & K_{\mathrm{a}}=1.8 \times 10^{-5} \end{array} $$ (a) Which is the strongest acid? (b) Which is the weakest acid? (c) Which acid has the weakest conjugate base? (d) Which acid has the strongest conjugate base?

Step-by-Step Solution

Answer

(a) HF, (b) HS⁻, (c) HF, (d) HS⁻

Step 1: Understanding Acid Strength

The strength of an acid is determined by its acid dissociation constant, \( K_{a} \). The larger the \( K_{a} \), the stronger the acid is because it dissociates more in solution.

Step 2: Analyzing the Equilibrium Constants

We are given the equilibrium constants for the acids: \( \mathrm{HF} \) has \( K_{ ext{a}} = 6.8 \times 10^{-4} \), \( \mathrm{HS}^{-} \) has \( K_{ ext{a}} = 1 \times 10^{-19} \), and \( \mathrm{CH}_3 \mathrm{COOH} \) has \( K_{ ext{a}} = 1.8 \times 10^{-5} \).

Step 3: Identifying the Strongest Acid

The strongest acid will have the largest \( K_{a} \). Comparing the constants, \( 6.8 \times 10^{-4} > 1.8 \times 10^{-5} > 1 \times 10^{-19} \). Thus, \( \mathrm{HF} \) is the strongest acid.

Step 4: Identifying the Weakest Acid

The weakest acid will have the smallest \( K_{a} \). From our comparison, \( 1 \times 10^{-19} \) is the smallest, which corresponds to \( \mathrm{HS}^{-} \). Thus, \( \mathrm{HS}^{-} \) is the weakest acid.

Step 5: Determining Weakest Conjugate Base

The weaker the conjugate base, the stronger the acid. Therefore, the acid with the highest \( K_{a} \) will have the weakest conjugate base. Since \( \mathrm{HF} \) is the strongest acid, its conjugate base, \( ext{F}^- \), is the weakest.

Step 6: Determining Strongest Conjugate Base

The stronger the conjugate base, the weaker the acid. Therefore, the acid with the smallest \( K_{a} \) will have the strongest conjugate base. Since \( \mathrm{HS}^{-} \) is the weakest acid, its conjugate base, \( ext{S}^{2-} \), is the strongest.

Key Concepts

Acid Dissociation Constant (Ka)

The Acid Dissociation Constant, often represented as \( K_{a} \), is a numerical value that helps us understand how an acid behaves in water. Essentially, it measures the extent to which an acid dissociates or ionizes in a solution. This ionization process can be depicted in a general reaction: HA \( \rightarrow \) H\(^+\) + A\(^-\).

• A high \( K_{a} \) means the acid ionizes significantly, releasing more \( H^{+} \) ions, and is thus considered a strong acid.
• A low \( K_{a} \) suggests limited ionization, meaning the acid is weaker.

When comparing acids, as demonstrated in the exercise, HF with \( K_{a} = 6.8 \times 10^{-4} \) is stronger than CH\(_3\)COOH with \( K_{a} = 1.8 \times 10^{-5} \),and much stronger than HS\(^-\) with its tiny \( K_{a} = 1 \times 10^{-19} \).Understanding \( K_{a} \) is crucial to predict how an acid will behave in reactions.

Conjugate Base

A conjugate base is what remains after an acid has donated a proton (\( H^+ \)). In every acid-base reaction, there is a conjugate acid-base pair. When an acid loses a proton, the remaining part is its conjugate base. For example, in the dissociation of hydrofluoric acid (HF):HF \(\rightarrow\) H\(^+\) + F\(^-\),

• F\(^-\) is the conjugate base of the acid HF.

Conjugate bases play a significant role in determining the strength of the corresponding acid. The weaker the acid, the stronger its conjugate base, and vice versa. In our exercise:

• The strongest acid, HF, forms a weak conjugate base, F\(^-\).
• The weakest acid, HS\(^-\), forms a strong conjugate base, S\(^{2-}\).

This inverse relationship helps us understand acid-base balance and predict possible reactions.

Acid Strength

Acid strength refers to an acid's ability to donate protons to a base. The ease with which an acid releases its protons to the surrounding solution determines its strength. This ability is quantified by the acid dissociation constant \( K_{a} \), and larger values of \( K_{a} \) indicate a stronger acid.Several factors influence acid strength:

• **Bond Strength:** In a molecule, the weaker the bond holding the hydrogen, the stronger the acid, as it more readily donates a proton.
• **Stability of Conjugate Base:** After donating a proton, the stability of the conjugate base affects the acid strength. More stable conjugate bases favor complete dissociation.
• **Electronegativity:** In around atoms, higher electronegativity can lead to stronger acids as the atoms pull electron density towards them, facilitating the release of H\(^+\).

In the exercise, HF is the strongest acid as it has the highest \( K_{a} \) value. Understanding these nuances can greatly assist in predicting the behavior of various acids in chemical reactions.