Problem 18 - Chemistry and Chemical Reactivity

Question

Several acids are listed here with their respective equilibrium constants. $$\begin{aligned} &\mathrm{HF}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftarrows \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{F}^{-}(\mathrm{aq})\\\ &K_{\mathrm{a}}=7.2 \times 10^{-4}\\\ &\mathrm{HPO}_{4}^{2-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{PO}_{4}^{3-}(\mathrm{aq})\\\ &K_{\mathrm{a}}=3.6 \times 10^{-13}\\\ &\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{CH}_{3} \mathrm{CO}_{2}^{-}(\mathrm{aq})\\\ &K_{\mathrm{a}}=1.8 \times 10^{-5} \end{aligned}$$ (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 acid: HF; Weakest acid: HPO4^2-. (b) F^- is the conjugate base of HF. (c) HF has the weakest conjugate base. (d) HPO4^2- has the strongest conjugate base.

Step 1: Identify the Strongest and Weakest Acids

The strength of an acid is determined by its equilibrium constant, \( K_a \). The larger the \( K_a \), the stronger the acid. Comparing the \( K_a \) values: \( \mathrm{HF} \) has \( 7.2 \times 10^{-4} \), \( \mathrm{CH}_3\mathrm{CO}_2\mathrm{H} \) has \( 1.8 \times 10^{-5} \), and \( \mathrm{HPO}_4^{2-} \) has \( 3.6 \times 10^{-13} \). Therefore, the strongest acid is \( \mathrm{HF} \), and the weakest acid is \( \mathrm{HPO}_4^{2-} \).

Step 2: Determine the Conjugate Base of HF

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

Step 3: Identify the Weakest Conjugate Base

An acid with a larger \( K_a \) has a weaker conjugate base because stronger acids dissociate more and leave fewer protons in solution, limiting the base's strength. \( \mathrm{HF} \) has the largest \( K_a \), so the weakest conjugate base is \( \mathrm{F}^- \) from \( \mathrm{HF} \).

Step 4: Identify the Strongest Conjugate Base

Conversely, the weakest acid will have the strongest conjugate base, as it remains mostly undissociated and retains its protons better. \( \mathrm{HPO}_4^{2-} \) with its smallest \( K_a \) results in the strongest conjugate base, which is \( \mathrm{PO}_4^{3-} \).

Key Concepts

Equilibrium Constants

In the realm of acid-base chemistry, equilibrium constants, symbolized as \( K_a \), provide vital information about an acid's strength and its tendency to donate protons. These constants are essential for understanding how different acids behave in solution. The equilibrium constant is derived from the balanced chemical equation of an acid reacting with water to form hydronium ions and its conjugate base. The formula to determine this is:

• \[ K_a = \frac{[H_3O^+][A^-]}{[HA]} \]

Where \([HA]\) represents the concentration of the acid, \([A^-]\) the concentration of its conjugate base, and \([H_3O^+]\) the concentration of hydronium ions. The larger the \( K_a \), the more the acid ionizes, indicating a stronger acid. Conversely, a smaller \( K_a \) implies a weak acid that ionizes minimally.

Conjugate Acid-Base Pairs

Conjugate acid-base pairs are foundational to acid-base equilibrium concepts. When an acid donates a proton, it forms its conjugate base, and when a base accepts a proton, it forms its conjugate acid. This transformation is a reversible process, often represented in a chemical equation involving a double arrow:

• \( HA + H_2O \rightleftharpoons H_3O^+ + A^- \)

Here, \( HA \) is the acid forming \( A^- \) as its conjugate base, and \( H_3O^+ \) is the conjugate acid of water, \( H_2O \). The understanding of conjugate pairs is crucial when examining the strength and weakness of acids and bases within a chemical context. It helps predict the behavior of acids and bases in different environments by how readily they donate or accept protons.

Acid Strength

The strength of an acid is a measure of its ability to donate protons to acceptor molecules, often water, in a given reaction. Strong acids fully dissociate in water, whereas weak acids only partially dissociate. This is clearly demonstrated by their equilibrium constant \( K_a \). For example, the exercise shows \( HF \) with a \( K_a \) of \( 7.2 \times 10^{-4} \), making it a stronger acid compared to \( CH_3CO_2H \) and \( HPO_4^{2-} \), which have smaller \( K_a \) values. Comparing these values:

• \( HF \) is the strongest, dissociating more in water.
• \( HPO_4^{2-} \) is the weakest, with a minuscule \( K_a \), meaning it barely donates protons.

Recognizing an acid’s strength is essential for predicting how it will react and interact in solution.

Chemical Equilibrium

Chemical equilibrium in acid-base reactions represents a state where the concentrations of reactants and products remain constant over time, indicating that the forward and reverse reactions occur at the same rate. In the case of acids in water, an equilibrium is established when the rate at which the acid donates protons equals the rate at which the conjugate base accepts protons back. This dynamic balance is crucial for acid-base reactions and is reflected by the \( K_a \) value:

• A larger \( K_a \) suggests the equilibrium lies more to the right, favoring the formation of ions in the solution.
• A smaller \( K_a \) indicates the reaction favors the undissociated acid, with the equilibrium positioned to the left.

Understanding equilibrium helps predict the concentrations of all species in solution, a key component of solving acid-base problems.