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?

Short answer

(a) HF, (b) HS⁻, (c) HF, (d) HS⁻

Step-by-step solution

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.

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 \( K_{ ext{a}} = 1.8 \times 10^{-5} \).

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.

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.

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.

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.