Problem 16 - Chemistry and Chemical Reactivity

Question

Several acids are listed here with their respective equilibrium constants. $$\begin{aligned} &\mathrm{HF}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{F}^{-}(\mathrm{aq})\\\ &K_{\mathrm{a}}=7.2 \times 10^{-4} \end{aligned}$$ $$\begin{aligned} &\mathrm{HPO}_{4}^{2-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{PO}_{4}^{3-}(\mathrm{aq})\\\ &K_{\mathrm{a}}=3.6 \times 10^{-13} \end{aligned}$$ $$\begin{aligned} &\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq})\\\ &K_{\mathrm{a}}=1.8 \times 10^{-5} \end{aligned}$$ (a) Which is the strongest acid? Which is the weakest acid? (b) What is the conjugate base of the acid HF? (c) Which acid has the weakest conjugate base? (d) Which acid has the strongest conjugate base?

Step-by-Step Solution

Answer

(a) Strongest: HF, Weakest: HPO₄²⁻. (b) F⁻. (c) HF. (d) HPO₄²⁻.

Step 1: Identify the Strongest Acid

The strength of an acid is indicated by its acid dissociation constant (\( K_a \)). The larger the \( K_a \) value, the stronger the acid, because it dissociates more in solution. Comparing the given \( K_a \) values:- \( \mathrm{HF}: \; K_a = 7.2 \times 10^{-4} \)- \( \mathrm{HPO}_4^{2-}: \; K_a = 3.6 \times 10^{-13} \)- \( \mathrm{CH}_3 \mathrm{CO}_2 \mathrm{H}: \; K_a = 1.8 \times 10^{-5} \)The largest \( K_a \) value is \( 7.2 \times 10^{-4} \) for \( \mathrm{HF} \), making it the strongest acid.

Step 2: Identify the Weakest Acid

Conversely, the smallest \( K_a \) value indicates the weakest acid because it dissociates the least. Comparing the values again, we see that the smallest \( K_a \) value is \( 3.6 \times 10^{-13} \) for \( \mathrm{HPO}_4^{2-} \), making it the weakest acid.

Step 3: Find the Conjugate Base of HF

The conjugate base is what remains of the acid after it donates a proton. For \( \mathrm{HF} \), after donating a proton, the remaining species is \( \mathrm{F}^- \). Thus, the conjugate base of \( \mathrm{HF} \) is \( \mathrm{F}^- \).

Step 4: Determine the Acid With the Weakest Conjugate Base

The strength of a conjugate base is inversely related to the strength of its acid. Therefore, the strongest acid has the weakest conjugate base. We've already identified \( \mathrm{HF} \) as the strongest acid, so its conjugate base \( \mathrm{F}^- \) is the weakest.

Step 5: Determine the Acid With the Strongest Conjugate Base

The weakest acid has the strongest conjugate base due to minimal dissociation in aqueous solution. \( \mathrm{HPO}_4^{2-} \) was identified as the weakest acid, thus its conjugate base \( \mathrm{PO}_4^{3-} \) is the strongest.

Key Concepts

Equilibrium Constant

When we talk about equilibrium constants, we're focusing on a measure of how far a chemical reaction proceeds before reaching a state of balance. For acids, this is represented by the acid dissociation constant, or \( K_a \). It tells us how much an acid dissociates into its ions in solution.
Here's how it works:

• A larger \( K_a \) value signals a stronger acid. More of the acid is dissociated into ions, meaning the reaction favors the products (ionized form).
• A smaller \( K_a \) value indicates a weaker acid. The acid does not easily dissociate and remains mostly in its original molecular form.

For example, if we look at the values given, \( \mathrm{HF} \) has the largest \( K_a \) value at \( 7.2 \times 10^{-4} \), making it the strongest acid in this set. This represents a higher degree of ionization compared to other acids like \( \mathrm{HPO}_4^{2-} \), with its much smaller \( K_a \) value, identifying it as the weakest acid.

Conjugate Base

The concept of a conjugate base is integral to understanding acid-base chemistry. A conjugate base is formed when an acid donates a proton (\( \text{H}^+ \)) to another species. This loss of a proton results in a new particle.In our example, the conjugate base for \( \mathrm{HF} \) is \( \mathrm{F}^- \). Here's why:

• \( \mathrm{HF} \) donates a proton, becoming \( \mathrm{F}^- \).
• The conjugate base, \( \mathrm{F}^- \), is the species left behind after the acid loses its proton.

Understanding conjugate bases helps to predict the behavior of acids and bases in a reaction. The weaker the conjugate base, the stronger its parent acid, because it means the parent acid gives up its protons easily. Conversely, a strong conjugate base means its parent acid holds onto protons tightly, indicating a weak acid.

Acid Strength

Acid strength is a central topic in chemistry. It tells us how readily an acid will donate a proton, thus initiating reactions with bases.A few key points about acid strength:

• Acid strength is directly related to the value of \( K_a \). The higher the \( K_a \), the stronger the acid.
• Acid strength also dictates the strength of its corresponding conjugate base. Strong acids have weak conjugate bases, and weak acids have strong conjugate bases.
• This is why \( \mathrm{HF} \), with the highest \( K_a \) value among the examples, is the strongest acid and has the weakest conjugate base, \( \mathrm{F}^- \).
• In contrast, \( \mathrm{HPO}_4^{2-} \) is the weakest acid, reflected by its extremely low \( K_a \) value of \( 3.6 \times 10^{-13} \), and has a strong conjugate base, \( \mathrm{PO}_4^{3-} \).

Carefully analyzing these properties gives you insight into how acids and bases will behave in different chemical contexts, providing a deeper understanding of chemical reactions.