Question

Given that the \(K_{\mathrm{a}}\) value for acetic acid is \(1.8 \times 10^{-5}\) and the \(K_{\mathrm{a}}\) value for hypochlorous acid is \(3.5 \times 10^{-8}\), which is the stronger base, \(\mathrm{OCl}^{-}\) or \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\) ?

Short answer

The stronger base is \(\mathrm{OCl}^{-}\) (hypochlorite ion), as its conjugate acid, Hypochlorous Acid (\(\mathrm{HOCl}\)), has a lower \(K_{\mathrm{a}}\) value compared to Acetic Acid (\(\mathrm{CH}_{3}\mathrm{COOH}\)).

Step-by-step solution

Write down the given values

The given \(K_{\mathrm{a}}\) values are: Acetic Acid (\(\mathrm{CH}_{3}\mathrm{COOH}\)): \(K_{\mathrm{a}} = 1.8 \times 10^{-5}\) Hypochlorous Acid (\(\mathrm{HOCl}\)): \(K_{\mathrm{a}} = 3.5 \times 10^{-8}\)

Compare the \(K_{\mathrm{a}}\) values

By comparing the \(K_{\mathrm{a}}\) values, we see that: \(K_{\mathrm{a}}\) for Acetic Acid (\(\mathrm{CH}_{3}\mathrm{COOH}\)) > \(K_{\mathrm{a}}\) for Hypochlorous Acid (\(\mathrm{HOCl}\)), i.e., \(1.8 \times 10^{-5} > 3.5 \times 10^{-8}\)

Determine the stronger acid and weaker base

Since Acetic Acid has a higher \(K_{\mathrm{a}}\) value, it's a stronger acid than Hypochlorous Acid. As a result, its conjugate base, \(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2}^{-}\) (acetate ion), is weaker than \(\mathrm{OCl}^{-}\) (hypochlorite ion).

Conclude which is the stronger base

Based on the comparison made in Step 3, we determine that \(\mathrm{OCl}^{-}\) (hypochlorite ion) is the stronger base compared to \(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2}^{-}\) (acetate ion).

Key concepts

Conjugate Base Comparison

In chemistry, the concept of conjugate base comparison is crucial for determining the relative strength of bases derived from weak acids. When an acid donates a proton ( ext{H}^+), it forms its conjugate base. The strength of this conjugate base is inversely related to the strength of the original acid.

If we have two acids, and one is stronger than the other (meaning it dissociates more in solution), then the conjugate base of the stronger acid will be weaker. This is because a strong acid holds onto its proton less tightly, making it easier to lose, which makes the resulting conjugate base have less tendency to pick up a proton and thus, makes it a weaker base.

In this exercise, by comparing acetic acid and hypochlorous acid's ability to donate protons, we can deduce their conjugate bases' strengths. The key here is the inverse relationship: stronger acid -> weaker conjugate base.

Equilibrium Constant

The equilibrium constant, denoted as \( K_a \) in the context of acids, is a vital concept for understanding acid strength. This constant measures the strength of an acid in solution, specifically its tendency to donate a proton. The higher the \( K_a \), the stronger the acid because it suggests more of the acid is dissociating into ions in solution.

Calculating the \( K_a \) involves analyzing the concentration of the products and reactants in a dissociation reaction at equilibrium. The formula is expressed as \( K_a = \frac{[H^+][A^-]}{[HA]} \), where \([H^+]\) is the hydrogen ion concentration, \([A^-]\) is the conjugate base concentration, and \([HA]\) is the remaining concentration of the acid.

In our scenario, comparing \( K_a \) values provides an immediate insight: acetic acid with a higher \( K_a \) is stronger than hypochlorous acid, leading to the conclusion that its conjugate base is weaker.

Acetic Acid

Acetic acid, known by the formula \( \mathrm{CH}_3 \mathrm{COOH} \), is a common weak acid with a notable presence not just in scientific contexts but everyday life—it’s what gives vinegar its characteristic sour smell and taste.

When acetic acid dissociates in water, it donates a proton to water, producing the acetate ion \( \mathrm{C}_2\mathrm{H}_3\mathrm{O}_2^- \). This process is represented by the equation:\[ \mathrm{CH}_3\mathrm{COOH} + \mathrm{H}_2\mathrm{O} \leftrightarrow \mathrm{C}_2\mathrm{H}_3\mathrm{O}_2^- + \mathrm{H}_3\mathrm{O}^+ \]

The \( K_a \) for acetic acid is \( 1.8 \times 10^{-5} \), indicating it's not very strong, as it does not fully dissociate in water. This leads us to conclude that the acetate ion is relatively weak in accepting protons back, making it a weak base.

Hypochlorous Acid

Hypochlorous acid, represented by the formula \( \mathrm{HOCl} \), is another weak acid but even less dissociated than acetic acid. It plays a key role in sanitation and disinfection, often found in bleach products.

Upon dissociation, hypochlorous acid releases a proton, forming the hypochlorite ion \( \mathrm{OCl}^- \). The equilibrium equation is:\[ \mathrm{HOCl} + \mathrm{H}_2\mathrm{O} \leftrightarrow \mathrm{OCl}^- + \mathrm{H}_3\mathrm{O}^+ \]

The \( K_a \) value for hypochlorous acid is \( 3.5 \times 10^{-8} \), signifying it dissociates even less than acetic acid. This suggests that its conjugate base, the hypochlorite ion \( \mathrm{OCl}^- \), is stronger because it has a higher tendency to pick up a proton compared to the acetate ion.