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 \(K_\mathrm{a}\) values for acetic acid and hypochlorous acid are \(1.8 \times 10^{-5}\) and \(3.5 \times 10^{-8}\), respectively. Since acetic acid is the stronger acid, its conjugate base, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\), is weaker than the conjugate base of hypochlorous acid, \(\mathrm{OCl}^{-}\). Therefore, the stronger base is \(\mathrm{OCl}^{-}\).

Step-by-step solution

Understand the relationship between \(K_\mathrm{a}\) and base strength

The \(K_\mathrm{a}\) values of conjugate acids are inversely proportional to the strength of their conjugate bases. Acids with a higher \(K_\mathrm{a}\) value will be stronger, which in turn will make their conjugate bases weaker.

Compare the \(K_\mathrm{a}\) values of acetic acid and hypochlorous acid

We are given the \(K_\mathrm{a}\) values for the following acids: - Acetic acid: \(1.8 \times 10^{-5}\) - Hypochlorous acid: \(3.5 \times 10^{-8}\) Since the higher \(K_\mathrm{a}\) value represents a stronger acid, we can determine that acetic acid is the stronger acid of the two, as \(1.8 \times 10^{-5} > 3.5 \times 10^{-8}\).

Determine the stronger conjugate base

Now that we know acetic acid is the stronger acid of the two, we can infer that its conjugate base, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}^{-}\), is weaker than the conjugate base of hypochlorous acid, \(\mathrm{OCl}^{-}\). Therefore, the stronger base is \(\mathrm{OCl}^{-}\).

Key concepts

Understanding the Conjugate Base

In the world of acid-base chemistry, the term "conjugate base" might seem a bit confusing at first. Let's break it down. When an acid donates a proton (which is a hydrogen ion, or H⁺), what remains is the conjugate base. For instance, if you take acetic acid ( abla), once it gives off a proton, what you get is the acetate ion ( abla). This acetate ion is now the conjugate base of the original acetic acid.

Knowing the conjugate base is essential because it helps you understand the whole acid-base balance. If you have a strong acid that willingly gives up its protons, its conjugate base tends to be weak—it doesn't want to take those protons back.

• Conjugate Base Example: When acetic acid loses a proton, it becomes abla.
• In contrast, for hypochlorous acid, the conjugate base is abla.

Recognizing conjugate bases helps us compare the relative strengths of acids and bases, which is crucial for predicting chemical reactions.

Deciphering Acid Strength

Acid strength is a concept that is fundamental in chemistry. It refers to an acid's ability to donate protons. The stronger the acid, the more readily it loses a proton and the higher its dissociation in water.

The strength of an acid is represented by its dissociation constant, known as the abla, in chemistry. A larger abla value means a stronger acid, while a smaller abla indicates a weaker acid.

• Acetic acid has a abla value of abla, indicating a stronger acid.
• Hypochlorous acid's weaker abla value of abla points to it being weaker compared to acetic acid.

Understanding acid strength helps in predicting the behavior of acids in reactions. The concept also helps to determine the extent of ionization, which has numerous practical applications, from industrial manufacturing to biological processes.

Interpreting the Ka Value

The abla value stands for the acid dissociation constant, which is a direct measure of an acid’s strength. It's one of the most critical numbers in acid-base chemistry because it tells you how well an acid dissociates into its ions in a solution.

The equation for abla is expressed as follows:\[K_a = \frac{[ ext{H}^+][ ext{A}^-]}{[ ext{HA}]} \]Here’s what it means:- abla signifies the concentration of the ions products.- abla denotes the non-dissociated acid concentration.
A high abla means the acid dissociates well (strong acid), and a low abla reflects a weak acid.

• Example: Acetic acid has a abla of abla, making it considerably handier at giving up protons than hypochlorous acid, with a abla of abla.
• Remember: Larger abla means stronger acid, weaker conjugate base.

Understanding abla values is crucial in acid-base chemistry because it defines both the behavior of acids and their potential utility in various chemical scenarios.